Local Lax-Friedrichs (Rusanov) Riemann flux for linear advection. Entropy-stable: provides symmetric dissipation at element interfaces. Uses the per-face spectral radius lambda = |u.n|, matching upwind (Godunov) for linear advection: tangential faces (u.n=0) contribute zero flux, avoiding spurious dissipation across element interfaces whose face normal is perpendicular to the velocity.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| class(ECAdvection2D_t), | intent(in) | :: | this | |||
| real(kind=prec), | intent(in) | :: | sL(1:this%nvar) | |||
| real(kind=prec), | intent(in) | :: | sR(1:this%nvar) | |||
| real(kind=prec), | intent(in) | :: | dsdx(1:this%nvar,1:2) | |||
| real(kind=prec), | intent(in) | :: | nhat(1:2) |
pure function riemannflux2d_ECAdvection2D_t(this,sL,sR,dsdx,nhat) result(flux)
!! Local Lax-Friedrichs (Rusanov) Riemann flux for linear advection.
!! Entropy-stable: provides symmetric dissipation at element interfaces.
!! Uses the per-face spectral radius lambda = |u.n|, matching upwind
!! (Godunov) for linear advection: tangential faces (u.n=0) contribute
!! zero flux, avoiding spurious dissipation across element interfaces
!! whose face normal is perpendicular to the velocity.
class(ECAdvection2D_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
real(prec) :: un,lam
un = this%u*nhat(1)+this%v*nhat(2)
lam = abs(un)
flux(1) = 0.5_prec*(un*(sL(1)+sR(1))-lam*(sR(1)-sL(1)))
if(.false.) flux(1) = flux(1)+dsdx(1,1) ! suppress unused-dummy-argument warning
endfunction riemannflux2d_ECAdvection2D_t