sll_m_advection_2d_tri_mesh Module Reference

Description

advection on triangular mesh.

Derived types and interfaces
type	sll_t_advection_tri_mesh
	2d advection on triangular mesh More...

Functions/Subroutines
type(sll_t_advection_tri_mesh) function, pointer, public	sll_f_new_advection_2d_tri_mesh (mesh)
	allocates the memory space for a new 2D advection on triangular mesh on the heap, initializes it with the given triangular mesh and returns a pointer to the object. More...
subroutine	compute_derivatives (f_val, f_der, f_der2, degree, epsilon)
	Computes degrees of freedom on one point. More...
subroutine	compute_coordinates_dof (x1_adv, x2_adv, x1_coo, x2_coo, degree, epsilon, x1_dof, x2_dof)
	computes the coordinates of the poisition of the degrees of freedom (dof) More...
real(kind=f64) function	eval_at_lambda (lam, func_loc, der_loc, der2_loc)
	evaluation at barycentric points of one cell More...
subroutine	interpolation_mitchell ()
subroutine, public	sll_s_advection_2d (adv, f_in, ex, ey, dt)
	Compute characterisitic origin in triangular mesh. More...

Function/Subroutine Documentation

compute_coordinates_dof()

subroutine sll_m_advection_2d_tri_mesh::compute_coordinates_dof ( real(kind=f64), intent(in)  x1_adv, real(kind=f64), intent(in)  x2_adv, real(kind=f64), dimension(:), intent(in)  x1_coo, real(kind=f64), dimension(:), intent(in)  x2_coo, real(kind=f64), dimension(:), intent(out)  degree, real(kind=f64), intent(in)  epsilon, real(kind=f64), dimension(:), intent(out)  x1_dof, real(kind=f64), dimension(:), intent(out)  x2_dof  )

private

computes the coordinates of the poisition of the degrees of freedom (dof)

computes the coordinates of the poisition of the degrees of freedom (dof) in respect to a point (advected or not). These positions won't be really advected because they are at a small distance from the meshes nodes

Parameters

x1_adv	real first coordinate of a mesh point (advected or not)
x2_adv	real second coordinate of a mesh point (advected or not)
x1_coo	real vector first coordinates of neighbouring vertices
x2_coo	real vector second coordinates of neighbouring vertices
degree	int containing the degree of the triangulation (ie the number of cells that have the point (x1_adv, x2_adv).
epsilon	real containting the small displacement of the dof
x1_dof	real vector containing the computed first coordinates of the dof
x2_dof	real vector containing the computed second coordinates of the dof

Definition at line 174 of file sll_m_advection_2d_tri_mesh.F90.

compute_derivatives()

subroutine sll_m_advection_2d_tri_mesh::compute_derivatives ( intent(in)  f_val, intent(out)  f_der, intent(out)  f_der2, intent(in)  degree, intent(in)  epsilon  )

private

Computes degrees of freedom on one point.

Computes on a point the degrees of freedom (dof): For every annexing triangle we compute the first derivatives (following the triangle edges e1, e2, and e3) and the crossed derivatives (following e1+e2, e2+e3, and e1+e3). they are computed using the values of the function at the vertices. @params f_val [intent IN] real vector containing the function values at the vertices of annexing triangles @params f_der [intent OUT] real vector containing the values of the first derivatives following the vertices @params f_der2 [intent OUT] real vector containing the values of the second derivatives aka. crossed derivatives (see details) @params degree [intent IN] integer value of the number of cells parting from the point @params epsilon [intent IN] real value of the small distance to compute the dof

Definition at line 138 of file sll_m_advection_2d_tri_mesh.F90.

eval_at_lambda()

real(kind=f64) function sll_m_advection_2d_tri_mesh::eval_at_lambda ( real(kind=f64), dimension(3), intent(in)  lam, real(kind=f64), dimension(3), intent(in)  func_loc, real(kind=f64), dimension(6), intent(in)  der_loc, real(kind=f64), dimension(3), intent(in)  der2_loc  )

private

evaluation at barycentric points of one cell

Parameters

lam	real vector containing the barycentric coordinates of the edges of the cell
func_loc	real vector containg values of the function at dof points of one cell func_loc = [f1, f2, f3]
der_loc	real vector containg values of the derivatives at dof points of one cell (edge by edge) der_loc = [df12, df13, df23, df21, df31, df32]
der2_loc	real vector containg values of the 2nd derivatives at dof points one cell (edge by edge) func_loc = [d2f1, d2f2, d2f3]

Sum over functions at edges func_loc = [f1, f2, f3] formula: out += fi * lam(i)**2 * ((3-2*lam(i) + 6*lam(j)*lam(k)) where i, j, k are the edges of the cell/triangle

der_loc = [df12, df13, df23, df21, df31, df32] fomula : out += dfij * lamb(i)**2 * lam(j) * (1 + 2 * lam(k)) where i, j, k are the edges of the cell/triangle

Sum over second derivatives func_loc = [d2f1, d2f2, d2f3] formula: out += d2fi * lam(i)**2 * lam(j) * lam(k) where i, j, k are the edges of the cell/triangle

Definition at line 212 of file sll_m_advection_2d_tri_mesh.F90.

interpolation_mitchell()

subroutine sll_m_advection_2d_tri_mesh::interpolation_mitchell

private

Definition at line 248 of file sll_m_advection_2d_tri_mesh.F90.

sll_f_new_advection_2d_tri_mesh()

type(sll_t_advection_tri_mesh) function, pointer, public sll_m_advection_2d_tri_mesh::sll_f_new_advection_2d_tri_mesh

(

type(sll_t_triangular_mesh_2d), intent(in), target

mesh

)

allocates the memory space for a new 2D advection on triangular mesh on the heap, initializes it with the given triangular mesh and returns a pointer to the object.

Parameters

mesh	triangular mesh

Returns

a pointer to the newly allocated object.

Definition at line 60 of file sll_m_advection_2d_tri_mesh.F90.

sll_s_advection_2d()

subroutine, public sll_m_advection_2d_tri_mesh::sll_s_advection_2d	(	type(sll_t_advection_tri_mesh), intent(inout)	adv,
		real(kind=f64), dimension(:), intent(inout)	f_in,
		real(kind=f64), dimension(:), intent(in)	ex,
		real(kind=f64), dimension(:), intent(in)	ey,
		real(kind=f64), intent(in)	dt
	)

Compute characterisitic origin in triangular mesh.

xlm1 - 1ere coordonnee barycentrique xlm2 - 2eme coordonnee barycentrique xlm3 - 3eme coordonnee barycentrique

coord - coordonnees des noeuds nodes - numero des sommets des triangles nvois - numero des voisins des elements aire - aire de chaque element

coef1 - tableau temporaire des determinants coef2 - tableau temporaire des determinants coef3 - tableau temporaire des determinants coef4 - tableau temporaire

numpt - tableau auxiliaire contenant les numeros des particules a eliminer nelet - tableau auxiliaire contenant les numeros des elements qui contenaient ces particules nlmloc - tableau auxiliaire contenant les numeros des elements ou l'on cherche les particules numres - tableau auxiliaire contenant les numeros des particules non encore localisees

itest - tableau auxiliaire pour preciser le comportement:

• si itest=0 la particules reste dans son triangle
• si itest=1,2,3 la particule traverse le cote 1,2ou3 mais ne traverse pas de frontiere
• si itest=11,12,13 la particule est absorbee par le cote frontiere 1,2,3
• si itest=21,22,23 la particule est reflechie par le cote frontiere 1,2,3 Dans tous les cas le chiffre des unites de itest designe le numero du cote traverse par la particule. Le type de frontiere est defini dans le tableau nvoiv
• si nvoiv(i,n) > 0 le cote i n'est pas une frontiere
• si nvoiv(i,n) = 0 le cote i absorbe les particules
• si nvoiv(i,n) =-1 le cote i reflechit les particules

nbpert - nombre de particules a eliminer rho - densite de charge ad1 - tableau temporaire (adresse de la 1ere particule de chaque maille dans le tableau ordonne des particules) indice - tableau temporaire (incrementation du nombre de particules dja reperees) itabor - tableau temporaire (numeros des particules ordonnes suivant les numeros des mailles) nbpama - tableau temporaire (nombre de particules par maille)

petitl - petite longueur de reference

Parameters

[in,out]	adv	mesh
[in,out]	f_in	distribution function on nodes
[in]	ex	electric field on x1
[in]	ey	electric field on x2
[in]	dt	time step

Definition at line 306 of file sll_m_advection_2d_tri_mesh.F90.