EVOLUTION: Implement estimation of the initial time step.
Signed-off-by: Grzegorz Kowal <grzegorz@amuncode.org>
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@ -70,6 +70,7 @@ module evolution
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logical , save :: error_control = .false.
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character(len=255), save :: name_int = ""
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character(len=255), save :: name_norm = ""
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integer , save :: order = 2
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integer , save :: stages = 2
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integer , save :: registers = 1
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real(kind=8) , save :: cfl = 5.0d-01
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@ -118,7 +119,7 @@ module evolution
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! declare public subroutines
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!
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public :: initialize_evolution, finalize_evolution, print_evolution
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public :: advance, new_time_step
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public :: initialize_time_step, advance, new_time_step
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! declare public variables
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!
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@ -222,12 +223,14 @@ module evolution
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case ("euler", "EULER", "rk1", "RK1")
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evolve => evolve_euler
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order = 1
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registers = 1
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name_int = "1st order Euler"
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case ("rk2", "RK2")
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evolve => evolve_rk2
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order = 2
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registers = 2
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name_int = "2nd order Runge-Kutta"
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@ -235,6 +238,7 @@ module evolution
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error_control = .true.
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evolve => evolve_ssprk2_m
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order = 2
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registers = 3
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stages = max(2, min(9, stages))
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cfl = (stages - 1) * cfl
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@ -243,12 +247,14 @@ module evolution
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case ("rk3", "RK3")
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evolve => evolve_rk3
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order = 3
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registers = 2
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name_int = "3rd order Runge-Kutta"
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case ("rk3.4", "RK3.4", "ssprk(4,3)", "SSPRK(4,3)")
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evolve => evolve_ssprk34
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order = 3
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registers = 2
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cfl = 2.0d+00 * cfl
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name_int = "3rd order SSPRK(4,3)"
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@ -256,6 +262,7 @@ module evolution
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case ("rk3.5", "RK3.5", "ssprk(5,3)", "SSPRK(5,3)")
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evolve => evolve_ssprk35
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order = 3
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registers = 2
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cfl = 2.65062919143939d+00 * cfl
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name_int = "3rd order SSPRK(5,3)"
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@ -264,6 +271,7 @@ module evolution
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error_control = .true.
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evolve => evolve_ssp324
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order = 3
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registers = 3
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stages = 4
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cfl = 2.0d+00 * cfl
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@ -281,6 +289,7 @@ module evolution
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error_control = .true.
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evolve => evolve_ssprk32m
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order = 3
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registers = 4
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n = 2
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do while(n**2 <= stages)
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@ -312,6 +321,7 @@ module evolution
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case ("rk4.10", "RK4.10", "ssprk(10,4)", "SSPRK(10,4)")
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evolve => evolve_ssprk4_10
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order = 4
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registers = 2
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cfl = 6.0d+00 * cfl
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name_int = "Optimal 4th order SSPRK(10,4)"
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@ -591,6 +601,197 @@ module evolution
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!
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!===============================================================================
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!
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! subroutine INITIALIZE_TIME_STEP:
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! -------------------------------
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!
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! Subroutine estimates the initial time step.
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!
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! References:
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!
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! [1] Courant, R., Friedrichs, K., Lewy, H.,
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! "Über die partiellen Differenzengleichungen der mathematischen Physik",
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! Mathematische Annalen, 1928, volume 100, pages 32–74,
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! DOI: 10.1007/BF01448839
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! [2] Hairer, E., Nørsett, S. P., Wanner, G.,
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! "Solving Ordinary Differential Equations I: Nonstiff Problems",
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! Springer-Verlag Berlin Heidelberg, 1993,
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! ISBN: 978-3-540-56670-0, DOI: 10.1007/978-3-540-78862-1
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!
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!===============================================================================
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!
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subroutine initialize_time_step()
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use blocks , only : block_data, list_data, get_nleafs
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use coordinates, only : nc => ncells, nb, ne, adx, ady
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#if NDIMS == 3
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use coordinates, only : adz
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#endif /* NDIMS == 3 */
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use equations , only : nf, maxspeed, cmax, cmax2
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#ifdef MPI
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use mpitools , only : reduce_maximum, reduce_sum
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#endif /* MPI */
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use sources , only : viscosity, resistivity, update_sources
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implicit none
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type(block_data), pointer :: pdata
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integer :: mlev
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real(kind=8) :: dx_min, fnorm, h0, h1
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real(kind=8), dimension(3) :: d
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#if NDIMS == 3
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real(kind=8), dimension(nf,nc,nc,nc) :: sc, df
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#else /* NDIMS == 3 */
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real(kind=8), dimension(nf,nc,nc, 1) :: sc, df
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#endif /* NDIMS == 3 */
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real(kind=8), parameter :: eps = tiny(cmax)
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!
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!-------------------------------------------------------------------------------
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!
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#ifdef PROFILE
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call start_timer(imi)
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#endif /* PROFILE */
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cmax = eps
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mlev = 1
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pdata => list_data
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do while (associated(pdata))
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mlev = max(mlev, pdata%meta%level)
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cmax = max(cmax, maxspeed(pdata%q(:,:,:,:)))
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pdata => pdata%next
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end do
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#ifdef MPI
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call reduce_maximum(cmax)
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call reduce_maximum(mlev)
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#endif /* MPI */
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cmax2 = cmax * cmax
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#if NDIMS == 2
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dx_min = min(adx(mlev), ady(mlev))
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#endif /* NDIMS == 2 */
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#if NDIMS == 3
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dx_min = min(adx(mlev), ady(mlev), adz(mlev))
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#endif /* NDIMS == 3 */
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! determine the time step due to the stability
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!
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dth = dx_min / max(cmax &
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+ 2.0d+00 * max(viscosity, resistivity) / dx_min, eps)
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dt = cfl * dth
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! determine the time step due to the error
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!
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if (error_control) then
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fnorm = 1.0d+00 / (get_nleafs() * nc**NDIMS)
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d(:) = 0.0d+00
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pdata => list_data
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do while (associated(pdata))
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call update_increment(pdata)
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call update_sources(pdata, 0.0d+00, 0.0d+00, pdata%du(:,:,:,:))
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#if NDIMS == 3
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sc(:,:,:,:) = atol + rtol * abs(pdata%uu(:,nb:ne,nb:ne,nb:ne,1))
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d(1) = d(1) + sum((pdata%uu(:,nb:ne,nb:ne,nb:ne,1) / sc(:,:,:,:))**2)
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d(2) = d(2) + sum((pdata%du(:,nb:ne,nb:ne,nb:ne) / sc(:,:,:,:))**2)
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#else /* NDIMS == 3 */
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sc(:,:,:,:) = atol + rtol * abs(pdata%uu(:,nb:ne,nb:ne, : ,1))
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d(1) = d(1) + sum((pdata%uu(:,nb:ne,nb:ne, : ,1) / sc(:,:,:,:))**2)
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d(2) = d(2) + sum((pdata%du(:,nb:ne,nb:ne, : ) / sc(:,:,:,:))**2)
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#endif /* NDIMS == 3 */
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pdata => pdata%next
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end do
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#ifdef MPI
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call reduce_sum(d(1:2))
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#endif /* MPI */
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d(1:2) = sqrt(fnorm * d(1:2))
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if (minval(d(1:2)) >= 1.0d-05) then
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h0 = 1.0d-02 * d(1) / d(2)
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else
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h0 = 1.0d-06
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end if
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pdata => list_data
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do while (associated(pdata))
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pdata%uu(:,:,:,:,2) = pdata%uu(:,:,:,:,1) + h0 * pdata%du(:,:,:,:)
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pdata%u => pdata%uu(:,:,:,:,2)
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pdata => pdata%next
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end do
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call update_variables(time + h0, h0)
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pdata => list_data
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do while (associated(pdata))
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#if NDIMS == 3
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df(:,:,:,:) = pdata%du(:,nb:ne,nb:ne,nb:ne)
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sc(:,:,:,:) = atol + rtol * abs(pdata%uu(:,nb:ne,nb:ne,nb:ne,1))
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#else /* NDIMS == 3 */
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df(:,:,:,:) = pdata%du(:,nb:ne,nb:ne, : )
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sc(:,:,:,:) = atol + rtol * abs(pdata%uu(:,nb:ne,nb:ne, : ,1))
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#endif /* NDIMS == 3 */
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call update_increment(pdata)
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call update_sources(pdata, time + h0, 0.0d+00, pdata%du(:,:,:,:))
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#if NDIMS == 3
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df(:,:,:,:) = df(:,:,:,:) - pdata%du(:,nb:ne,nb:ne,nb:ne)
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#else /* NDIMS == 3 */
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df(:,:,:,:) = df(:,:,:,:) - pdata%du(:,nb:ne,nb:ne, : )
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#endif /* NDIMS == 3 */
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d(3) = d(3) + sum((df(:,:,:,:) / sc(:,:,:,:))**2)
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pdata%u => pdata%uu(:,:,:,:,1)
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pdata => pdata%next
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end do
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#ifdef MPI
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call reduce_sum(d(3:3))
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#endif /* MPI */
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d(3) = sqrt(fnorm * d(3)) / h0
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if (max(d(2), d(3)) > 1.0d-15) then
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h1 = (1.0d-02 / max(d(2), d(3)))**(1.0d+00 / (order + 1))
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else
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h1 = max(1.0d-06, 1.0d-03 * h0)
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end if
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dte = min(1.0d+02 * h0, h1)
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dt = min(dt, dte)
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end if
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#ifdef PROFILE
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call stop_timer(imi)
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#endif /* PROFILE */
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!-------------------------------------------------------------------------------
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!
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end subroutine initialize_time_step
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!
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!===============================================================================
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!
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! subroutine NEW_TIME_STEP:
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! ------------------------
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!
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