Procedures

Function that computes the time derivative of the internal bubble pressure @param fvflux Vapour flux @param fR Current bubble radius @param fV Current bubble velocity @param fpb Current internal bubble pressure @param fmass_v Current mass of vapour @param iR0 Bubble size index

Function that computes the sound speed for the bubble @param fCpinf Driving bubble pressure @param fntait Tait EOS parameter @param fBtait Tait EOS parameter @param fH Bubble enthalpy

Function that computes that bubble wall pressure for Gilmore bubbles

Function that computes the bubble wall pressure for Keller--Miksis bubbles @param fR0 Equilibrium bubble radius @param fR Current bubble radius @param fV Current bubble velocity @param fpb Internal bubble pressure

Function that computes the time derivative of the driving pressure @param fRho Local liquid density @param fP Local pressure @param falf Local void fraction @param fntait Tait EOS parameter @param fBtait Tait EOS parameter @param advsrc Advection equation source term @param divu Divergence of velocity

Function that computes the bubble enthalpy @param fCpbw Bubble wall pressure @param fCpinf Driving bubble pressure @param fntait Tait EOS parameter @param fBtait Tait EOS parameter

Function that computes the time derivative of the enthalpy @param fCpbw Bubble wall pressure @param fCpinf Driving bubble pressure @param fCpinf_dot Time derivative of the driving pressure @param fntait Tait EOS parameter @param fBtait Tait EOS parameter @param fR0 Equilibrium bubble radius @param fR Current bubble radius @param fV Current bubble velocity @param fpbdot Time derivative of the internal bubble pressure

Function that computes the bubble radial acceleration @param fCpbw Bubble wall pressure @param fR Current bubble radius @param fV Current bubble velocity @param fH Current enthalpy @param fHdot Current time derivative of the enthalpy @param fcgas Current gas sound speed @param fntait Tait EOS parameter @param fBtait Tait EOS parameter

Function that computes the bubble radial acceleration for Keller--Miksis bubbles @param fpbdot Time-derivative of internal bubble pressure @param fCp Driving pressure @param fCpbw Bubble wall pressure @param fRho Current density @param fR Current bubble radius @param fV Current bubble velocity @param fR0 Equilibrium bubble radius @param fC Current sound speed

Function that computes the bubble radial acceleration for Rayleigh-Plesset bubbles @param fCp Driving pressure @param fRho Current density @param fR Current bubble radius @param fV Current bubble velocity @param fR0 Equilibrium bubble radius @param fCpbw Boundary wall pressure

Function that computes the vapour flux @param fR Current bubble radius @param fV Current bubble velocity @param fmass_v Current mass of vapour @param iR0 Bubble size index

1st order TVD RK time-stepping algorithm @param t_step Current time step

2nd order TVD RK time-stepping algorithm @param t_step Current time-step

3rd order TVD RK time-stepping algorithm @param t_step Current time-step

Assigns default values to the user inputs before reading them in. This enables for an easier consistency check of these parameters once they are read from the input file.

Subroutine that computes bubble wall properties for vapor bubbles @param pb Internal bubble pressure @param iR0 Current bubble size index

The goal of this procedure is to verify that each of the user provided inputs is valid and that their combination consitutes a meaningful configuration for the simulation.

Computes the bubble number density n from the conservative variables \f$ n = \sqrt{ \frac{4 \pi}{3} } \frac{ nR^3}{\alpha} \f$ @param vftmp is the void fraction @param nRtmp is the bubble number density times the bubble radii @param ntmp is the output number bubble density

Computes the bubble number density n from the primitive variables \f$ n = \sqrt{ \frac{3}{4 \pi} } \frac{ \alpha }{ R^3} \f$ @param vftmp is the void fraction @param Rtmp is the bubble radii @param ntmp is the output number bubble density

The purpose of this procedure is to compute the source terms that are needed for the bubble modeling @param idir Dimension splitting index @param q_prim_vf Primitive variables @param q_cons_vf Conservative variables @param mydivu Divergence of velocity @param bub_adv_src Advection equation source due to bubble compression/expansion @param bub_r_src Bubble radius equation source @param bub_v_src Bubble velocity equation source @param bub_p_src Bubble pressure equation source @param bub_m_src Bubble mass equation source

Writes coherent body information, communication files, and probes. @param t_step Current time-step

The following procedure handles the conversion between the conservative variables and the primitive variables. @param qK_cons_vf Conservative variables @param qK_prim_vf Primitive variables @param gm_alphaK_vf Gradient magnitude of the volume fraction @param ix Index bounds in first coordinate direction @param iy Index bounds in second coordinate direction @param iz Index bounds in third coordinate direction

This procedure is used alongside with the gamma/pi_inf model to transfer the density, the specific heat ratio function and liquid stiffness function from the vector of conservative or primitive variables to their scalar counterparts. @param qK_vf conservative or primitive variables @param i cell index to transfer mixture variables @param j cell index to transfer mixture variables @param k cell index to transfer mixture variables @param rho_K density @param gamma_K specific heat ratio function @param pi_inf_K liquid stiffness @param Re_k Reynolds number

The following procedure handles the conversion between the primitive variables and the conservative variables. @param qK_prim_vf Primitive variables @param qK_cons_vf Conservative variables @param gm_alphaK_vf Gradient magnitude of the volume fractions @param ix Index bounds in the first coordinate direction @param iy Index bounds in the second coordinate direction @param iz Index bounds in the third coordinate direction

The following subroutine handles the conversion between the primitive variables and the Eulerian flux variables. @param qK_prim_vf Primitive variables @param FK_vf Flux variables @param FK_src_vf Flux source variables @param ix Index bounds in the first coordinate direction @param iy Index bounds in the second coordinate direction @param iz Index bounds in the third coordinate direction

This subroutine is designed for the volume fraction model and provided a set of either conservative or primitive variables, computes the density, the specific heat ratio function and the liquid stiffness function from q_vf and stores the results into rho, gamma and pi_inf. @param qK_vf primitive variables @param rho_K density @param gamma_K specific heat ratio @param pi_inf_K liquid stiffness @param Re_K mixture Reynolds number @param k Cell index @param l Cell index @param r Cell index

This procedure is used alongside with the gamma/pi_inf model to transfer the density, the specific heat ratio function and liquid stiffness function from the vector of conservative or primitive variables to their scalar counterparts. Specifially designed for when subgrid bubbles must be included. @param qK_vf primitive variables @param rho_K density @param gamma_K specific heat ratio @param pi_inf_K liquid stiffness @param Re_K mixture Reynolds number @param i Cell index @param j Cell index @param k Cell index

Deallocation procedures for the module

Module deallocation and/or disassociation procedures

Module deallocation and/or disassociation procedures

Module deallocation and/or disassociation procedures

Module deallocation and/or disassociation procedures

Module deallocation and/or disassociation procedures

This subroutine compute the TVD flux function @param q_cons_vf Cell-averaged conservative variables @param q_prim_vf Cell-averaged primitive variables @param rhs_vf Cell-averaged RHS variables @param i Dimensional splitting index Computes viscous terms @param q_cons_vf Cell-averaged conservative variables @param q_prim_vf Cell-averaged primitive variables @param rhs_vf Cell-averaged RHS variables

This procedure is the implementation of the Harten, Lax, van Leer, and contact (HLLC) approximate Riemann solver, see Toro (1999) and Johnsen (2007). The viscous and the surface tension effects have been included by modifying the exact Riemann solver of Perigaud and Saurel (2005). @param qL_prim_vf The left WENO-reconstructed cell-boundary values of the cell-average primitive variables @param qR_prim_vf The right WENO-reconstructed cell-boundary values of the cell-average primitive variables @param dqL_prim_dx_vf The left WENO-reconstructed cell-boundary values of the first-order x-dir spatial derivatives @param dqL_prim_dy_vf The left WENO-reconstructed cell-boundary values of the first-order y-dir spatial derivatives @param dqL_prim_dz_vf The left WENO-reconstructed cell-boundary values of the first-order z-dir spatial derivatives @param dqR_prim_dx_vf The right WENO-reconstructed cell-boundary values of the first-order x-dir spatial derivatives @param dqR_prim_dy_vf The right WENO-reconstructed cell-boundary values of the first-order y-dir spatial derivatives @param dqR_prim_dz_vf The right WENO-reconstructed cell-boundary values of the first-order z-dir spatial derivatives @param gm_alphaL_vf Left averaged gradient magnitude @param gm_alphaR_vf Right averaged gradient magnitude @param flux_vf Intra-cell fluxes @param flux_src_vf Intra-cell fluxes sources @param flux_gsrc_vf Intra-cell geometric fluxes sources @param norm_dir Dir. splitting direction @param ix Index bounds in the x-dir @param iy Index bounds in the y-dir @param iz Index bounds in the z-dir @param q_prim_vf Cell-averaged primitive variables

Allocate and open derived variables. Computing FD coefficients.

Computation of parameters, allocation procedures, and/or any other tasks needed to properly setup the module

The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

The purpose of this procedure is to initialize the values of the internal-energy equations of each phase from the mass of each phase, the mixture momentum and mixture-total-energy equations. @param v_vf conservative variables

The subroutine that initializes MPI data structures @param q_cons_vf Conservative variables

The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

Initializes non-polydisperse bubble modeling ! thermal properties !!!

Initializes parallel infrastructure

The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

The computation of parameters, the allocation of memory, the association of pointers and/or the execution of any other procedures that are necessary to setup the module.

$acc loop seq

The subroutine terminates the MPI execution environment.

The following subroutine takes the input local variable from all processors and reduces to the maximum of all values. The reduced variable is recorded back onto the original local variable on each processor. @param var_loc Some variable containing the local value which should be reduced amongst all the processors in the communicator. @param var_glb The globally reduced value

The following subroutine takes the input local variable from all processors and reduces to the minimum of all values. The reduced variable is recorded back onto the original local variable on each processor. @param var_loc Some variable containing the local value which should be reduced amongst all the processors in the communicator. @param var_glb The globally reduced value

The following subroutine takes the input local variable from all processors and reduces to the sum of all values. The reduced variable is recorded back onto the original local variable on each processor. @param var_loc Some variable containing the local value which should be reduced amongst all the processors in the communicator. @param var_glb The globally reduced value

Halts all processes until all have reached barrier.

Since only the processor with rank 0 reads and verifies the consistency of user inputs, these are initially not available to the other processors. Then, the purpose of this subroutine is to distribute the user inputs to the remaining processors in the communicator.

The purpose of this procedure is to optimally decompose the computational domain among the available processors. This is performed by attempting to award each processor, in each of the coordinate directions, approximately the same number of cells, and then recomputing the affected global parameters.

The subroutine finalizes the MPI execution environment.

The subroutine intializes the MPI execution environment and queries both the number of processors which will be available for the job and the local processor rank.

The goal of this subroutine is to determine the global extrema of the stability criteria in the computational domain. This is performed by sifting through the local extrema of each stability criterion. Note that each of the local extrema is from a single process, within its assigned section of the computational domain. Finally, note that the global extrema values are only bookkeept on the rank 0 processor. @param icfl_max_loc Local maximum ICFL stability criterion @param vcfl_max_loc Local maximum VCFL stability criterion @param ccfl_max_loc Local maximum CCFL stability criterion @param Rc_min_loc Local minimum Rc stability criterion @param icfl_max_glb Global maximum ICFL stability criterion @param vcfl_max_glb Global maximum VCFL stability criterion @param ccfl_max_glb Global maximum CCFL stability criterion @param Rc_min_glb Global minimum Rc stability criterion

The goal of this procedure is to populate the buffers of the cell-average conservative variables by communicating with the neighboring processors. @param q_cons_vf Cell-average conservative variables @param mpi_dir MPI communication coordinate direction @param pbc_loc Processor boundary condition (PBC) location

The goal of this procedure is to populate the buffers of the grid variables by communicating with the neighboring processors. Note that only the buffers of the cell-width distributions are handled in such a way. This is because the buffers of cell-boundary locations may be calculated directly from those of the cell-width distributions. @param mpi_dir MPI communication coordinate direction @param pbc_loc Processor boundary condition (PBC) location

The purpose of this subroutine is to populate the buffers of the grid variables, which are constituted of the cell- boundary locations and cell-width distributions, based on the boundary conditions.

The purpose of this procedure is to populate the buffers of the conservative variables, depending on the selected boundary conditions. @param v_vf Scalar field for which buffers are populated

The purpose of this procedure is to infinitely relax the pressures from the internal-energy equations to a unique pressure, from which the corresponding volume fraction of each phase are recomputed. For conservation purpose, this pressure is finally corrected using the mixture-total-energy equation. @param q_cons_vf Cell-average conservative variables

Computes the quadrature for polydisperse bubble populations @param func is the bubble dynamic variables for each bin @param mom is the computed moment

The purpose of this procedure is to first verify that an input file has been made available by the user. Provided that this is so, the input file is then read in.

Computes the Simpson weights for quadrature

This subroutine saves the temporary q_prim_vf vector into the q_prim_ts vector that is then used in p_main @param t_step current time-step

Computes transfer coefficient for non-polydisperse bubble modeling (Preston 2007) @param omega Frequency @param peclet Peclet number @param Re_trans Real part of transfer coefficient @param Im_trans Imaginary part of transfer coefficient