The time integration of the semi discrete form is performed with Runge Kutta methods.
At the momento only Cartesian 1D uniform mesh available, using FVMesh(N,a,b,boundary) command. Where
N = Number of cells
xinit,xend = start and end coordinates.
bdtype = boundary type (ZERO_FLUX, PERIODIC)
- Problem types: System of Conservation Laws with diffusion term (
CLS1DDiffusionProblem).
(LIMEX1DAlgorithm)
(Flux reconstruction uses Comp WENO5)
For IMEX Scheme available RK methods are: H-CN(2,2,2) H_CN_222, H-DIRK2(2,2,2) H_DIRK2_222, H-LDIRK2(2,2,2) H_LDIRK2_222, H-LDIRK3(2,2,2) H_LDIRK3_222, SSP-LDIRK(3,3,2) SSP_LDIRK_332.
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S. Boscarino, R. Bürger, P. Mulet, G. Russo, L. Villada, Linearly implicit IMEX Runge Kutta methods for a class of degenerate convection diffusion problems, SIAM J. Sci. Comput., 37(2), B305–B331
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S. Boscarino, P.G. LeFloch and G. Russo. High order asymptotic-preserving methods for fully nonlinear relaxation problems. SIAM J. Sci. Comput., 36 (2014), A377–A395.
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S. Boscarino, F. Filbet and G. Russo. High order semi-implicit schemes for time dependent partial differential equations. SIAM J. Sci. Comput. September 2016, Volume 68, Issue 3, pp 975–1001
! Initialize variables
Tend = 0.2_dp ! Final Time
CFL = 0.25_dp
L = 10.0
M = 4
bdtype = PERIODIC
!Run numerical schemes
N = 100 ! Number of nodes
CALL setup_problem(0.0_dp, L, N, M, mesh, uinit, bdtype)
CALL prob%Initialize(mesh, uinit, M, Tend, Flux, JacF, BB)
! Save initial data
name = 'test_1_ini'
ALLOCATE(results(N, M+1), names(M+1))
names = ['x ', 'y1 ','y2 ', 'y3 ', 'y4 ']
results(:,1) = mesh%x
results(:,2:5) = uinit(:,1:4)
CALL save_matrix(results, names, name, 0)
! Compute solution
CALL solve(prob, SSP_LDIRK_332, LIMEX_Alg, CFL)
! Save solution
results(:,2:5) = prob%uu(:,1:4)
name = 'test_1'
CALL save_matrix(results, names, name, 0)** Modules developed for personal use, some of them have not been tested enough !!!**