spongeLayer_plane_polyn5_for_coord Function

private function spongeLayer_plane_polyn5_for_coord(me, coord, n) result(res)

This function calculates the sigma for the spongeLayer from coord for the polynomial order 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.

Arguments

Type IntentOptional Attributes Name
type(tem_spongeLayer_plane_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 real(kind=rk), (n)

return value


Source Code

  function spongeLayer_plane_polyn5_for_coord(me, coord, n)  result(res)
    ! --------------------------------------------------------------------------
    !> Spatial sponge layer to evaluate
    type(tem_spongeLayer_plane_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), normal(3), vec1(3), vec2(3)
    real(kind=rk) :: proj_len1, proj_len2, const_fac
    ! --------------------------------------------------------------------------
    origin(:) = me%origin
    normal(:) = me%normal
    const_fac = 3125_rk/(256_rk*me%thickness**5)

    do i = 1,n
      vec1(:) = coord(i,:) - origin(:)
      vec2(:) = me%thickness*normal(:) + origin(:) - coord(i,:)
      proj_len1 = vec1(1)*normal(1) + vec1(2)*normal(2) + vec1(3)*normal(3)
      proj_len2 = vec2(1)*normal(1) + vec2(2)*normal(2) + vec2(3)*normal(3)

      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_plane_polyn5_for_coord