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diff --git a/documentation/final-2D_backward_facing_step-example.png b/documentation/final-2D_backward_facing_step-example.png
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diff --git a/documentation/md_examples.html b/documentation/md_examples.html
index 8c6157fe..5484a50a 100644
--- a/documentation/md_examples.html
+++ b/documentation/md_examples.html
@@ -235,65 +235,78 @@ <h2><a class="anchor" id="autotoc_md61"></a>
 <div class="line">             -e batch -p mypartition -N 8 -n 2 -w &quot;01:00:00&quot; -# &quot;MFC Weak Scaling&quot; \</div>
 <div class="line">             --case-optimization -j 32 -- --scaling weak --memory 4</div>
 </div><!-- fragment --><h1><a class="anchor" id="autotoc_md62"></a>
-Rayleigh-Taylor Instability (3D)</h1>
+Backward Facing Step (2D)</h1>
 <h2><a class="anchor" id="autotoc_md63"></a>
+Final Condition (Density)</h2>
+<p><img src="final-2D_backward_facing_step-example.png" alt="" class="inline"/></p>
+<h1><a class="anchor" id="autotoc_md64"></a>
+Forward Facing Step (2D)</h1>
+<p>Reference: </p><blockquote class="doxtable">
+<p>Woodward, P. <em>(1984). The numerical simulation of two-dimensional fluid flow with strong shocks. Journal of Computational Physics, 54(1), 115–173. <a href="https://doi.org/10.1016/0021-9991(84)90140-2">https://doi.org/10.1016/0021-9991(84)90140-2</a></em> </p>
+</blockquote>
+<h2><a class="anchor" id="autotoc_md65"></a>
+Final Condition (Density)</h2>
+<p><img src="final-2D_forward_facing_step-example.png" alt="" class="inline"/></p>
+<h1><a class="anchor" id="autotoc_md66"></a>
+Rayleigh-Taylor Instability (3D)</h1>
+<h2><a class="anchor" id="autotoc_md67"></a>
 Final Condition and Linear Theory</h2>
 <p><img src="final_condition-3D_rayleigh_taylor-example.png" alt="" height="400" class="inline"/> <img src="linear_theory-3D_rayleigh_taylor-example.png" alt="" height="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md64"></a>
+<h1><a class="anchor" id="autotoc_md68"></a>
 Rayleigh-Taylor Instability (2D)</h1>
-<h2><a class="anchor" id="autotoc_md65"></a>
+<h2><a class="anchor" id="autotoc_md69"></a>
 Final Condition and Linear Theory</h2>
 <p><img src="result-2D_rayleigh_taylor-example.png" alt="" height="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md66"></a>
+<h1><a class="anchor" id="autotoc_md70"></a>
 Gas Jet (2D)</h1>
-<h2><a class="anchor" id="autotoc_md67"></a>
+<h2><a class="anchor" id="autotoc_md71"></a>
 Final Condition</h2>
 <p><img src="final_condition-2D_jet-example.png" alt="" height="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md68"></a>
+<h1><a class="anchor" id="autotoc_md72"></a>
 3D Turbulent Mixing layer (3D)</h1>
-<h2><a class="anchor" id="autotoc_md69"></a>
+<h2><a class="anchor" id="autotoc_md73"></a>
 Liutex visualization at transitional state</h2>
 <p><img src="result-3D_turb_mixing-example.png" alt="" height="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md70"></a>
+<h1><a class="anchor" id="autotoc_md74"></a>
 2D Riemann Test (2D)</h1>
 <p>Reference: </p><blockquote class="doxtable">
 <p>Chamarthi, A., &amp; Hoffmann, N., &amp; Nishikawa, H., &amp; Frankel S. (2023). Implicit gradients based conservative numerical scheme for compressible flows. arXiv:2110.05461 </p>
 </blockquote>
-<h2><a class="anchor" id="autotoc_md71"></a>
+<h2><a class="anchor" id="autotoc_md75"></a>
 Density Initial and Final Conditions</h2>
 <p><img src="alpha_rho1_initial-2D_riemann_test-example.png" alt="" width="45%" class="inline"/> <img src="alpha_rho1_final-2D_riemann_test-example.png" alt="" width="45%" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md72"></a>
+<h1><a class="anchor" id="autotoc_md76"></a>
 Taylor-Green Vortex (3D)</h1>
 <p>Reference: </p><blockquote class="doxtable">
 <p>Hillewaert, K. (2013). TestCase C3.5 - DNS of the transition of the Taylor-Green vortex, Re=1600 - Introduction and result summary. 2nd International Workshop on high-order methods for CFD. </p>
 </blockquote>
-<h2><a class="anchor" id="autotoc_md73"></a>
+<h2><a class="anchor" id="autotoc_md77"></a>
 Final Condition</h2>
 <p>This figure shows the isosurface with zero q-criterion.</p>
 <p><img src="result-3D_TaylorGreenVortex-example.png" alt="" height="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md74"></a>
+<h1><a class="anchor" id="autotoc_md78"></a>
 Titarev-Toro problem (1D)</h1>
 <p>Reference: </p><blockquote class="doxtable">
 <p>V. A. Titarev, E. F. Toro, Finite-volume WENO schemes for three-dimensional conservation laws, Journal of Computational Physics 201 (1) (2004) 238–260. </p>
 </blockquote>
-<h2><a class="anchor" id="autotoc_md75"></a>
+<h2><a class="anchor" id="autotoc_md79"></a>
 Initial Condition</h2>
 <p><img src="initial-1D_titarevtorro-example.png" alt="" heiht="400" class="inline"/></p>
-<h2><a class="anchor" id="autotoc_md76"></a>
+<h2><a class="anchor" id="autotoc_md80"></a>
 Result</h2>
 <p><img src="result-1D_titarevtorro-example.png" alt="" heiht="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md77"></a>
+<h1><a class="anchor" id="autotoc_md81"></a>
 Lax shock tube problem (1D)</h1>
 <p>Reference: </p><blockquote class="doxtable">
 <p>P. D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Communications on pure and applied mathematics 7 (1) (1954) 159–193. </p>
 </blockquote>
-<h2><a class="anchor" id="autotoc_md78"></a>
+<h2><a class="anchor" id="autotoc_md82"></a>
 Initial Condition</h2>
 <p><img src="initial-1D_laxshocktube-example.png" alt="" height="400" class="inline"/></p>
-<h2><a class="anchor" id="autotoc_md79"></a>
+<h2><a class="anchor" id="autotoc_md83"></a>
 Result</h2>
 <p><img src="result-1D_laxshocktube-example.png" alt="" height="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md80"></a>
+<h1><a class="anchor" id="autotoc_md84"></a>
 1D Multi-Component Reactive Shock Tube</h1>
 <p>References: </p><blockquote class="doxtable">
 <p>P. J. Martínez Ferrer, R. Buttay, G. Lehnasch, and A. Mura, “A detailed verification procedure for compressible reactive multicomponent Navier–Stokes solvers”, Computers &amp; Fluids, vol. 89, pp. 88–110, Jan. 2014. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1016/j.compfluid.2013.10.014">https://doi.org/10.1016/j.compfluid.2013.10.014</a> </p>
@@ -301,20 +314,20 @@ <h1><a class="anchor" id="autotoc_md80"></a>
 <blockquote class="doxtable">
 <p>H. Chen, C. Si, Y. Wu, H. Hu, and Y. Zhu, “Numerical investigation of the effect of equivalence ratio on the propagation characteristics and performance of rotating detonation engine”, Int. J. Hydrogen Energy, Mar. 2023. Accessed: Oct. 13, 2024. [Online]. Available: <a href="https://doi.org/10.1016/j.ijhydene.2023.03.190">https://doi.org/10.1016/j.ijhydene.2023.03.190</a> </p>
 </blockquote>
-<h2><a class="anchor" id="autotoc_md81"></a>
+<h2><a class="anchor" id="autotoc_md85"></a>
 Initial Condition</h2>
 <p><img src="initial-1D_reactive_shocktube-example.png" alt="" height="400" class="inline"/></p>
-<h2><a class="anchor" id="autotoc_md82"></a>
+<h2><a class="anchor" id="autotoc_md86"></a>
 Results</h2>
 <p><img src="result-1D_reactive_shocktube-example.png" alt="" height="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md83"></a>
+<h1><a class="anchor" id="autotoc_md87"></a>
 IBM Bow Shock (3D)</h1>
-<h2><a class="anchor" id="autotoc_md84"></a>
+<h2><a class="anchor" id="autotoc_md88"></a>
 Final Condition</h2>
 <p><img src="result-3D_ibm_bowshock-example.png" alt="" height="400" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md85"></a>
+<h1><a class="anchor" id="autotoc_md89"></a>
 2D Hardcodied IC Example</h1>
-<h2><a class="anchor" id="autotoc_md86"></a>
+<h2><a class="anchor" id="autotoc_md90"></a>
 Initial Condition and Result</h2>
 <p><img src="initial-2D_hardcoded_ic-example.png" alt="" width="45%" class="inline"/> <img src="result-2D_hardcoded_ic-example.png" alt="" width="45%" class="inline"/> </p>
 </div></div><!-- contents -->
diff --git a/documentation/md_expectedPerformance.html b/documentation/md_expectedPerformance.html
index f1c90bae..e83322c7 100644
--- a/documentation/md_expectedPerformance.html
+++ b/documentation/md_expectedPerformance.html
@@ -135,9 +135,9 @@
   <div class="headertitle"><div class="title">Performance</div></div>
 </div><!--header-->
 <div class="contents">
-<div class="textblock"><p><a class="anchor" id="autotoc_md87"></a></p>
+<div class="textblock"><p><a class="anchor" id="autotoc_md91"></a></p>
 <p>MFC has been benchmarked on several CPUs and GPU devices. This page is a summary of these results.</p>
-<h1><a class="anchor" id="autotoc_md88"></a>
+<h1><a class="anchor" id="autotoc_md92"></a>
 Figure of merit: Grind time performance</h1>
 <p>The following table outlines observed performance as nanoseconds per grid point (ns/gp) per equation (eq) per right-hand side (rhs) evaluation (lower is better), also known as the grind time. We solve an example 3D, inviscid, 5-equation model problem with two advected species (8 PDEs) and 8M grid points (158-cubed uniform grid). The numerics are WENO5 finite volume reconstruction and HLLC approximate Riemann solver. This case is located in <code>examples/3D_performance_test</code>. You can run it via <code>./mfc.sh run -n &lt;num_processors&gt; -j $(nproc) ./examples/3D_performance_test/case.py -t pre_process simulation --case-optimization</code> for CPU cases right after building MFC, which will build an optimized version of the code for this case then execute it. For benchmarking GPU devices, you will likely want to use <code>-n &lt;num_gpus&gt;</code> where <code>&lt;num_gpus&gt;</code> should likely be <code>1</code>. If the above does not work on your machine, see the rest of this documentation for other ways to use the <code>./mfc.sh run</code> command.</p>
 <p>Results are for MFC v4.9.3 (July 2024 release), though numbers have not changed meaningfully since then. Similar performance is also seen for other problem configurations, such as the Euler equations (4 PDEs). All results are for the compiler that gave the best performance. Note:</p><ul>
@@ -249,34 +249,34 @@ <h1><a class="anchor" id="autotoc_md88"></a>
 <td class="markdownTableBodyRight">Fujitsu A64FX   </td><td class="markdownTableBodyRight">Arm   </td><td class="markdownTableBodyRight">CPU   </td><td class="markdownTableBodyRight">48 cores   </td><td class="markdownTableBodyRight">63   </td><td class="markdownTableBodyLeft">GNU 13.2.0   </td><td class="markdownTableBodyLeft">SBU Ookami   </td></tr>
 </table>
 <p><b>All grind times are in nanoseconds (ns) per grid point (gp) per equation (eq) per right-hand side (rhs) evaluation, so X ns/gp/eq/rhs. Lower is better.</b></p>
-<h1><a class="anchor" id="autotoc_md89"></a>
+<h1><a class="anchor" id="autotoc_md93"></a>
 Weak scaling</h1>
 <p>Weak scaling results are obtained by increasing the problem size with the number of processes so that work per process remains constant.</p>
-<h2><a class="anchor" id="autotoc_md90"></a>
+<h2><a class="anchor" id="autotoc_md94"></a>
 AMD MI250X GPU</h2>
 <p>MFC weask scales to (at least) 65,536 AMD MI250X GPUs on OLCF Frontier with 96% efficiency. This corresponds to 87% of the entire machine.</p>
 <p><img src="../res/weakScaling/frontier.svg" alt="" style="height: 50%; width:50%; border-radius: 10pt pointer-events: none;" class="inline"/></p>
-<h2><a class="anchor" id="autotoc_md91"></a>
+<h2><a class="anchor" id="autotoc_md95"></a>
 NVIDIA V100 GPU</h2>
 <p>MFC weak scales to (at least) 13,824 V100 NVIDIA V100 GPUs on OLCF Summit with 97% efficiency. This corresponds to 50% of the entire machine.</p>
 <p><img src="../res/weakScaling/summit.svg" alt="" style="height: 50%; width:50%; border-radius: 10pt pointer-events: none;" class="inline"/></p>
-<h2><a class="anchor" id="autotoc_md92"></a>
+<h2><a class="anchor" id="autotoc_md96"></a>
 IBM Power9 CPU</h2>
 <p>MFC Weak scales to 13,824 Power9 CPU cores on OLCF Summit to within 1% of ideal scaling.</p>
 <p><img src="../res/weakScaling/cpuScaling.svg" alt="" style="height: 50%; width:50%; border-radius: 10pt pointer-events: none;" class="inline"/></p>
-<h1><a class="anchor" id="autotoc_md93"></a>
+<h1><a class="anchor" id="autotoc_md97"></a>
 Strong scaling</h1>
 <p>Strong scaling results are obtained by keeping the problem size constant and increasing the number of processes so that work per process decreases.</p>
-<h2><a class="anchor" id="autotoc_md94"></a>
+<h2><a class="anchor" id="autotoc_md98"></a>
 NVIDIA V100 GPU</h2>
 <p>The base case utilizes 8 GPUs with one MPI process per GPU for these tests. The performance is analyzed at two problem sizes: 16M and 64M grid points. The "base case" uses 2M and 8M grid points per process.</p>
-<h3><a class="anchor" id="autotoc_md95"></a>
+<h3><a class="anchor" id="autotoc_md99"></a>
 16M Grid Points</h3>
 <p><img src="../res/strongScaling/strongScaling16.svg" alt="" style="width: 50%; border-radius: 10pt pointer-events: none;" class="inline"/></p>
-<h3><a class="anchor" id="autotoc_md96"></a>
+<h3><a class="anchor" id="autotoc_md100"></a>
 64M Grid Points</h3>
 <p><img src="../res/strongScaling/strongScaling64.svg" alt="" style="width: 50%; border-radius: 10pt pointer-events: none;" class="inline"/></p>
-<h2><a class="anchor" id="autotoc_md97"></a>
+<h2><a class="anchor" id="autotoc_md101"></a>
 IBM Power9 CPU</h2>
 <p>CPU strong scaling tests are done with problem sizes of 16, 32, and 64M grid points, with the base case using 2, 4, and 8M cells per process.</p>
 <p><img src="../res/strongScaling/cpuStrongScaling.svg" alt="" style="width: 50%; border-radius: 10pt pointer-events: none;" class="inline"/> </p>
diff --git a/documentation/md_getting-started.html b/documentation/md_getting-started.html
index 8e4220fa..276491d7 100644
--- a/documentation/md_getting-started.html
+++ b/documentation/md_getting-started.html
@@ -135,13 +135,13 @@
   <div class="headertitle"><div class="title">Getting Started</div></div>
 </div><!--header-->
 <div class="contents">
-<div class="textblock"><p><a class="anchor" id="autotoc_md98"></a></p>
-<h1><a class="anchor" id="autotoc_md99"></a>
+<div class="textblock"><p><a class="anchor" id="autotoc_md102"></a></p>
+<h1><a class="anchor" id="autotoc_md103"></a>
 Fetching MFC</h1>
 <p>You can either download MFC's <a href="https://github.com/MFlowCode/MFC/releases/latest">latest release from GitHub</a> or clone the repository:</p>
 <div class="fragment"><div class="line">git clone https://github.com/MFlowCode/MFC.git</div>
 <div class="line">cd MFC</div>
-</div><!-- fragment --><h1><a class="anchor" id="autotoc_md100"></a>
+</div><!-- fragment --><h1><a class="anchor" id="autotoc_md104"></a>
 Build Environment</h1>
 <p>MFC can be built in multiple ways on various operating systems. Please select your desired configuration from the list bellow:</p>
 <h2>*nix</h2>
@@ -207,7 +207,7 @@ <h3>MacOS</h3>
 <div class="line">. ~/.bash_profile 2&gt;/dev/null || . ~/.zshrc 2&gt;/dev/null</div>
 <div class="line">! [ -z &quot;${BOOST_INCLUDE+x}&quot; ] &amp;&amp; echo &#39;Environment is ready!&#39; || echo &#39;Error: $BOOST_INCLUDE is unset. Please adjust the previous commands to fit with your environment.&#39;</div>
 </div><!-- fragment --><p>They will download the dependencies MFC requires to build itself.</p>
-<h1><a class="anchor" id="autotoc_md101"></a>
+<h1><a class="anchor" id="autotoc_md105"></a>
 Building MFC</h1>
 <p>MFC can be built with support for various (compile-time) features:</p>
 <table class="markdownTable">
@@ -236,12 +236,12 @@ <h1><a class="anchor" id="autotoc_md101"></a>
 <li>Build MFC using a single thread without MPI, GPU, and Debug support: <code>./mfc.sh build --no-mpi</code>.</li>
 <li>Build MFC's <code>simulation</code> code in Debug mode with MPI and GPU support: <code>./mfc.sh build --debug --gpu -t simulation</code>.</li>
 </ul>
-<h1><a class="anchor" id="autotoc_md102"></a>
+<h1><a class="anchor" id="autotoc_md106"></a>
 Running the Test Suite</h1>
 <p>Run MFC's test suite with 8 threads:</p>
 <div class="fragment"><div class="line">./mfc.sh test -j 8</div>
 </div><!-- fragment --><p>Please refer to the <a class="el" href="md_testing.html">Testing</a> document for more information.</p>
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 Running an Example Case</h1>
 <p>MFC has example cases in the <code>examples</code> folder. You can run such a case interactively using 2 tasks by typing:</p>
 <div class="fragment"><div class="line">./mfc.sh run examples/2D_shockbubble/case.py -n 2</div>
diff --git a/documentation/md_gpuParallelization.html b/documentation/md_gpuParallelization.html
index deadbc4c..ed174ac5 100644
--- a/documentation/md_gpuParallelization.html
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@@ -135,16 +135,16 @@
   <div class="headertitle"><div class="title">GPU Parallelization</div></div>
 </div><!--header-->
 <div class="contents">
-<div class="textblock"><p><a class="anchor" id="autotoc_md104"></a></p>
+<div class="textblock"><p><a class="anchor" id="autotoc_md108"></a></p>
 <p>MFC compiles GPU code via OpenACC and in the future OpenMP as well.</p>
 <p>In order to swap between OpenACC and OpenMP, custom GPU macros are used that translate to equivalent OpenACC and OpenMP directives. FYPP is used to process the GPU macros.</p>
 <p><a href="https://openacc-best-practices-guide.readthedocs.io/en/latest/01-Introduction.html">OpenACC Quick start Guide</a></p>
 <p><a href="https://www.openacc.org/sites/default/files/inline-files/API%20Guide%202.7.pdf">OpenACC API Documentation</a></p>
 <hr  />
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 Macro API Documentation</h1>
 <p>Note: Ordering is not guaranteed or stable, so use key-value pairing when using macros</p>
-<h2><a class="anchor" id="autotoc_md107"></a>
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 Data Type Meanings</h2>
 <ul>
 <li>Integer is a number</li>
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 </ul>
 </li>
 </ul>
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 Data Flow</h2>
 <ul>
 <li>Data on the GPU has a reference counter</li>
@@ -168,7 +168,7 @@ <h2><a class="anchor" id="autotoc_md108"></a>
 <li>When data is referred to being detached, it means that the attachment counter is decremented. If attachment counter is zero, then actually detached</li>
 </ul>
 <hr  />
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 Computation Macros</h2>
 <details >
 <summary >
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 </div><!-- fragment --><p></p>
 </details>
 <hr  />
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 Data Control Macros</h2>
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 </details>
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 Synchronization Macros</h2>
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 <summary >
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 </details>
 <hr  />
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 Miscellaneous Macros</h2>
 <details >
 <summary >
@@ -709,11 +709,11 @@ <h2><a class="anchor" id="autotoc_md116"></a>
 </div><!-- fragment --><p></p>
 </details>
 <hr  />
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 Debugging Tools and Tips for GPUs</h1>
-<h2><a class="anchor" id="autotoc_md119"></a>
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 Compiler agnostic tools</h2>
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 OpenMP tools</h2>
 <div class="fragment"><div class="line">OMP_DISPLAY_ENV=true | false | verbose</div>
 </div><!-- fragment --><ul>
@@ -734,9 +734,9 @@ <h2><a class="anchor" id="autotoc_md120"></a>
 </div><!-- fragment --><ul>
 <li>Will display affinity bindings for each OpenMP thread, containing hostname, process identifier, OS thread identifier, OpenMP thread identifier, and affinity binding.</li>
 </ul>
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 Cray Compiler Tools</h2>
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 Cray General Options</h3>
 <div class="fragment"><div class="line">CRAY_ACC_DEBUG: 0 (off), 1, 2, 3 (very noisy)</div>
 </div><!-- fragment --><ul>
@@ -754,7 +754,7 @@ <h3><a class="anchor" id="autotoc_md122"></a>
 <li>Default behavior without an environment variable is to defer initialization on first use</li>
 <li>Device initialization includes initializing the GPU vendor’s low-level device runtime library (e.g., libcuda for NVIDIA GPUs) and establishing all necessary software contexts for interacting with the device</li>
 </ul>
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 Cray OpenACC Options</h3>
 <div class="fragment"><div class="line">CRAY_ACC_PRESENT_DUMP_SAVE_NAMES=1</div>
 </div><!-- fragment --><ul>
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 </ul>
 </li>
 </ul>
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 NVHPC Compiler Options</h2>
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 NVHPC General Options</h3>
 <div class="fragment"><div class="line">STATIC_RANDOM_SEED=1</div>
 </div><!-- fragment --><ul>
@@ -778,7 +778,7 @@ <h3><a class="anchor" id="autotoc_md125"></a>
 <li><code>[no]debug</code>: Enables/disables just-in-time debugging (debugging invoked on error)</li>
 <li><code>[no]trace</code>: Enables/disables stack traceback on error</li>
 </ul>
-<h3><a class="anchor" id="autotoc_md126"></a>
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 NVHPC OpenACC Options</h3>
 <div class="fragment"><div class="line">NVCOMPILER_ACC_NOTIFY= &lt;bitmask&gt;</div>
 </div><!-- fragment --><ul>
@@ -807,7 +807,7 @@ <h3><a class="anchor" id="autotoc_md126"></a>
 </ul>
 </li>
 </ul>
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 NVHPC OpenMP Options</h3>
 <div class="fragment"><div class="line">LIBOMPTARGET_PROFILE=run.json</div>
 </div><!-- fragment --><ul>
@@ -847,7 +847,7 @@ <h3><a class="anchor" id="autotoc_md127"></a>
 <li>If set, the image will only be passed through the backend.</li>
 <li>The backend is invoked with the <code>LIBOMPTARGET_JIT_OPT_LEVEL</code> flag.</li>
 </ul>
-<h2><a class="anchor" id="autotoc_md128"></a>
+<h2><a class="anchor" id="autotoc_md132"></a>
 Compiler Documentation</h2>
 <ul>
 <li><a href="https://cpe.ext.hpe.com/docs/24.11/cce/man7/intro_openmp.7.html#environment-variables">Cray &amp; OpenMP Docs</a></li>
diff --git a/documentation/md_papers.html b/documentation/md_papers.html
index b0700a4f..f33ee386 100644
--- a/documentation/md_papers.html
+++ b/documentation/md_papers.html
@@ -135,7 +135,7 @@
   <div class="headertitle"><div class="title">Papers</div></div>
 </div><!--header-->
 <div class="contents">
-<div class="textblock"><p><a class="anchor" id="autotoc_md129"></a></p>
+<div class="textblock"><p><a class="anchor" id="autotoc_md133"></a></p>
 <p>MFC 5.0: An exascale many-physics flow solver. <a href="https://doi.org/10.48550/arXiv.2503.07953"><b>Wilfong, B., Le Berre, H., Radhakrishnan, A.,</b> Gupta, A., Vaca-Revelo, D., Adam , D., Yu, H., Lee, H., Chreim, J. R., Carcana Barbosa, M., Zhang, Y., Cisneros-Garibay, E., Gnanaskandan, A., Rodriguez Jr., M., Budiardja, R. D., Abbott, S., Colonius, T., &amp; Bryngelson, S. H. (2025) MFC 5.0: An exascale many-physics flow solver. arXiv:2503.07953. <b>Equal contribution.</b></a></p>
 <div class="fragment"><div class="line">@article{Wilfong_2025,</div>
 <div class="line">  author = {Wilfong, Benjamin and {Le Berre}, Henry and Radhakrishnan, Anand and Gupta, Ansh and Vaca-Revelo, Diego and Adam, Dimitrios and Yu, Haocheng and Lee, Hyeoksu and Chreim, Jose Rodolfo and {Carcana Barbosa}, Mirelys and Zhang, Yanjun and Cisneros-Garibay, Esteban and Gnanaskandan, Aswin and {Rodriguez Jr.}, Mauro and Budiardja, Reuben D. and Abbott, Stephen and Colonius, Tim and Bryngelson, Spencer H.},</div>
diff --git a/documentation/md_readme.html b/documentation/md_readme.html
index f421b845..168f5042 100644
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 User Documentation</h1>
 <ul>
 <li><a class="el" href="md_getting-started.html">Getting Started</a></li>
@@ -150,7 +150,7 @@ <h1><a class="anchor" id="autotoc_md131"></a>
 <li><a class="el" href="md_authors.html">Authors</a></li>
 <li><a class="el" href="md_references.html">References</a></li>
 </ul>
-<h1><a class="anchor" id="autotoc_md132"></a>
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 Code/API Documentation</h1>
 <p>MFC's three codes have their own documentation:</p>
 <ul>
diff --git a/documentation/md_references.html b/documentation/md_references.html
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 <ul>
 <li><a class="anchor" id="Allaire02"></a>Allaire, G., Clerc, S., and Kokh, S. (2002). A five-equation model for the simulation of interfaces between compressible fluids. Journal of Computational Physics, 181(2):577–616.</li>
 </ul>
diff --git a/documentation/md_running.html b/documentation/md_running.html
index 4f195500..becae5c4 100644
--- a/documentation/md_running.html
+++ b/documentation/md_running.html
@@ -135,7 +135,7 @@
   <div class="headertitle"><div class="title">Running</div></div>
 </div><!--header-->
 <div class="contents">
-<div class="textblock"><p><a class="anchor" id="autotoc_md134"></a></p>
+<div class="textblock"><p><a class="anchor" id="autotoc_md138"></a></p>
 <p>MFC can be run using <code>mfc.sh</code>'s <code>run</code> command. It supports interactive and batch execution. Batch mode is designed for multi-node distributed systems (supercomputers) equipped with a scheduler such as PBS, SLURM, or LSF. A full (and up-to-date) list of available arguments can be acquired with <code>./mfc.sh run -h</code>.</p>
 <p>MFC supports running simulations locally (Linux, MacOS, and Windows) as well as several supercomputer clusters, both interactively and through batch submission.</p>
 <dl class="section important"><dt>Important</dt><dd>Running simulations locally should work out of the box. On supported clusters, you can append <code>-c &lt;computer name&gt;</code> on the command line to instruct the MFC toolchain to make use of the template file <code>toolchain/templates/&lt;computer name&gt;.mako</code>. You can browse that directory and contribute your own files. Since systems and their schedulers do not have a standardized syntax to request certain resources, MFC can only provide support for a restricted subset of common or user-contributed configuration options. <br  />
@@ -149,7 +149,7 @@
 </ul>
 </dd></dl>
 <p>Please refer to <code>./mfc.sh run -h</code> for a complete list of arguments and options, along with their defaults.</p>
-<h1><a class="anchor" id="autotoc_md135"></a>
+<h1><a class="anchor" id="autotoc_md139"></a>
 Interactive Execution</h1>
 <p>To run all stages of MFC, that is <a href="https://github.com/MFlowCode/MFC/tree/master/src/pre_process/">pre_process</a>, <a href="https://github.com/MFlowCode/MFC/tree/master/src/simulation/">simulation</a>, and <a href="https://github.com/MFlowCode/MFC/tree/master/src/post_process/">post_process</a> on the sample case <a href="https://github.com/MFlowCode/MFC/tree/master/examples/2D_shockbubble/">2D_shockbubble</a>,</p>
 <div class="fragment"><div class="line">./mfc.sh run examples/2D_shockbubble/case.py</div>
@@ -163,7 +163,7 @@ <h1><a class="anchor" id="autotoc_md135"></a>
 <li>Running <a href="https://github.com/MFlowCode/MFC/tree/master/src/simulation/">simulation</a> and <a href="https://github.com/MFlowCode/MFC/tree/master/src/post_process/">post_process</a> using 4 cores:</li>
 </ul>
 <div class="fragment"><div class="line">./mfc.sh run examples/2D_shockbubble/case.py -t simulation post_process -n 4</div>
-</div><!-- fragment --><h1><a class="anchor" id="autotoc_md136"></a>
+</div><!-- fragment --><h1><a class="anchor" id="autotoc_md140"></a>
 Batch Execution</h1>
 <p>The MFC detects which scheduler your system is using and handles the creation and execution of batch scripts. The batch engine is requested via the <code>-e batch</code> option. The number of nodes can be specified with the <code>-N</code> (i.e., <code>--nodes</code>) option.</p>
 <p>We provide a list of (baked-in) submission batch scripts in the <code>toolchain/templates</code> folder.</p>
@@ -178,22 +178,22 @@ <h1><a class="anchor" id="autotoc_md135"></a>
 </ul>
 <p>As an example, one might request GPUs on a SLURM system using the following:</p>
 <p><b>Disclaimer</b>: IBM's JSRUN on LSF-managed computers does not use the traditional node-based approach to allocate resources. Therefore, the MFC constructs equivalent resource sets in the task and GPU count.</p>
-<h2><a class="anchor" id="autotoc_md137"></a>
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 GPU Profiling</h2>
-<h3><a class="anchor" id="autotoc_md138"></a>
+<h3><a class="anchor" id="autotoc_md142"></a>
 NVIDIA GPUs</h3>
 <p>MFC provides two different arguments to facilitate profiling with NVIDIA Nsight. <b>Please ensure the used argument is placed at the end so their respective flags can be appended.</b></p><ul>
 <li>Nsight Systems (Nsys): <code>./mfc.sh run ... -t simulation --nsys [nsys flags]</code> allows one to visualize MFC's system-wide performance with <a href="https://developer.nvidia.com/nsight-systems">NVIDIA Nsight Systems</a>. NSys is best for understanding the order and execution times of major subroutines (WENO, Riemann, etc.) in MFC. When used, <code>--nsys</code> will run the simulation and generate <code>.nsys-rep</code> files in the case directory for all targets. These files can then be imported into Nsight System's GUI, which can be downloaded <a href="https://developer.nvidia.com/nsight-systems/get-started#latest-Platforms">here</a>. To keep the report files small, it is best to run case files with a few timesteps. Learn more about NVIDIA Nsight Systems <a href="https://docs.nvidia.com/nsight-systems/UserGuide/index.html">here</a>.</li>
 <li>Nsight Compute (NCU): <code>./mfc.sh run ... -t simulation --ncu [ncu flags]</code> allows one to conduct kernel-level profiling with <a href="https://developer.nvidia.com/nsight-compute">NVIDIA Nsight Compute</a>. NCU provides profiling information for every subroutine called and is more detailed than NSys. When used, <code>--ncu</code> will output profiling information for all subroutines, including elapsed clock cycles, memory used, and more after the simulation is run. Adding this argument will significantly slow the simulation and should only be used on case files with a few timesteps. Learn more about NVIDIA Nsight Compute <a href="https://docs.nvidia.com/nsight-compute/NsightCompute/index.html">here</a>.</li>
 </ul>
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+<h3><a class="anchor" id="autotoc_md143"></a>
 AMD GPUs</h3>
 <ul>
 <li>Rocprof Systems (RSYS): <code>./mfc.sh run ... -t simulation --rsys --hip-trace [rocprof flags]</code> allows one to visualize MFC's system-wide performance with <a href="https://ui.perfetto.dev/">Perfetto UI</a>. When used, <code>--roc</code> will run the simulation and generate files in the case directory for all targets. <code>results.json</code> can then be imported in <a href="https://ui.perfetto.dev/">Perfetto's UI</a>. Learn more about AMD Rocprof <a href="https://rocm.docs.amd.com/projects/rocprofiler/en/docs-5.5.1/rocprof.html">here</a> It is best to run case files with few timesteps to keep the report file sizes manageable.</li>
 <li>Rocprof Compute (RCU): <code>./mfc.sh run ... -t simulation --rcu -n &lt;name&gt; [rocprof-compute flags]</code> allows one to conduct kernel-level profiling with <a href="https://rocm.docs.amd.com/projects/rocprofiler-compute/en/latest/what-is-rocprof-compute.html">ROCm Compute Profiler</a>. When used, <code>--rcu</code> will output profiling information for all subroutines, including rooflines, cache usage, register usage, and more, after the simulation is run. Adding this argument will moderately slow down the simulation and run the MFC executable several times. For this reason, it should only be used with case files with few timesteps.</li>
 </ul>
 <p><a class="anchor" id="restarting-cases"></a> </p>
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+<h2><a class="anchor" id="autotoc_md144"></a>
 Restarting Cases</h2>
 <p>When running a simulation, MFC generates a <code>./restart_data</code> folder in the case directory that contains <code>lustre_*.dat</code> files that can be used to restart a simulation from saved timesteps. This allows a user to simulate some timestep $X$, then continue it to run to another timestep $Y$, where $Y &gt; X$. The user can also choose to add new patches at the intermediate timestep.</p>
 <p>If you want to restart a simulation,</p>
@@ -289,7 +289,7 @@ <h2><a class="anchor" id="autotoc_md140"></a>
 <div class="line">./mfc.sh run examples/1D_vacuum_restart/restart_case.py -t pre_process simulation</div>
 <div class="line">./mfc.sh run examples/1D_vacuum_restart/case.py -t post_process</div>
 <div class="line">./mfc.sh run examples/1D_vacuum_restart/restart_case.py -t post_process</div>
-</div><!-- fragment --><h2><a class="anchor" id="autotoc_md141"></a>
+</div><!-- fragment --><h2><a class="anchor" id="autotoc_md145"></a>
 Example Runs</h2>
 <ul>
 <li>Oak Ridge National Laboratory's <a href="https://www.olcf.ornl.gov/summit/">Summit</a>:</li>
diff --git a/documentation/md_testing.html b/documentation/md_testing.html
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 </div><!--header-->
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 <p>To run MFC's test suite, run </p><div class="fragment"><div class="line">./mfc.sh test -j &lt;thread count&gt;</div>
 </div><!-- fragment --><p>It will generate and run test cases, comparing their output to previous runs from versions of MFC considered accurate. <em>golden files</em>, stored in the <code>tests/</code> directory contain this data, aggregating <code>.dat</code> files generated when running MFC. A test is considered passing when our error tolerances are met in order to maintain a high level of stability and accuracy. <code>./mfc.sh test</code> has the following unique options:</p><ul>
 <li><code>-l</code> outputs the full list of tests</li>
@@ -149,7 +149,7 @@
 </ul>
 <p>To specify a computer, pass the <code>-c</code> flag to <code>./mfc.sh run</code> like so: </p><div class="fragment"><div class="line">./mfc.sh test -j &lt;thread count&gt; -- -c &lt;computer name&gt;</div>
 </div><!-- fragment --><p> where <code>&lt;computer name&gt;</code> could be <code>phoenix</code> or any of the others in the <a href="https://github.com/MFlowCode/MFC/tree/master/toolchain/templates">templates</a>). You can create new templates with the appropriate run commands or omit this option. The use of <code>--</code> in the above command passes options to the <code>./mfc.sh run</code> command underlying the <code>./mfc.sh test</code>.</p>
-<h2><a class="anchor" id="autotoc_md143"></a>
+<h2><a class="anchor" id="autotoc_md147"></a>
 Creating Tests</h2>
 <p>Creating and updating test cases can be done with the following command line arguments:</p><ul>
 <li><code>--generate</code> to generate golden files for a new test case</li>
@@ -196,7 +196,7 @@ <h2><a class="anchor" id="autotoc_md143"></a>
 </ul>
 <p>If a trace is empty (that is, the empty string <code>""</code>), it will not appear in the final trace, but any case parameter variations associated with it will still be applied.</p>
 <p>Finally, the case is appended to the <code>cases</code> list, which will be returned by the <code>list_cases</code> function.</p>
-<h2><a class="anchor" id="autotoc_md144"></a>
+<h2><a class="anchor" id="autotoc_md148"></a>
 Testing Post Process</h2>
 <p>To test the post-processing code, append the <code>-a</code> or <code>--test-all</code> option: </p><div class="fragment"><div class="line">./mfc.sh test -a -j 8</div>
 </div><!-- fragment --><p>This argument will re-run the test stack with &lsquo;parallel_io='T&rsquo;<code>, which generates silo_hdf5 files. It will also turn most write parameters (</code>*_wrt<code>) on. Then, it searches through the silo files using</code>h5dump<code>to ensure that there are no</code>NaN<code>s or</code>Infinity<code>s. Although adding this option does not guarantee that accurate</code>.silo` files are generated, it does ensure that the post-process code does not fail or produce malformed data. </p>
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 </div><!--header-->
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-<div class="textblock"><p><a class="anchor" id="autotoc_md145"></a></p>
+<div class="textblock"><p><a class="anchor" id="autotoc_md149"></a></p>
 <p>A post-processed database in Silo-HDF5 format can be visualized and analyzed using Paraview and VisIt. After the post-processing of simulation data (see section <a class="el" href="md_running.html">Running</a>), a directory named <code>silo_hdf5</code> contains a silo-HDF5 database. Here, <code>silo_hdf5/</code> includes a directory named <code>root/</code> that contains index files for flow field data at each saved time step.</p>
-<h2><a class="anchor" id="autotoc_md146"></a>
+<h2><a class="anchor" id="autotoc_md150"></a>
 Visualizing with Paraview</h2>
 <p>Paraview is an open-source interactive parallel visualization and graphical analysis tool for viewing scientific data. Paraview 5.11.0 has been confirmed to work with the MFC databases for some parallel environments. Nevertheless, the installation and configuration of Paraview can be environment-dependent and are left to the user.</p>
 <p>The user can launch Paraview and open the index files under <code>/silo_hdf5/root</code>. Once the database is loaded, flow field variables contained in the database can be added to the render view. Further information on Paraview can be found in its <a href="https://docs.paraview.org/en/latest/">documentation</a>. The figure below shows the iso-contour of the liquid void fraction (<code>alpha1</code>) in the database generated by the example case <code>3D_sphbubcollapse</code>.</p>
 <p><img src="../res/paraview.png" alt="" class="inline"/></p>
-<h2><a class="anchor" id="autotoc_md147"></a>
+<h2><a class="anchor" id="autotoc_md151"></a>
 Visualizing data in cylindrical coordinates</h2>
 <p>Visualizing data in cylindrical coordinates requires a coordinate transformation of the raw data in the database file. In Paraview, this coordinate transformation can be accomplished with the following steps:</p>
 <ol type="1">
@@ -156,13 +156,13 @@ <h2><a class="anchor" id="autotoc_md147"></a>
 </li>
 </ol>
 <p>These steps will transform the raw data into cylindrical coordinates. For many cases, this step will require resizing the render view window.</p>
-<h1><a class="anchor" id="autotoc_md148"></a>
+<h1><a class="anchor" id="autotoc_md152"></a>
 Visualizing with VisIt</h1>
 <p>VisIt is an alternative open-source interactive parallel visualization and graphical analysis tool for viewing scientific data. Versions of VisIt after 2.6.0 have been confirmed to work with the MFC databases for some parallel environments. Nevertheless, installation and configuration of VisIt can be environment-dependent and are left to the user. Further remarks on parallel flow visualization, analysis, and processing of the MFC database using VisIt can also be found in <a class="el" href="md_references.html">Coralic (2015)</a> and <a class="el" href="md_references.html">Meng (2016)</a>.</p>
 <p>The user can launch VisIt and open the index files under <code>/silo_hdf5/root</code>. Once the database is loaded, flow field variables contained in the database can be added to the plot. The figure below shows the iso-contour of the liquid void fraction (<code>alpha1</code>) in the database generated by the example case <code>3D_sphbubcollapse</code>. For analysis and processing of the database using VisIt's capability, the user is encouraged to address <a href="https://wci.llnl.gov/simulation/computer-codes/visit/manuals">VisIt user manual</a>.</p>
 <p><img src="../res/visit.png" alt="" class="inline"/></p>
 <p><em>Iso-contour of the liquid void fraction (<code>alpha1</code>) in the database generated by example case <code>3D_sphbubcollapse</code></em></p>
-<h1><a class="anchor" id="autotoc_md149"></a>
+<h1><a class="anchor" id="autotoc_md153"></a>
 Serial data output</h1>
 <p>If <code>parallel_io = 'F'</code>, MFC will output the conservative variables to a directory <code>D/</code>. If multiple cores are used ($\mathtt{ppn &gt; 1}$), then a separate file is created for each core. If only one coordinate dimension (<code>n = 0</code> and <code>p = 0</code>) exists, the primitive variables will also be written to <code>D/</code>. The file names correspond to the variables associated with each equation solved by MFC. They are written at every <code>t_step_save</code> time step. The conservative variables are</p>
 <p>$$ {(\rho \alpha)}_{1}, \dots, (\rho\alpha)_{N_c}, \rho u_{1}, \dots, \rho u_{N_d}, E, \alpha_1, \dots, \alpha_{N_c} $$</p>
@@ -172,9 +172,9 @@ <h1><a class="anchor" id="autotoc_md149"></a>
 <p>$$ n_b R_1, n_b {\dot R}_1, \dots, n_b R_{N_b}, n_b {\dot R}_{N_b} $$</p>
 <p>where $n_B$ is the bubble number density, and $N_b$ is the number of bubble sizes (see the matching variable in the input file, <code>Nb</code>). The primitive bubble variables do not include $n_B$:</p>
 <p>$$ R_1, {\dot R}_1, \dots, R_{N_b}, {\dot R}_{N_b} $$</p>
-<h1><a class="anchor" id="autotoc_md150"></a>
+<h1><a class="anchor" id="autotoc_md154"></a>
 Remote Visualization on PACE Phoenix</h1>
-<h2><a class="anchor" id="autotoc_md151"></a>
+<h2><a class="anchor" id="autotoc_md155"></a>
 Step 1: Setting up your Environment</h2>
 <p>Begin by downloading the <code>.zip</code> file <a href="https://www.dropbox.com/scl/fi/bdk8702oas8zqu0mk24vx/paceParaview.zip?rlkey=bov1s6lra0z7dhhrh6etniucx&amp;st=2m9xvls4&amp;dl=0">here</a>. This file contains two things:</p>
 <ul>
@@ -182,7 +182,7 @@ <h2><a class="anchor" id="autotoc_md151"></a>
 <li>A prebuilt Paraview 5.11 binary</li>
 </ul>
 <p>Place the file <code>paceParview.zip</code> in your scratch direction on Phoenix and unzip it using <code>unzip paceParaview.zip</code>. Enter the new directory <code>paceParaview</code> and run <code>tar -xvf ParaView-5.11.0-egl-MPI-Linux-Python3.9-x86_64.tar.gz</code> to decompress the compiled binary. Now that you have the binary on Phoenix, you must download Paraview 5.11 on your local machine. Paraview binaries can be downloaded <a href="https://www.paraview.org/download/">here</a>. Select <code>v5.11</code> from the version drop-down bar and install a <code>5.11.0</code> version of Paraview.</p>
-<h2><a class="anchor" id="autotoc_md152"></a>
+<h2><a class="anchor" id="autotoc_md156"></a>
 Step 2: Customizing the script</h2>
 <p>While all of the bash script's options could be passed as command-line arguments, hardcoding certain unlikely-to-change options saves time. The following is a list of required and suggested updates to make to <code>pace-paraview-server</code>.</p>
 <ul>
@@ -191,7 +191,7 @@ <h2><a class="anchor" id="autotoc_md152"></a>
 <li>(Optional) Update line 51 to reflect the default account you'll use to run Paraview jobs</li>
 <li>(Optional) Update line 52 to reflect the default wall time requested for your job</li>
 </ul>
-<h2><a class="anchor" id="autotoc_md153"></a>
+<h2><a class="anchor" id="autotoc_md157"></a>
 Step 3: Running pace-paraview-server</h2>
 <p>Before running <code>pace-paraview-server</code> for the first time, you must update its permissions by running <code>chmod u+x pace-paraview-server</code> in your command line. Once this has been done, you can run <code>./pace-paraview-server</code> with the following options:</p>
 <ul>
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