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documentation/architecture.html

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<li><b>Add the module to <span class="tt">docs/module_categories.json</span></b> so it appears in this page</li>
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</ol>
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<p>Follow the pattern of existing modules like <span class="tt">m_body_forces</span> (simple) or <span class="tt">m_viscous</span> (more involved) as a template.</p>
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<div style="text-align:center; font-size:0.75rem; color:#888; padding:16px 0 0;">Page last updated: 2026-08-10</div> </div></div><!-- contents -->
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</div><!-- PageDoc -->
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</div><!-- doc-content -->
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documentation/case.html

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<td class="markdownTableBodyRight"><span class="tt">n</span> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Number of grid cells in the $y$-coordinate direction </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><span class="tt">p</span> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Number of grid cells in the $z$-coordinate direction </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><span class="tt">pref</span> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Reference pressure </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><span class="tt">rhoref</span> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Reference density </td></tr>
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</table>
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<p>The parameters define the boundaries of the spatial and temporal domains, and their discretization that are used in simulation.</p>
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<ul>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><span class="tt">bc_[x,y,z]%ve[1,2,3]</span></td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Velocity in the (x,1), (y, 2), (z,3) direction applied to <span class="tt">bc_[x,y,z]%end</span> </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><span class="tt">model_eqns</span> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Multicomponent model: [1] \(\Gamma/\Pi_\infty\); [2] 5-equation; [3] 6-equation; [4] 4-equation </td></tr>
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<td class="markdownTableBodyRight"><span class="tt">model_eqns</span> </td><td class="markdownTableBodyCenter">Integer </td><td class="markdownTableBodyLeft">Multicomponent model: [1] \(\Gamma/\Pi_\infty\); [2] 5-equation; [3] 6-equation </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><span class="tt">alt_soundspeed</span> * </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Alternate sound speed and \(K \nabla \cdot u\) for 5-equation model </td></tr>
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<tr class="markdownTableRowEven">
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><span class="tt">Re_inv</span> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Inverse Reynolds number </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><span class="tt">pref</span> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Reference pressure for bubble models </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><span class="tt">rhoref</span> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Reference density for bubble models </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><span class="tt">fluid_rho</span> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Reference fluid density </td></tr>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><span class="tt">bub_pp%R0ref</span>*†‡ </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Reference bubble radius </td></tr>

documentation/case_constraints.html

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<li><b>Note:</b> Not compatible with bubbles or 3D cylindrical </li>
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</ul>
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</details>
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<details >
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<summary >
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<b>Model 4: 4-Equation</b></summary>
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<p></p>
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<ul>
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<li><b>Use for:</b> Single-component flows with bubbles</li>
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<li><b>Value:</b> <span class="tt">model_eqns = 4</span></li>
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<li><b>Requirements:</b> Set <span class="tt">rhoref</span>, Set <span class="tt">pref</span>, <span class="tt">num_fluids</span> = <span class="tt">1</span> (1) </li>
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</ul>
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</details>
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<h2 class="doxsection"><a class="anchor" id="riemann-solvers"></a>
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⚙️ Riemann Solvers</h2>
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<table class="markdownTable">
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<b>Euler-Euler (<span class="tt">bubbles_euler</span>)</b></summary>
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<p></p>
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<p><b>Requirements:</b></p><ul>
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<li><span class="tt">model_eqns</span> = <span class="tt">2</span> (5-Equation) or <span class="tt">4</span> (4-Equation)</li>
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<li><span class="tt">model_eqns</span> = <span class="tt">2</span> (5-Equation)</li>
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<li><span class="tt">riemann_solver</span> = <span class="tt">2</span> (HLLC)</li>
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<li><span class="tt">avg_state</span> = <span class="tt">2</span> (arithmetic)</li>
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<li>Recommended to also set: <span class="tt">nb</span>, <span class="tt">polytropic</span></li>
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<b>Euler-Euler Bubble Model</b> (<span class="tt">bubbles_euler</span>)</summary>
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<p></p>
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<p><b>Dependencies:</b></p><ul>
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<li>When enabled, requires <span class="tt">model_eqns</span> = <span class="tt">2</span> (5-Equation) or <span class="tt">4</span> (4-Equation), <span class="tt">riemann_solver</span> = <span class="tt">2</span> (HLLC), <span class="tt">avg_state</span> = <span class="tt">2</span> (arithmetic)</li>
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<li>When enabled, requires <span class="tt">model_eqns</span> = <span class="tt">2</span> (5-Equation), <span class="tt">riemann_solver</span> = <span class="tt">2</span> (HLLC), <span class="tt">avg_state</span> = <span class="tt">2</span> (arithmetic)</li>
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<li>When enabled, recommends: <span class="tt">nb</span>, <span class="tt">polytropic</span></li>
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</ul>
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<p><b>Requirements</b> (errors):</p><ul>
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<b>Model Equations</b> (<span class="tt">model_eqns</span>)</summary>
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<p></p>
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<p><b>Schema constraints:</b></p><ul>
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<li>Choices: <span class="tt">1</span> = Gamma-law, <span class="tt">2</span> = 5-Equation, <span class="tt">3</span> = 6-Equation, <span class="tt">4</span> = 4-Equation</li>
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<li>Choices: <span class="tt">1</span> = Gamma-law, <span class="tt">2</span> = 5-Equation, <span class="tt">3</span> = 6-Equation</li>
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</ul>
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<p><b>Dependencies:</b></p><ul>
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<li>When = 2, requires: <span class="tt">num_fluids</span></li>
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<li>When = 3, requires <span class="tt">riemann_solver</span> = <span class="tt">2</span> (HLLC), <span class="tt">avg_state</span> = <span class="tt">2</span> (arithmetic), <span class="tt">wave_speeds</span> = <span class="tt">1</span> (direct)</li>
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<li>When = 4, requires: <span class="tt">rhoref</span>, <span class="tt">pref</span></li>
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<li>When = 4, requires <span class="tt">num_fluids</span> = <span class="tt">1</span> (1)</li>
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</ul>
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<p><b>Requirements</b> (errors):</p><ul>
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<li>5-equation model (model_eqns = 2) requires num_fluids to be set</li>
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<li>6-equation model (model_eqns = 3) requires num_fluids to be set</li>
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<li>4-equation model (model_eqns = 4) requires num_fluids to be set</li>
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<li>hypoelasticity requires model_eqns = 2</li>
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</ul>
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<p><b>Incompatibilities</b> (errors):</p><ul>
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<li>num_fluids is not supported for model_eqns = 1</li>
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<li>model_eqns = 1 does not support mpp_lim</li>
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<li>6-equation model (model_eqns = 3) does not support cylindrical coordinates (cyl_coord = T and p != 0)</li>
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</ul>
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<p><b>Valid values</b> (errors):</p><ul>
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<li>model_eqns must be 1, 2, 3, or 4</li>
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<li>model_eqns must be 1, 2, or 3</li>
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</ul>
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<p></p>
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</details>
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<p><b>Requirements</b> (errors):</p><ul>
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<li>5-equation model (model_eqns = 2) requires num_fluids to be set</li>
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<li>6-equation model (model_eqns = 3) requires num_fluids to be set</li>
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<li>4-equation model (model_eqns = 4) requires num_fluids to be set</li>
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<li>int_comp &gt; 0 requires num_fluids = 2</li>
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</ul>
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<p><b>Incompatibilities</b> (errors):</p><ul>
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<li>num_fluids is not supported for model_eqns = 1</li>
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</table>
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<hr />
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<p>💡 <b>Tip:</b> If you encounter a validation error, check the relevant section above or review <a href="https://github.com/MFlowCode/MFC/blob/master/toolchain/mfc/case_validator.py"><span class="tt">case_validator.py</span></a> for complete validation logic.</p>
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documentation/cli-reference.html

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<h3 class="doxsection"><a class="anchor" id="autotoc_md83"></a>
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Debug Logging (<span class="tt">-d, --debug-log</span>)</h3>
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<p>Enables debug logging for the Python toolchain (mfc.sh internals). This is for troubleshooting the build system, not the MFC simulation code.</p>
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documentation/contributing.html

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<h3 class="doxsection"><a class="anchor" id="autotoc_md102"></a>
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Physics and Model Consistency</h3>
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<ul>
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<li><b>Pressure formula</b> must match <span class="tt">model_eqns</span> value. Model 2/3 (multi-fluid), model 4 (bubbles), MHD, and hypoelastic each use different EOS formulations. Wrong formula = wrong physics.</li>
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<li><b>Pressure formula</b> must match <span class="tt">model_eqns</span> value. Model 2/3 (multi-fluid), MHD, and hypoelastic each use different EOS formulations. Wrong formula = wrong physics.</li>
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<li><b>Conservative-primitive conversion:</b> Density recovery, kinetic energy, and pressure each have model-specific paths. Verify the correct branch is taken.</li>
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<li><b>Volume fractions</b> must sum to 1. <span class="tt">alpha_rho_K</span> must be non-negative. Species mass fractions should be clipped to [0,1].</li>
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<li><b>Boundary conditions:</b> Periodic BCs must match at both ends (<span class="tt">bc_x%beg</span> and <span class="tt">bc_x%end</span>). Cylindrical coordinates have special requirements (<span class="tt">bc_y%beg = -14</span> for axis in 3D).</li>

documentation/equations.html

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<li>\(\mathbf{h}(\mathbf{q})\,\nabla \cdot \mathbf{u}\) contains non-conservative terms (volume fraction advection),</li>
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<li>\(\mathbf{s}(\mathbf{q})\) is the source vector (bubbles, body forces, chemistry, etc.).</li>
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<p>The parameter <span class="tt">model_eqns</span> (1, 2, 3, or 4) selects the governing equation set.</p>
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<p>The parameter <span class="tt">model_eqns</span> (1, 2, or 3) selects the governing equation set.</p>
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<p><b>Key source files:</b> <span class="tt">src/simulation/m_rhs.fpp</span> (RHS evaluation), <span class="tt">src/common/m_variables_conversion.fpp</span> (EOS and variable conversion).</p>
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<h2 class="doxsection"><a class="anchor" id="sec-units-dimensions"></a>
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2.3 Other Model Variants</h3>
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<li><span class="tt">model_eqns = 1</span>: <b>Gamma/pi_inf model</b> — simplified single-fluid formulation using mixture \(\gamma\) and \(\pi_\infty\) directly without tracking individual volume fractions (Johnsen <a class="el" href="citelist.html#CITEREF_johnsen08">[24]</a>).</li>
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<li><span class="tt">model_eqns = 4</span>: <b>Four-equation model</b> — reduced model from the six-equation system after full pressure-temperature equilibrium relaxation (Tait-like compressible liquid).</li>
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<h2 class="doxsection"><a class="anchor" id="autotoc_md151"></a>

documentation/examples.html

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<ul>
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<li>Papanastasiou, T. C. (1987). Flows of materials with yield. <em>J. Rheol.</em> 31, 385.</li>
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</ul>
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