IMEXSfloW  1.0
templategithubproject
 All Classes Files Functions Variables Pages
Public Member Functions | Public Attributes | List of all members
solver Module Reference

Numerical solver. More...

Public Member Functions

subroutine allocate_solver_variables
 Memory allocation. More...
 
subroutine deallocate_solver_variables
 Memory deallocation. More...
 
subroutine timestep
 Time-step computation. More...
 
subroutine imex_rk_solver
 Runge-Kutta integration. More...
 
subroutine solve_rk_step (Bj, Bprimej, qj, qj_old, a_tilde, a_dirk, a_diag)
 Runge-Kutta single step integration. More...
 
subroutine lnsrch (Bj, Bprimej, qj_rel_NR_old, qj_org, qj_old, scal_f_old, grad_f, desc_dir, coeff_f, qj_rel, scal_f, right_term, stpmax, check)
 Search the descent stepsize. More...
 
subroutine eval_f (Bj, Bprimej, qj, qj_old, a_tilde, a_dirk, a_diag, coeff_f, f_nl, scal_f)
 Evaluate the nonlinear system. More...
 
subroutine eval_jacobian (Bj, Bprimej, qj_rel, qj_org, coeff_f, left_matrix)
 Evaluate the jacobian. More...
 
subroutine eval_explicit_terms (q_expl, expl_terms)
 Evaluate the explicit terms. More...
 
subroutine eval_hyperbolic_terms (q_expl, F_x)
 Semidiscrete finite volume central scheme. More...
 
subroutine eval_flux_kt
 Semidiscrete numerical fluxes. More...
 
subroutine average_kt (aL, aR, wL, wR, w_avg)
 
subroutine eval_flux_gforce
 Numerical fluxes GFORCE. More...
 
subroutine eval_flux_lxf
 Numerical fluxes Lax-Friedrichs. More...
 
subroutine reconstruction_cons
 Linear reconstruction. More...
 
subroutine reconstruction_phys1
 Linear reconstruction. More...
 
subroutine reconstruction_phys2
 Linear reconstruction. More...
 
subroutine eval_speeds
 Characteristic speeds. More...
 
subroutine limit (v, z, limiter, slope_lim)
 Slope limiter. More...
 
real *8 function minmod (a, b)
 
real *8 function maxmod (a, b)
 

Public Attributes

real *8, dimension(:,:),
allocatable 		q
 Conservative variables. More...
 
real *8, dimension(:,:),
allocatable 		q0
 Conservative variables. More...
 
real *8, dimension(:,:),
allocatable 		q_fv
 Solution of the finite-volume semidiscrete cheme. More...
 
real *8, dimension(:,:),
allocatable 		q_interfacel
 Reconstructed value at the left of the interface. More...
 
real *8, dimension(:,:),
allocatable 		q_interfacer
 Reconstructed value at the right of the interface. More...
 
real *8, dimension(:,:),
allocatable 		a_interfacel
 Local speeds at the left of the interface. More...
 
real *8, dimension(:,:),
allocatable 		a_interfacer
 Local speeds at the right of the interface. More...
 
real *8, dimension(:,:),
allocatable 		h_interface
 Semidiscrete numerical interface fluxes. More...
 
real *8, dimension(:,:),
allocatable 		qp
 Physical variables ( $\alpha_1, p_1, p_2, \rho u, w, T$) More...
 
real *8 dt
 Time step. More...
 
logical, dimension(:,:),
allocatable 		mask22
 
logical, dimension(:,:),
allocatable 		mask21
 
logical, dimension(:,:),
allocatable 		mask11
 
logical, dimension(:,:),
allocatable 		mask12
 
real *8, dimension(:,:),
allocatable 		a_tilde_ij
 Butcher Tableau for the explicit part of the Runge-Kutta scheme. More...
 
real *8, dimension(:,:),
allocatable 		a_dirk_ij
 Butcher Tableau for the implicit part of the Runge-Kutta scheme. More...
 
real *8, dimension(:), allocatable omega_tilde
 Coefficients for the explicit part of the Runge-Kutta scheme. More...
 
real *8, dimension(:), allocatable omega
 Coefficients for the implicit part of the Runge-Kutta scheme. More...
 
real *8, dimension(:), allocatable a_tilde
 Explicit coefficients for the hyperbolic part for a single step of the R-K scheme. More...
 
real *8, dimension(:), allocatable a_dirk
 Explicit coefficients for the non-hyperbolic part for a single step of the R-K scheme. More...
 
real *8 a_diag
 Implicit coefficient for the non-hyperbolic part for a single step of the R-K scheme. More...
 
real *8, dimension(:,:,:),
allocatable 		q_rk
 Intermediate solutions of the Runge-Kutta scheme. More...
 
real *8, dimension(:,:,:),
allocatable 		f_x
 Intermediate hyperbolic terms of the Runge-Kutta scheme. More...
 
real *8, dimension(:,:,:),
allocatable 		nh
 Intermediate non-hyperbolic terms of the Runge-Kutta scheme. More...
 
real *8, dimension(:,:,:),
allocatable 		expl_terms
 Intermediate explicit terms of the Runge-Kutta scheme. More...
 
real *8, dimension(:,:),
allocatable 		fxj
 Local Intermediate hyperbolic terms of the Runge-Kutta scheme. More...
 
real *8, dimension(:,:),
allocatable 		nhj
 Local Intermediate non-hyperbolic terms of the Runge-Kutta scheme. More...
 
real *8, dimension(:,:),
allocatable 		expl_terms_j
 Local Intermediate explicit terms of the Runge-Kutta scheme. More...
 
logical normalize_q
 
logical normalize_f
 
logical opt_search_nl
 
real *8, dimension(:,:),
allocatable 		residual_term
 

Detailed Description

Numerical solver.

This module contains the variables and the subroutines for the numerical solution of the equations.

Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 12 of file solver.f90.

Member Function/Subroutine Documentation

subroutine solver::allocate_solver_variables ( )

Memory allocation.

This subroutine allocate the memory for the variables of the solver module.

Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 112 of file solver.f90.

Here is the caller graph for this function:

subroutine solver::average_kt ( real*8, dimension(:), intent(in)  aL,
real*8, dimension(:), intent(in)  aR,
real*8, dimension(:), intent(in)  wL,
real*8, dimension(:), intent(in)  wR,
real*8, dimension(:), intent(out)  w_avg 
)

Definition at line 1499 of file solver.f90.

Here is the caller graph for this function:

subroutine solver::deallocate_solver_variables ( )

Memory deallocation.

This subroutine de-allocate the memory for the variables of the solver module.

Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 270 of file solver.f90.

Here is the caller graph for this function:

subroutine solver::eval_explicit_terms ( real*8, dimension(n_vars,comp_cells), intent(in)  q_expl,
real*8, dimension(n_eqns,comp_cells), intent(out)  expl_terms 
)

Evaluate the explicit terms.

This subroutine evaluate the explicit terms (non-fluxes) of the non-linear system with respect to the conservative variables.

Parameters
[in]q_explconservative variables
[out]expl_termsexplicit terms
Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 1265 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::eval_f ( real*8, intent(in)  Bj,
real*8, intent(in)  Bprimej,
real*8, dimension(n_vars), intent(in)  qj,
real*8, dimension(n_vars), intent(in)  qj_old,
real*8, dimension(n_rk), intent(in)  a_tilde,
real*8, dimension(n_rk), intent(in)  a_dirk,
real*8, intent(in)  a_diag,
real*8, dimension(n_eqns), intent(in)  coeff_f,
real*8, dimension(n_eqns), intent(out)  f_nl,
real*8, intent(out)  scal_f 
)

Evaluate the nonlinear system.

This subroutine evaluate the value of the nonlinear system in the state defined by the variables qj.

Parameters
[in]Bjbatimetry at the cell center
[in]Bprimejbatimetry slope at the cell center
[in]qjconservative variables
[in]qj_oldconservative variables at the old time step
[in]a_tildeexplicit coefficients for the hyperbolic terms
[in]a_dirkexplicit coefficients for the non-hyperbolic terms
[in]a_diagimplicit coefficient for the non-hyperbolic term
[in]coeff_fcoefficient to rescale the nonlinear functions
[out]f_nlvalues of the nonlinear functions
[out]scal_fvalue of the scalar function f=0.5*<F,F>
Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 1145 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::eval_flux_gforce ( )

Numerical fluxes GFORCE.

Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 1536 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::eval_flux_kt ( )

Semidiscrete numerical fluxes.

This subroutine evaluates the numerical fluxes H at the cells interfaces according to Kurganov et al. 2001.

Author
Mattia de' Michieli Vitturi
Date
16/08/2011

Definition at line 1428 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::eval_flux_lxf ( )

Numerical fluxes Lax-Friedrichs.

Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 1605 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::eval_hyperbolic_terms ( real*8, dimension(n_vars,comp_cells), intent(in)  q_expl,
real*8, dimension(n_eqns,comp_cells), intent(out)  F_x 
)

Semidiscrete finite volume central scheme.

This subroutine solve the hyperbolic part of the system of the eqns, with a modified finite volume scheme from Kurganov et al. 2001, coupled with a MUSCL-Hancock scheme (Van Leer, 1984) applied to a set of physical variables derived from the conservative vriables.

Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 1303 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::eval_jacobian ( real*8, intent(in)  Bj,
real*8, intent(in)  Bprimej,
real*8, dimension(n_vars), intent(in)  qj_rel,
real*8, dimension(n_vars), intent(in)  qj_org,
real*8, dimension(n_eqns), intent(in)  coeff_f,
real*8, dimension(n_eqns,n_vars), intent(out)  left_matrix 
)

Evaluate the jacobian.

This subroutine evaluate the jacobian of the non-linear system with respect to the conservative variables.

Parameters
[in]Bjbatimetry at the cell center
[in]Bprimejbatimetry slope at the cell center
[in]qj_relrelative variation (qj=qj_rel*qj_org)
[in]qj_orgconservative variables at the old time step
[in]coeff_fcoefficient to rescale the nonlinear functions
[out]left_matrixmatrix from the linearization of the system
Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 1197 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::eval_speeds ( )

Characteristic speeds.

This subroutine evaluates the largest characteristic speed at the cells interfaces from the reconstructed states.

Author
Mattia de' Michieli Vitturi
Date
16/08/2011

Definition at line 2553 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::imex_rk_solver ( )

Runge-Kutta integration.

This subroutine integrate the hyperbolic conservation law with non-hyperbolic terms using an implicit-explicit runge-kutta scheme. The fluxes are integrated explicitely while the non-hyperbolic terms are integrated implicitely.

Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 414 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::limit ( real*8, dimension(3), intent(in)  v,
real*8, dimension(3), intent(in)  z,
integer, intent(in)  limiter,
real*8, intent(out)  slope_lim 
)

Slope limiter.

This subroutine limits the slope of the linear reconstruction of the physical variables, accordingly to the parameter "solve_limiter":

  • 'none' => no limiter (constant value);
  • 'minmod' => minmod slope;
  • 'superbee' => superbee limiter (Roe, 1985);
  • 'van_leer' => monotonized central-difference limiter (van Leer, 1977)
Parameters
[in]v3-point stencil value array
[in]z3-point stencil location array
[out]slope_limlimited slope
Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 2603 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::lnsrch ( real*8, intent(in)  Bj,
real*8, intent(in)  Bprimej,
real*8, dimension(:), intent(in)  qj_rel_NR_old,
real*8, dimension(:), intent(in)  qj_org,
real*8, dimension(:), intent(in)  qj_old,
real*8, intent(in)  scal_f_old,
real*8, dimension(:), intent(in)  grad_f,
real*8, dimension(:), intent(inout)  desc_dir,
real*8, dimension(:), intent(in)  coeff_f,
real*8, dimension(:), intent(out)  qj_rel,
real*8, intent(out)  scal_f,
real*8, dimension(n_eqns), intent(out)  right_term,
real*8, intent(in)  stpmax,
logical, intent(out)  check 
)

Search the descent stepsize.

This subroutine search for the lenght of the descent step in order to have a decrease in the nonlinear function.

Parameters
[in]Bjbatimetry at the cell center
[in]Bprimejbatimetry slope at the cell center
[in]qj_rel_NR_old
[in]qj_org
[in]qj_old
[in]scal_f_old
[in]grad_f
[in,out]desc_dir
[in]coeff_f
[out]qj_rel
[out]scal_f
[out]right_term
[in]stpmax
[out]check
Date
07/10/2016
Author
Mattia de' Michieli Vitturi
Parameters
[in]qj_rel_nr_oldInitial point
[in]qj_orgInitial point
[in]qj_oldInitial point
[in]grad_fGradient at xold
[in]scal_f_oldValue of the function at xold
[in,out]desc_dirDescent direction (usually Newton direction)
[in]coeff_fCoefficients to rescale the nonlinear function
[out]qj_relUpdated solution
[out]scal_fValue of the scalar function at x
[out]right_termValue of the scalar function at x
[out]checkOutput quantity check is false on a normal exit

Definition at line 924 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

real*8 function solver::maxmod ( real*8  a,
real*8  b 
)

Definition at line 2675 of file solver.f90.

Here is the caller graph for this function:

real*8 function solver::minmod ( real*8  a,
real*8  b 
)

Definition at line 2654 of file solver.f90.

Here is the caller graph for this function:

subroutine solver::reconstruction_cons ( )

Linear reconstruction.

In this subroutine a linear reconstruction with slope limiters is applied to a set of conservative variables describing the state of the system.

Author
Mattia de' Michieli Vitturi
Date
17/11/2016

Definition at line 1664 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::reconstruction_phys1 ( )

Linear reconstruction.

In this subroutine a linear reconstruction with slope limiters is applied to a set of physical variables (h+B,u) describing the state of the system.

Author
Mattia de' Michieli Vitturi
Date
17/11/2016

Definition at line 1950 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::reconstruction_phys2 ( )

Linear reconstruction.

In this subroutine a linear reconstruction with slope limiters is applied to a set of physical variables (h,u) describing the state of the system.

Author
Mattia de' Michieli Vitturi
Date
17/11/2016

Definition at line 2252 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::solve_rk_step ( real*8, intent(in)  Bj,
real*8, intent(in)  Bprimej,
real*8, dimension(n_vars), intent(inout)  qj,
real*8, dimension(n_vars), intent(in)  qj_old,
real*8, dimension(n_rk), intent(in)  a_tilde,
real*8, dimension(n_rk), intent(in)  a_dirk,
real*8, intent(in)  a_diag 
)

Runge-Kutta single step integration.

This subroutine find the solution of the non-linear system given the a step of the implicit-explicit Runge-Kutta scheme for a cell:
$ Q^{(i)} = Q^n - dt \sum_{j=1}^{i-1}\tilde{a}_{j}\partial_x F(Q^{(j)}) + dt \sum_{j=1}^{i-1} a_j NH(Q^{(j)}) + dt a_{diag} NH(Q^{(i)}) $

Parameters
[in]Bjbatimetry at the cell center
[in]Bprimejbatimetry slope at the cell center
[in,out]qjconservative variables
[in]qj_oldconservative variables at the old time step
[in]a_tildeexplicit coefficents for the fluxes
[in]a_dirkexplicit coefficient for the non-hyperbolic terms
[in]a_diagimplicit coefficient for the non-hyperbolic terms
Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 605 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine solver::timestep ( )

Time-step computation.

This subroutine evaluate the maximum time step according to the CFL condition. The local speed are evaluated with the characteristic polynomial of the Jacobian of the fluxes.

Date
07/10/2016
Author
Mattia de' Michieli Vitturi

Definition at line 322 of file solver.f90.

Here is the call graph for this function:

Here is the caller graph for this function:

Member Data Documentation

real*8 solver::a_diag

Implicit coefficient for the non-hyperbolic part for a single step of the R-K scheme.

Definition at line 72 of file solver.f90.

real*8, dimension(:), allocatable solver::a_dirk

Explicit coefficients for the non-hyperbolic part for a single step of the R-K scheme.

Definition at line 70 of file solver.f90.

real*8, dimension(:,:), allocatable solver::a_dirk_ij

Butcher Tableau for the implicit part of the Runge-Kutta scheme.

Definition at line 60 of file solver.f90.

real*8, dimension(:,:), allocatable solver::a_interfacel

Local speeds at the left of the interface.

Definition at line 43 of file solver.f90.

real*8, dimension(:,:), allocatable solver::a_interfacer

Local speeds at the right of the interface.

Definition at line 45 of file solver.f90.

real*8, dimension(:), allocatable solver::a_tilde

Explicit coefficients for the hyperbolic part for a single step of the R-K scheme.

Definition at line 68 of file solver.f90.

real*8, dimension(:,:), allocatable solver::a_tilde_ij

Butcher Tableau for the explicit part of the Runge-Kutta scheme.

Definition at line 58 of file solver.f90.

real*8 solver::dt

Time step.

Definition at line 53 of file solver.f90.

real*8, dimension(:,:,:), allocatable solver::expl_terms

Intermediate explicit terms of the Runge-Kutta scheme.

Definition at line 82 of file solver.f90.

real*8, dimension(:,:), allocatable solver::expl_terms_j

Local Intermediate explicit terms of the Runge-Kutta scheme.

Definition at line 89 of file solver.f90.

real*8, dimension(:,:,:), allocatable solver::f_x

Intermediate hyperbolic terms of the Runge-Kutta scheme.

Definition at line 77 of file solver.f90.

real*8, dimension(:,:), allocatable solver::fxj

Local Intermediate hyperbolic terms of the Runge-Kutta scheme.

Definition at line 85 of file solver.f90.

real*8, dimension(:,:), allocatable solver::h_interface

Semidiscrete numerical interface fluxes.

Definition at line 47 of file solver.f90.

logical, dimension(:,:), allocatable solver::mask11

Definition at line 55 of file solver.f90.

logical, dimension(:,:), allocatable solver::mask12

Definition at line 55 of file solver.f90.

logical, dimension(:,:), allocatable solver::mask21

Definition at line 55 of file solver.f90.

logical, dimension(:,:), allocatable solver::mask22

Definition at line 55 of file solver.f90.

real*8, dimension(:,:,:), allocatable solver::nh

Intermediate non-hyperbolic terms of the Runge-Kutta scheme.

Definition at line 79 of file solver.f90.

real*8, dimension(:,:), allocatable solver::nhj

Local Intermediate non-hyperbolic terms of the Runge-Kutta scheme.

Definition at line 87 of file solver.f90.

logical solver::normalize_f

Definition at line 92 of file solver.f90.

logical solver::normalize_q

Definition at line 91 of file solver.f90.

real*8, dimension(:), allocatable solver::omega

Coefficients for the implicit part of the Runge-Kutta scheme.

Definition at line 65 of file solver.f90.

real*8, dimension(:), allocatable solver::omega_tilde

Coefficients for the explicit part of the Runge-Kutta scheme.

Definition at line 63 of file solver.f90.

logical solver::opt_search_nl

Definition at line 93 of file solver.f90.

real*8, dimension(:,:), allocatable solver::q

Conservative variables.

Definition at line 33 of file solver.f90.

real*8, dimension(:,:), allocatable solver::q0

Conservative variables.

Definition at line 35 of file solver.f90.

real*8, dimension(:,:), allocatable solver::q_fv

Solution of the finite-volume semidiscrete cheme.

Definition at line 37 of file solver.f90.

real*8, dimension(:,:), allocatable solver::q_interfacel

Reconstructed value at the left of the interface.

Definition at line 39 of file solver.f90.

real*8, dimension(:,:), allocatable solver::q_interfacer

Reconstructed value at the right of the interface.

Definition at line 41 of file solver.f90.

real*8, dimension(:,:,:), allocatable solver::q_rk

Intermediate solutions of the Runge-Kutta scheme.

Definition at line 75 of file solver.f90.

real*8, dimension(:,:), allocatable solver::qp

Physical variables ( $\alpha_1, p_1, p_2, \rho u, w, T$)

Definition at line 49 of file solver.f90.

real*8, dimension(:,:), allocatable solver::residual_term

Definition at line 95 of file solver.f90.

The documentation for this module was generated from the following file:
Generated on Tue Nov 22 2016 16:23:07 for IMEXSfloW by   doxygen 1.8.7