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<tdclass="markdownTableBodyRight"><code>geometry</code></td><tdclass="markdownTableBodyCenter">Integer </td><tdclass="markdownTableBodyLeft">Geometry configuration of the patch. </td></tr>
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<tdclass="markdownTableBodyRight"><code>x[y,z]_centroid</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyLeft">Centroid of the applied geometry in the [x,y,z]-direction. </td></tr>
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<tdclass="markdownTableBodyRight"><code>geometry</code></td><tdclass="markdownTableBodyCenter">Integer</td><tdclass="markdownTableBodyCenter">Geometry configuration of the patch. </td></tr>
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<tdclass="markdownTableBodyRight"><code>length_x[y,z]</code></td><tdclass="markdownTableBodyCenter">Real</td><tdclass="markdownTableBodyLeft">Length, if applicable, in the [x,y,z]-direction. </td></tr>
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<tdclass="markdownTableBodyRight"><code>x[y,z]_centroid</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyCenter">Centroid of the applied geometry in the [x,y,z]-direction. </td></tr>
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<tdclass="markdownTableBodyRight"><code>radius</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyLeft">Radius, if applicable, of the applied geometry. </td></tr>
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<tdclass="markdownTableBodyRight"><code>length_x[y,z]</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyCenter">Length, if applicable, in the [x,y,z]-direction.</td></tr>
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<tdclass="markdownTableBodyRight"><code>theta</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyLeft">Angle of attach applied to airfoil IB patches</td></tr>
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<tdclass="markdownTableBodyRight"><code>radius</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyCenter">Radius, if applicable, of the applied geometry.</td></tr>
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<tdclass="markdownTableBodyRight"><code>c</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyLeft">NACA airfoil parameters (see below)</td></tr>
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<tdclass="markdownTableBodyRight"><code>theta</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyCenter">Angle of attach applied to airfoil IB patches </td></tr>
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<tdclass="markdownTableBodyRight"><code>t</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyLeft">NACA airfoil parameters (see below) </td></tr>
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<tdclass="markdownTableBodyRight"><code>m</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyLeft">NACA airfoil parameters (see below) </td></tr>
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<tdclass="markdownTableBodyRight"><code>p</code></td><tdclass="markdownTableBodyCenter">Real </td><tdclass="markdownTableBodyLeft">NACA airfoil parameters (see below) </td></tr>
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<tdclass="markdownTableBodyRight"><code>slip</code></td><tdclass="markdownTableBodyCenter">Logical </td><tdclass="markdownTableBodyLeft">Apply a slip boundary </td></tr>
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</table>
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<p>| <code>c</code> | Real | | <code>t</code> | Real | | <code>m</code> | Real | | <code>p</code> | Real | | <code>slip</code> | Logical | Apply a slip boundary |</p>
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<p>These parameters should be prepended with <code>patch_ib(j)%</code> where $j$ is the patch index.</p>
<li>* Options that work only with <code>model_eqns =2</code>.</li>
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<li>† Options that work only with ‘cyl_coord = 'F’<code>.</code></li>
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<li><code>‡ Options that work only with</code>bc_[x,y,z]%[beg,end] = -15<code>and/or</code>bc_[x,y,z]%[beg,end] = -16`</li>
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<li>† Options that work only with <code>cyl_coord = 'F'</code>.</li>
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<li>‡ Options that work only with<code>bc_[x,y,z]%[beg,end] = -15</code>and/or<code>bc_[x,y,z]%[beg,end] = -16</code></li>
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</ul>
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<p>The table lists simulation algorithm parameters. The parameters are used to specify options in algorithms that are used to integrate the governing equations of the multi-component flow based on the initial condition. Models and assumptions that are used to formulate and discritize the governing equations are described in <ahref="references.md#Bryngelson19">Bryngelson et al. (2019)</a>. Details of the simulation algorithms and implementation of the WENO scheme can be found in <ahref="references.md#Coralic15">Coralic (2015)</a>.</p>
<li><code>adv_alphan</code> activates the advection equations of all the components of fluid. If this parameter is set false, the void fraction of $N$-th component is computed as the residual of the void fraction of the other components at each cell:</li>
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</ul>
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<p>$$ \alpha_N=1-\sum^{N-1}_{i=1} \alpha_i $$</p>
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<p>where $\alpha_i$ is the void fraction of $i$-th component. When a single-component flow is simulated, it requires that ‘adv_alphan = 'T’`.</p>
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<p>where $\alpha_i$ is the void fraction of $i$-th component. When a single-component flow is simulated, it requires that <code>adv_alphan = 'T'</code>.</p>
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<ul>
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<li><code>adv_n</code> activates the direct computation of number density by the Riemann solver instead of computing number density from the void fraction in the method of classes.</li>
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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 $\alpha_i>\varepsilon$ 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 (<ahref="references.md#Gottlieb98">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 ‘bubbles = 'T’<code>,</code>polytropic = 'T'<code>,</code>adv_n = 'T'<code>and</code>time_stepper = 3`.</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>weno_order</code> specifies the order of WENO scheme that is used for spatial reconstruction of variables by an integer of 1, 3, and 5, that correspond to the 1st, 3rd, and 5th order, respectively.</li>
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<li><code>weno_eps</code> specifies the lower bound of the WENO nonlinear weights. Practically, <code>weno_eps</code> $<10^{-6}$ is used.</li>
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<li><code>mapped_weno</code> activates the WENO-M scheme in place of the default WENO-JS scheme (<ahref="references.md#Henrick05">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>
<li><code>perturb_sph</code> activates the perturbation of initial partial density by random noise.</li>
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<li><code>perturb_sph_fluid</code> specifies the fluid component whose partial density is to be perturbed.</li>
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<li><code>vel_profile</code> activates setting the mean streamwise velocity to hyperbolic tangent profile. This option works only for 2D and 3D cases.</li>
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<li><code>instability_wave</code> activates the perturbation of initial velocity by instability waves obtained from linear stability analysis for a mixing layer with hyperbolic tangent mean streamwise velocity profile. This option only works for <code>n > 0</code>, <code>bc_y%[beg,end] = -5</code>, and ‘vel_profile = 'T’`.</li>
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<li><code>instability_wave</code> activates the perturbation of initial velocity by instability waves obtained from linear stability analysis for a mixing layer with hyperbolic tangent mean streamwise velocity profile. This option only works for <code>n > 0</code>, <code>bc_y%[beg,end] = -5</code>, and <code>vel_profile = 'T'</code>.</li>
<p>*: This boundary condition is only used for <code>bc_ybeg</code> when using cylindrical coordinates (‘cyl_coord = 'T’<code>and 3D). For axisymmetric problems, use</code>bc_ybeg = -2<code>with</code>cyl_coord = 'T'` in 2D.</p>
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<p>*: This boundary condition is only used for <code>bc_ybeg</code> when using cylindrical coordinates (<code>cyl_coord = 'T'</code>and 3D). For axisymmetric problems, use<code>bc_ybeg = -2</code>with<code>cyl_coord = 'T'</code> in 2D.</p>
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<p>The boundary condition supported by the MFC are listed in table Boundary Conditions. Their number (<code>#</code>) corresponds to the input value in <code>input.py</code> labeled <code>bc_[x,y,z]%[beg,end]</code> (see table Simulation Algorithm Parameters). The entries labeled "Characteristic." are characteristic boundary conditions based on <ahref="references.md#Thompson87">Thompson (1987)</a> and <ahref="references.md#Thompson90">Thompson (1990)</a>.</p>
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