Advection

Advection methods for level sets. More...

Namespaces
module	mod_lsm_advect
	Contains a wrapper for the various advection schemes for the Level Set representation.
module	mod_lsm_advect_eulerian
	Contains a wrapper for the various advection schemes for the Level Set standard representation.
module	mod_lsm_advect_eulerian_euler
	The Level Set advection module.
module	mod_lsm_compute_ugradphi
	Computation of the advection term.
module	mod_lsm_compute_ugradphi_conservative
	Computation of the advection with a conservative approach.

Functions
subroutine	mod_lsm_advect::levelset_advect (ls, dt, velocity_nm1, velocity_n, velocity_np1, dt_nm1, dt_n)
	Solve the advection with various advection schemes for the Level Set representation.
subroutine	mod_lsm_advect_eulerian::levelset_advect_eulerian (ls, dt, velocity_nm1, velocity_n, velocity_np1, dt_nm1, dt_n)
	Solve the advection with various advection schemes for the Level Set standard (Eulerian) representation.
subroutine	mod_lsm_advect_eulerian_euler::levelset_advect_eulerian_weno5_euler (levelset, velocity_nm1, velocity_n, velocity_np1, local_time, dt_nm1, dt_n, time_step)
	Advect the level set with a WENO5-Euler scheme.
subroutine	mod_lsm_advect_eulerian_euler::levelset_advect_eulerian_weno5_rk2_tvd (levelset, velocity_nm1, velocity_n, velocity_np1, local_time, dt_nm1, dt_n, time_step)
	Advect the level set with a WENO5-RK2-TVD (with given velocity at next time step) scheme.
subroutine	mod_lsm_advect_eulerian_euler::levelset_advect_eulerian_weno5_nssp32 (levelset, velocity_nm1, velocity_n, velocity_np1, local_time, dt_nm1, dt_n, time_step)
	Advect the level set with a WENO5-NSSP32 scheme.
subroutine	mod_lsm_advect_eulerian_euler::levelset_advect_eulerian_weno5_nssp53 (levelset, velocity_nm1, velocity_n, velocity_np1, local_time, dt_nm1, dt_n, time_step)
	Advect the level set with a WENO5-NSSP53 scheme.
double precision function	mod_lsm_check_cfl::levelset_compute_time_step_cfl_advection (my_levelset, velocity, velocity_np1, cfl_coef)
	Compute the time step according to the CFL restriction.
subroutine	mod_lsm_compute_ugradphi::compute_ugradphi_weno5 (phi, velocity, time_step, ugradphi, band)
	Compute the \( \vec{u} \cdot \nabla \phi \) term with a WENO5 scheme.
subroutine	mod_lsm_compute_ugradphi_conservative::compute_ugradphi_weno5_conservative (phi, velocity, time_step, ugradphi, band, flux_type)
	Compute the \( \nabla \cdot ( \vec{u} \phi ) \) conservative term with a WENO5 scheme.

Detailed Description

This module provides several methods for solving the advection equation for level sets.

Function Documentation

compute_ugradphi_weno5()

subroutine mod_lsm_compute_ugradphi::compute_ugradphi_weno5	(	double precision, dimension(nx,ny,nz), intent(in)	phi,
		type(t_face_field), intent(in)	velocity,
		double precision, intent(in)	time_step,
		double precision, dimension(nx,ny,nz), intent(inout)	ugradphi,
		integer, dimension(nx,ny,nz), intent(in)	band )

Parameters

[in]	phi	the level set
[in]	velocity	the velocity field on faces
[in,out]	ugradphi	the resulting field
[in]	band	the band (integers)
[in]	time_step	the time step (unused, but might be used for high-order fluxes)

Note

A high-order (WENO5) scheme is used inside the close band (band(i,j,k)={1,2}). A first order scheme is used outside (band/={1,2}).

levelset_advect()

subroutine mod_lsm_advect::levelset_advect	(	class(t_levelset), intent(inout)	ls,
		double precision, intent(in)	dt,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n )

Todo

MCO: plug back refined grid (bnd cond not ready for it)

Precondition

The Dirichlet (equivalent) boundary values are stored in is-1 and ie+1 (identicaly for the other dimensions)

Note

The temporal method is stored in the lsparameters type

levelset_advect_eulerian()

subroutine mod_lsm_advect_eulerian::levelset_advect_eulerian	(	class(t_levelset), intent(inout)	ls,
		double precision, intent(in)	dt,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n )

Precondition

The boundary conditions are stored in the corresponding attribute

Parameters

[in,out]	ls	the levelset to advect
[in]	dt	the time step to advance to, usualy \(dt = t^{n+1} - t^n\)
[in]	velocity_nm1	the velocity at time \(t^{n-1}\)
[in]	velocity_n	the velocity at time \(t^{n}\)
[in]	velocity_np1	the velocity at time \(t^{n+1}\)
[in]	dt_nm1	the time step between \(dt_nm1 = t^{n} - t^{n-1}\)
[in]	dt_n	the time step between \(dt_n = t^{n+1} - t^{n}\)

levelset_advect_eulerian_weno5_euler()

subroutine mod_lsm_advect_eulerian_euler::levelset_advect_eulerian_weno5_euler	(	class(t_levelset)	levelset,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, intent(in)	local_time,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		double precision, intent(in)	time_step )

Advect the level set from time \( t^n \) to \(t = t^l + \delta t \)

Parameters

[in,out]	levelset	the level set
[in]	velocity_nm1	the velocity at time \(t=t_n - \delta t^{n-1}\)
[in]	velocity_n	the velocity at time \(t=t_n\)
[in]	velocity_np1	the velocity at time \(t=t^{n+1}=t^{n} + \delta t^{n}\)
[in]	local_time	the local time \(t^{l}\) relative to \(t^n\)
[in]	dt_nm1	the time step between \(t^{n}\) and \(t^{n-1}\)
[in]	dt_n	the time step between \(t^{n+1}\) and \(t^{n}\)
[in]	time_step	the time step \(\delta t\) over which to integrate the levelset: \(t^{l} + \delta t \)

levelset_advect_eulerian_weno5_nssp32()

subroutine mod_lsm_advect_eulerian_euler::levelset_advect_eulerian_weno5_nssp32	(	class(t_levelset)	levelset,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, intent(in)	local_time,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		double precision, intent(in)	time_step )

Advect the level set from time \( t^n \) to \(t = t^l + \delta t \)

Parameters

[in,out]	levelset	the level set
[in]	velocity_nm1	the velocity at time \(t=t_n - \delta t^{n-1}\)
[in]	velocity_n	the velocity at time \(t=t_n\)
[in]	velocity_np1	the velocity at time \(t=t^{n+1}=t^{n} + \delta t^{n}\)
[in]	local_time	the local time \(t^{l}\) relative to \(t^n\)
[in]	dt_nm1	the time step between \(t^{n}\) and \(t^{n-1}\)
[in]	dt_n	the time step between \(t^{n+1}\) and \(t^{n}\)
[in]	time_step	the time step \(\delta t\) over which to integrate the levelset: \(t^{l} + \delta t \)

Todo

MCO: the boundary conditions are at time \(t^n\), even during the RK integration!

levelset_advect_eulerian_weno5_nssp53()

subroutine mod_lsm_advect_eulerian_euler::levelset_advect_eulerian_weno5_nssp53	(	class(t_levelset)	levelset,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, intent(in)	local_time,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		double precision, intent(in)	time_step )

Advect the level set from time \( t^n \) to \(t = t^l + \delta t \)

Parameters

[in,out]	levelset	the level set
[in]	velocity_nm1	the velocity at time \(t=t_n - \delta t^{n-1}\)
[in]	velocity_n	the velocity at time \(t=t_n\)
[in]	velocity_np1	the velocity at time \(t=t^{n+1}=t^{n} + \delta t^{n}\)
[in]	local_time	the local time \(t^{l}\) relative to \(t^n\)
[in]	dt_nm1	the time step between \(t^{n}\) and \(t^{n-1}\)
[in]	dt_n	the time step between \(t^{n+1}\) and \(t^{n}\)
[in]	time_step	the time step \(\delta t\) over which to integrate the levelset: \(t^{l} + \delta t \)

levelset_advect_eulerian_weno5_rk2_tvd()

subroutine mod_lsm_advect_eulerian_euler::levelset_advect_eulerian_weno5_rk2_tvd	(	class(t_levelset)	levelset,
		type(t_face_field), intent(in)	velocity_nm1,
		type(t_face_field), intent(in)	velocity_n,
		type(t_face_field), intent(in)	velocity_np1,
		double precision, intent(in)	local_time,
		double precision, intent(in)	dt_nm1,
		double precision, intent(in)	dt_n,
		double precision, intent(in)	time_step )

Advect the level set from time \( t^n \) to \(t = t^l + \delta t \)

Parameters

[in,out]	levelset	the level set
[in]	velocity_nm1	the velocity at time \(t=t_n - \delta t^{n-1}\)
[in]	velocity_n	the velocity at time \(t=t_n\)
[in]	velocity_np1	the velocity at time \(t=t^{n+1}=t^{n} + \delta t^{n}\)
[in]	local_time	the local time \(t^{l}\) relative to \(t^n\)
[in]	dt_nm1	the time step between \(t^{n}\) and \(t^{n-1}\)
[in]	dt_n	the time step between \(t^{n+1}\) and \(t^{n}\)
[in]	time_step	the time step \(\delta t\) over which to integrate the levelset: \(t^{l} + \delta t \)