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documentation/md_case.html

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@@ -550,7 +550,7 @@ <h2><a class="anchor" id="autotoc_md15"></a>
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<li><code>mpp_lim</code> activates correction of solutions to avoid a negative void fraction of each component in each grid cell, such that $\alpha_i&gt;\varepsilon$ is satisfied at each time step.</li>
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<li><code>mixture_err</code> activates correction of solutions to avoid imaginary speed of sound at each grid cell.</li>
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<li><code>time_stepper</code> specifies the order of the Runge-Kutta (RK) time integration scheme that is used for temporal integration in simulation, from the 1st to 5th order by corresponding integer. Note that <code>time_stepper = 3</code> specifies the total variation diminishing (TVD), third order RK scheme (<a class="el" href="md_references.html">Gottlieb and Shu, 1998</a>).</li>
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<li><code>adap_dt</code> activates the Strang operator splitting scheme which splits flux and source terms in time marching, and an adaptive time stepping strategy is implemented for the source term. It requires <code>bubbles = 'T'</code>, <code>polytropic = 'T'</code>, <code>adv_n = 'T'</code> and <code>time_stepper = 3</code>.</li>
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<li><code>adap_dt</code> activates the Strang operator splitting scheme which splits flux and source terms in time marching, and an adaptive time stepping strategy is implemented for the source term. It requires <code>bubbles_euler = 'T'</code>, <code>polytropic = 'T'</code>, <code>adv_n = 'T'</code> and <code>time_stepper = 3</code>. Additionally, it can be used with <code>bubbles_lagrange = 'T'</code> and <code>time_stepper = 3</code></li>
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<li><code>weno_order</code> specifies the order of WENO scheme that is used for spatial reconstruction of variables by an integer of 1, 3, 5, and 7, that correspond to the 1st, 3rd, 5th, and 7th order, respectively.</li>
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<li><code>weno_eps</code> specifies the lower bound of the WENO nonlinear weights. It is recommended to set <code>weno_eps</code> to $10^{-6}$ for WENO-JS, and to $10^{-40}$ for other WENO variants.</li>
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<li><code>mapped_weno</code> activates the WENO-M scheme in place of the default WENO-JS scheme (<a class="el" href="md_references.html">Henrick et al., 2005</a>). WENO-M a variant of the WENO scheme that remaps the nonlinear WENO-JS weights by assigning larger weights to non-smooth stencils, reducing dissipation compared to the default WENO-JS scheme, at the expense of higher computational cost. Only one of <code>mapped_weno</code>, <code>wenoz</code>, and <code>teno</code> can be activated.</li>
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<li><code>null_weights</code> activates nullification of the nonlinear WENO weights at the buffer regions outside the domain boundaries when the Riemann extrapolation boundary condition is specified (<code>bc_[x,y,z]%beg[end]} = -4</code>).</li>
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<li><code>mp_weno</code> activates monotonicity preservation in the WENO reconstruction (MPWENO) such that the values of reconstructed variables do not reside outside the range spanned by WENO stencil (<a class="el" href="md_references.html">Balsara and Shu, 2000</a>; <a class="el" href="md_references.html">Suresh and Huynh, 1997</a>).</li>
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<li><code>riemann_solver</code> specifies the choice of the Riemann solver that is used in simulation by an integer from 1 through 3. <code>riemann_solver = 1</code>, <code>2</code>, and <code>3</code> correspond to HLL, HLLC, and Exact Riemann solver, respectively (<a class="el" href="md_references.html">Toro, 2013</a>). <code>riemann_solver = 4</code> is only for MHD simulations. It resolves 5 of the full seven-wave structure of the MHD equations (<a class="el" href="md_references.html">Miyoshi and Kusano, 2005</a>).</li>
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<li><code>low_Mach</code> specifies the choice of the low Mach number correction scheme for the HLLC Riemann solver. <code>low_Mach = 0</code> is default value and does not apply any correction scheme. <code>low_Mach = 1</code> and <code>2</code> apply the anti-dissipation pressure correction method (<a class="el" href="md_references.html">Chen et al., 2022</a>) and the improved velocity reconstruction method (<a class="el" href="md_references.html">Thornber et al., 2008</a>). This feature requires <code>riemann_solver = 2</code> and <code>model_eqns = 2</code>.</li>
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<li><code>low_Mach</code> specifies the choice of the low Mach number correction scheme for the HLLC Riemann solver. <code>low_Mach = 0</code> is default value and does not apply any correction scheme. <code>low_Mach = 1</code> and <code>2</code> apply the anti-dissipation pressure correction method (<a class="el" href="md_references.html">Chen et al., 2022</a>) and the improved velocity reconstruction method (<a class="el" href="md_references.html">Thornber et al., 2008</a>). This feature requires <code>model_eqns = 2</code> or <code>3</code>. <code>low_Mach = 1</code> works for <code>riemann_solver = 1</code> and <code>2</code>, but <code>low_Mach = 2</code> only works for <code>riemann_solver = 2</code>.</li>
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<li><code>avg_state</code> specifies the choice of the method to compute averaged variables at the cell-boundaries from the left and the right states in the Riemann solver by an integer of 1 or 2. <code>avg_state = 1</code> and <code>2</code> correspond to Roe- and arithmetic averages, respectively.</li>
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<li><code>wave_speeds</code> specifies the choice of the method to compute the left, right, and middle wave speeds in the Riemann solver by an integer of 1 and 2. <code>wave_speeds = 1</code> and <code>2</code> correspond to the direct method (<a class="el" href="md_references.html">Batten et al., 1997</a>), and indirect method that approximates the pressures and velocity (<a class="el" href="md_references.html">Toro, 2013</a>), respectively.</li>
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<li><code>weno_Re_flux</code> activates the scalar divergence theorem in computing the velocity gradients using WENO-reconstructed cell boundary values. If this option is false, velocity gradient is computed using finite difference scheme of order 2 which is independent of the WENO order.</li>
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<tr class="markdownTableRowEven">
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<td class="markdownTableBodyRight"><code>Thost</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Temperature of the surrounding liquid (host) </td></tr>
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<tr class="markdownTableRowOdd">
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<td class="markdownTableBodyRight"><code>diffcoefvap</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Vapor diffusivity in the gas </td></tr>
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<td class="markdownTableBodyRight"><code>rkck_adap_dt</code> </td><td class="markdownTableBodyCenter">Logical </td><td class="markdownTableBodyLeft">Activates the adaptive rkck time stepping algorithm </td></tr>
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<td class="markdownTableBodyRight"><code>rkck_tolerance</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Admissible error truncation tolerance in the rkck stepper </td></tr>
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<td class="markdownTableBodyRight"><code>diffcoefvap</code> </td><td class="markdownTableBodyCenter">Real </td><td class="markdownTableBodyLeft">Vapor diffusivity in the gas </td></tr>
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</table>
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<ul>
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<li><code>nBubs_glb</code> Total number of bubbles. Their initial conditions need to be specified in the ./input/lag_bubbles.dat file. See the example cases for additional information.</li>
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<li><code>smooth_type</code> Specifies the smoothening method of projecting the lagrangian bubbles in the Eulerian field: [1] activates the gaussian kernel function described in <a class="el" href="md_references.html">Maeda and Colonius (2018)</a>, while [2] activates the delta kernel function where the effect of the bubble is only seen in the specific bubble location cell.</li>
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<li><code>heatTransfer_model</code> Activates the heat transfer model at the bubble's interface based on (<a class="el" href="md_references.html">Preston et al., 2007</a>).</li>
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<li><code>massTransfer_model</code> Activates the mass transfer model at the bubble's interface based on (<a class="el" href="md_references.html">Preston et al., 2007</a>).</li>
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<li><code>rkck_adap_dt</code> Activates the adaptive 4th/5th order Runge—Kutta–Cash–Karp (RKCK) time-stepping algorithm (requires <code>time_stepper ==4</code>). A maximum error between the 4th and 5th order Runge-Kutta-Cash-Karp solutions for the same time step size is calculated. If the error is smaller than a tolerance (<code>rkck_tolerance</code>), then the algorithm employs the 5th order solution, while if not, both eulerian/lagrangian variables are re-calculated with a smaller time step size.</li>
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<h2><a class="anchor" id="autotoc_md23"></a>
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10. Velocity Field Setup</h2>

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