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THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ! ! //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// ! module self_advection_diffusion_2d_t use self_dgmodel2d use self_mesh use SELF_BoundaryConditions implicit none type,extends(dgmodel2d) :: advection_diffusion_2d_t real(prec) :: nu ! diffusion coefficient real(prec) :: u ! constant x-component of velocity real(prec) :: v ! constant y-component of velocity contains procedure :: AdditionalInit => AdditionalInit_advection_diffusion_2d_t procedure :: riemannflux2d => riemannflux2d_advection_diffusion_2d_t procedure :: flux2d => flux2d_advection_diffusion_2d_t procedure :: entropy_func => entropy_func_advection_diffusion_2d_t endtype advection_diffusion_2d_t contains subroutine AdditionalInit_advection_diffusion_2d_t(this) !! Register boundary conditions for the advection-diffusion model. !! Hyperbolic: mirror (no-normal-flow) wall condition on the solution. !! Parabolic: no-stress condition that zeros the normal gradient at !! the boundary, giving zero diffusive flux through walls. This is !! stable with the Bassi-Rebay (BR1) method. implicit none class(advection_diffusion_2d_t),intent(inout) :: this ! Local procedure(SELF_bcMethod),pointer :: bcfunc bcfunc => hbc2d_NoNormalFlow_advection_diffusion_2d_t call this%hyperbolicBCs%RegisterBoundaryCondition( & SELF_BC_NONORMALFLOW,"no_normal_flow",bcfunc) bcfunc => pbc2d_NoStress_advection_diffusion_2d_t call this%parabolicBCs%RegisterBoundaryCondition( & SELF_BC_NONORMALFLOW,"no_normal_flow",bcfunc) endsubroutine AdditionalInit_advection_diffusion_2d_t subroutine hbc2d_NoNormalFlow_advection_diffusion_2d_t(bc,mymodel) !! Mirror boundary condition on the solution: sets the exterior !! state equal to the interior state. With LLF this zeroes the !! upwind dissipation at the wall. class(BoundaryCondition),intent(in) :: bc class(Model),intent(inout) :: mymodel ! Local integer :: n,i,iEl,s select type(m => mymodel) class is(advection_diffusion_2d_t) do n = 1,bc%nBoundaries iEl = bc%elements(n) s = bc%sides(n) do i = 1,m%solution%interp%N+1 m%solution%extBoundary(i,s,iEl,1:m%nvar) = & m%solution%boundary(i,s,iEl,1:m%nvar) enddo enddo endselect endsubroutine hbc2d_NoNormalFlow_advection_diffusion_2d_t subroutine pbc2d_NoStress_advection_diffusion_2d_t(bc,mymodel) !! No-stress boundary condition for the BR1 diffusive flux. !! Reflects the interior gradient so that the normal component !! of the averaged gradient vanishes at the boundary: !! sigma_ext = sigma_int - 2 (sigma_int . nhat) nhat !! This gives zero diffusive flux through the wall and is !! unconditionally stable for Bassi-Rebay. class(BoundaryCondition),intent(in) :: bc class(Model),intent(inout) :: mymodel ! Local integer :: n,i,iEl,s,ivar real(prec) :: nhat(1:2),sigma_n select type(m => mymodel) class is(advection_diffusion_2d_t) do n = 1,bc%nBoundaries iEl = bc%elements(n) s = bc%sides(n) do i = 1,m%solution%interp%N+1 nhat(1:2) = m%geometry%nHat%boundary(i,s,iEl,1,1:2) do ivar = 1,m%nvar sigma_n = m%solutionGradient%boundary(i,s,iEl,ivar,1)*nhat(1)+ & m%solutionGradient%boundary(i,s,iEl,ivar,2)*nhat(2) m%solutionGradient%extBoundary(i,s,iEl,ivar,1) = & m%solutionGradient%boundary(i,s,iEl,ivar,1)-2.0_prec*sigma_n*nhat(1) m%solutionGradient%extBoundary(i,s,iEl,ivar,2) = & m%solutionGradient%boundary(i,s,iEl,ivar,2)-2.0_prec*sigma_n*nhat(2) enddo enddo enddo endselect endsubroutine pbc2d_NoStress_advection_diffusion_2d_t pure function entropy_func_advection_diffusion_2d_t(this,s) result(e) class(advection_diffusion_2d_t),intent(in) :: this real(prec),intent(in) :: s(1:this%solution%nvar) real(prec) :: e ! Local integer :: ivar e = 0.0_prec do ivar = 1,this%solution%nvar e = e+0.5_prec*s(ivar)*s(ivar) enddo endfunction entropy_func_advection_diffusion_2d_t pure function flux2d_advection_diffusion_2d_t(this,s,dsdx) result(flux) class(advection_diffusion_2d_t),intent(in) :: this real(prec),intent(in) :: s(1:this%solution%nvar) real(prec),intent(in) :: dsdx(1:this%solution%nvar,1:2) real(prec) :: flux(1:this%solution%nvar,1:2) ! Local integer :: ivar do ivar = 1,this%solution%nvar flux(ivar,1) = this%u*s(ivar)-this%nu*dsdx(ivar,1) ! advective flux + diffusive flux flux(ivar,2) = this%v*s(ivar)-this%nu*dsdx(ivar,2) ! advective flux + diffusive flux enddo endfunction flux2d_advection_diffusion_2d_t pure function riemannflux2d_advection_diffusion_2d_t(this,sL,sR,dsdx,nhat) result(flux) class(advection_diffusion_2d_t),intent(in) :: this real(prec),intent(in) :: sL(1:this%nvar) real(prec),intent(in) :: sR(1:this%nvar) real(prec),intent(in) :: dsdx(1:this%nvar,1:2) real(prec),intent(in) :: nhat(1:2) real(prec) :: flux(1:this%nvar) ! Local integer :: ivar real(prec) :: un,dsdn un = this%u*nhat(1)+this%v*nhat(2) do ivar = 1,this%nvar dsdn = dsdx(ivar,1)*nhat(1)+dsdx(ivar,2)*nhat(2) flux(ivar) = 0.5_prec*( & (sL(ivar)+sR(ivar))+abs(un)*(sL(ivar)-sR(ivar)))- & ! advective flux this%nu*dsdn enddo endfunction riemannflux2d_advection_diffusion_2d_t endmodule self_advection_diffusion_2d_t