This function calculates the sigma for the box shape sponge layer from coord for polynomial n5. Sponge profile: where, \sigma_A - sponge strength, L - thickness, x0 - start of sponge.
Profile is taken from: Xu, Hui; Sagaut, Pierre (2013): Analysis of the absorbing layers for the weakly-compressible lattice Boltzmann methods. In Journal of Computational Physics 245, pp. 14-42. DOI: 10.1016/j.jcp.2013.02.051.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| type(tem_spongeLayer_box_type) | :: | me |
Spatial sponge layer to evaluate |
|||
| real(kind=rk), | intent(in) | :: | coord(n,3) |
barycentric Ids of an elements. 1st index goes over number of elements and 2nd index goes over x,y,z coordinates |
||
| integer, | intent(in) | :: | n |
Number of arrays to return |
return value
function spongeLayer_box_sharpCornerPolyn5_for_coord(me, coord, n) &
& result(res)
! --------------------------------------------------------------------------
!> Spatial sponge layer to evaluate
type(tem_spongeLayer_box_type) :: me
!> Number of arrays to return
integer, intent(in) :: n
!> barycentric Ids of an elements.
!! 1st index goes over number of elements and
!! 2nd index goes over x,y,z coordinates
real(kind=rk), intent( in ) :: coord(n,3)
!> return value
real(kind=rk) :: res(n)
! --------------------------------------------------------------------------
integer :: i
real(kind=rk) :: sigma, origin(3), extent(3), coordLoc(3), normal
real(kind=rk) :: proj_len1, proj_len2
real(kind=rk) :: vec_min(3), vec_max(3), vec_minSqr(3), vec_maxSqr(3)
real(kind=rk) :: rad, const_fac, box_max(3)
! --------------------------------------------------------------------------
origin(:) = me%origin
extent(:) = me%extent
box_max(:) = origin(:) + extent(:)
const_fac = 3125_rk/(256_rk*me%thickness**5)
do i = 1,n
coordLoc = coord(i,:)
vec_min(:) = coordLoc(:) - origin(:)
vec_max(:) = coordLoc(:) - box_max(:)
vec_minSqr(:) = vec_min(:)**2
vec_maxSqr(:) = vec_max(:)**2
proj_len1 = 0_rk
proj_len2 = 0_rk
normal = 1_rk
rad = 0_rk
! Bottom-South-West: -x,-y,-z
if (all(coordLoc(:) < origin(:))) then
rad = sqrt( max(vec_minSqr(1), vec_minSqr(2), vec_minSqr(3)) )
else if (coordLoc(1) > box_max(1) .and. coordLoc(2) < origin(2) &
& .and. coordLoc(3) < origin(3)) then ! Bottom-South-East: x, -y, -z
rad = sqrt( max(vec_maxSqr(1), vec_minSqr(2), vec_minSqr(3)) )
else if (coordLoc(1) < origin(1) .and. coordLoc(2) > box_max(2) &
& .and. coordLoc(3) < origin(3)) then ! Bottom-North-West: -x, y, -z
rad = sqrt( max(vec_minSqr(1), vec_maxSqr(2), vec_minSqr(3)) )
else if (coordLoc(1) > box_max(1) .and. coordLoc(2) > box_max(2) &
& .and. coordLoc(3) < origin(3)) then ! Bottom-North-East: x, y, -z
rad = sqrt( max(vec_maxSqr(1), vec_maxSqr(2), vec_minSqr(3)) )
else if (coordLoc(1) < origin(1) .and. coordLoc(2) < origin(2) &
& .and. coordLoc(3) > box_max(3)) then ! Top-South-West: -x, -y, z
rad = sqrt( max(vec_minSqr(1), vec_minSqr(2), vec_maxSqr(3)) )
else if (coordLoc(1) > box_max(1) .and. coordLoc(2) < origin(2) &
& .and. coordLoc(3) > box_max(3)) then ! Top-South-East: x, -y, z
rad = sqrt( max(vec_maxSqr(1), vec_minSqr(2), vec_maxSqr(3)) )
else if (coordLoc(1) < origin(1) .and. coordLoc(2) > box_max(2) &
& .and. coordLoc(3) > box_max(3)) then ! Top-North-West: -x, y, z
rad = sqrt( max(vec_minSqr(1), vec_maxSqr(2), vec_maxSqr(3)) )
else if (all(coordLoc(:) > box_max(:))) then ! Top-North-East: x, y, z
rad = sqrt( max(vec_maxSqr(1), vec_maxSqr(2), vec_maxSqr(3)) )
else if (coordLoc(2) < origin(2) .and. coordLoc(3) < origin(3)) then
! Botton-South: -y,-z
rad = sqrt( max(vec_minSqr(2), vec_minSqr(3)) )
else if (coordLoc(2) < origin(2) .and. coordLoc(3) > box_max(3)) then
! Top-South: -y, z
rad = sqrt( max(vec_minSqr(2), vec_maxSqr(3)) )
else if (coordLoc(2) > box_max(2) .and. coordLoc(3) < origin(3)) then
! Botom-North: -y, z
rad = sqrt( max(vec_maxSqr(2), vec_minSqr(3)) )
else if (coordLoc(2) > box_max(2) .and. coordLoc(3) > box_max(3)) then
! Top-North: y, z
rad = sqrt( max(vec_maxSqr(2), vec_maxSqr(3)) )
else if (coordLoc(1) < origin(1) .and. coordLoc(3) < origin(3)) then
! Botton-West: -x,-z
rad = sqrt( max(vec_minSqr(1), vec_minSqr(3)) )
else if (coordLoc(1) > box_max(1) .and. coordLoc(3) < origin(3)) then
! Bottom-East: x,-z
rad = sqrt( max(vec_maxSqr(1), vec_minSqr(3)) )
else if (coordLoc(1) < origin(1) .and. coordLoc(3) > box_max(3)) then
! Top-West: -x, z
rad = sqrt( max(vec_minSqr(1), vec_maxSqr(3)) )
else if (coordLoc(1) > box_max(1) .and. coordLoc(3) > box_max(3)) then
! Top-East: x, z
rad = sqrt( max(vec_maxSqr(1), vec_maxSqr(3)) )
else if (coordLoc(1) < origin(1) .and. coordLoc(2) < origin(2)) then
! South-West: -x,-y
rad = sqrt( max(vec_minSqr(1), vec_minSqr(2)) )
else if (coordLoc(1) < origin(1) .and. coordLoc(2) > box_max(2)) then
! North-West: -x, y
rad = sqrt( max(vec_minSqr(1), vec_maxSqr(2)) )
else if (coordLoc(1) > box_max(1) .and. coordLoc(2) < origin(2)) then
! South-East: x, -y
rad = sqrt( max(vec_maxSqr(1), vec_minSqr(2)) )
else if (coordLoc(1) > box_max(1) .and. coordLoc(2) > box_max(2)) then
! North-East: x, y
rad = sqrt( max(vec_maxSqr(1), vec_maxSqr(2)) )
else if (coordLoc(1) < origin(1)) then ! West: -x
normal = -1_rk
rad = vec_min(1)
else if (coordLoc(2) < origin(2)) then ! South: -y
normal = -1_rk
rad = vec_min(2)
else if (coordLoc(3) < origin(3)) then ! Bottom: -z
normal = -1_rk
rad = vec_min(3)
else if (coordLoc(1) > box_max(1)) then ! East: x
normal = 1_rk
rad = vec_max(1)
else if (coordLoc(2) > box_max(2)) then ! North: y
normal = 1_rk
rad = vec_max(2)
else if (coordLoc(3) > box_max(3)) then ! Top: z
normal = 1_rk
rad = vec_max(3)
end if
proj_len1 = rad*normal
proj_len2 = (me%thickness*normal - rad)*normal
if (proj_len1 > 0 .and. proj_len2 > 0) then
sigma = const_fac * proj_len2 * (proj_len1**4)
res(i) = sigma*me%dampFactor
else if (proj_len2 < 0) then ! If coord is beyond thickness
res(i) = me%dampFactor
else
res(i) = 0.0_rk
end if
end do
end function spongeLayer_box_sharpCornerPolyn5_for_coord