[yzeyue]

Hi everyone,

I program a 2D AUSM code. But I do not know how to deal with the pressure part and the use of vector.

There is pressure part on the energy equation in some codes I see on the website, but some there is not. I see the paper about AUSM scheme, and I find that the pressure part is only in one motion equation. Should the pressure part in all the motion equation?

Appreciate it very much if anyone can help me with the problem.

My AUSM code is as follows.

! i direction
            nx = XLNI(I,J) / SLNI(I,J)
        ny = YLNI(I,J) / SLNI(I,J)

!  Left state
          rhoL = DENSL
            vL = VELXL  ! velocity of x direction
           vyL = VELYL  ! velocity of y direction
           qnL = vL*nx + vyL*ny
            pL = PRESL
            aL = sqrt(gamma*pL/rhoL)
            mL = qnL / aL
            eL = pL/(gamma-one)+half*(vL*vL+vyL+vyL)
            hL = eL + pL/rhoL
!  Left state
          rhoR = DENSR
            vR = VELXR  ! velocity of x direction
           vyR = VELYR  ! velocity of y direction
           qnR = vR*nx + vyR*ny
            pR = PRESR
            aR = sqrt(gamma*pR/rhoR)
            mR = qnR / aR
            eR = pR/(gamma-one)+half*(vR*vR+vyR+vyR)
            hR = eR + pR/rhoR


           if(ABS(mL).le.one)then
                mLP = quarter*(mL + one)**two
                pLP = quarter*pL*(mL+one)**two*(two-mL)
           else
                mLP = half*(mL + ABS(mL))
                pLP = half*pL*(mL+ABS(mL))/mL
           end if

           if(ABS(mR).le.one)then
                mRN = -quarter*(mR - one)**two
                pRN = quarter*pR*(mR-one)**two*(two+mR)
           else
                mRN = half*(mR - ABS(mR))
                pRN = half*pR*(mR-ABS(mR))/mR
           end if

         m_Mid = mLP+mRN
         

   FLUXI(1,I,J) = half*m_Mid*(rhoL*aL + rhoR*aR)-half*ABS(m_Mid)*(rhoR*aR - rhoL*aL)

   FLUXI(2,I,J) = half*m_Mid*(rhoL*aL*vL + rhoR*aR*vR) - half*ABS(m_Mid)*(rhoR*aR*vR - rhoL*aL*vL)+ (pLP + pRN)*nx
                  
   FLUXI(3,I,J) = half*m_Mid*(rhoL*aL*vyL + rhoR*aR*vyR) - half*ABS(m_Mid)*(rhoR*aR*vyR - rhoL*aL*vyL)+ (pLP + pRN)*ny

   FLUXI(4,I,J) = half*m_Mid*(rhoL*aL*hL + rhoR*aR*hR) - half*ABS(m_Mid)*(rhoR*aR*hR - rhoL*aL*hL)

    

! j direction
            nx = XLNJ(I,J) / SLNJ(I,J)
            ny = YLNJ(I,J) / SLNJ(I,J)

!  Left state
          rhoL = DENSL
            vL = VELXL  ! velocity of x direction
           vyL = VELYL  ! velocity of y direction
           qnL = vL*nx + vyL*ny
            pL = PRESL
            aL = sqrt(gamma*pL/rhoL)
            mL = qnL / aL
            eL = pL/(gamma-one)+half*(vL*vL+vyL+vyL)
            hL = eL + pL/rhoL
!  Left state
          rhoR = DENSR
            vR = VELXR  ! velocity of x direction
           vyR = VELYR  ! velocity of y direction
           qnR = vR*nx + vyR*ny
            pR = PRESR
            aR = sqrt(gamma*pR/rhoR)
            mR = qnR / aR
            eR = pR/(gamma-one)+half*(vR*vR+vyR+vyR)
            hR = eR + pR/rhoR


           if(ABS(mL).le.one)then
                mLP = quarter*(mL + one)**two
                pLP = quarter*pL*(mL+one)**two*(two-mL)
           else
                mLP = half*(mL + ABS(mL))
                pLP = half*pL*(mL+ABS(mL))/mL
           end if

           if(ABS(mR).le.one)then
                mRN = -quarter*(mR - one)**two
                pRN = quarter*pR*(mR-one)**two*(two+mR)
           else
                mRN = half*(mR - ABS(mR))
                pRN = half*pR*(mR-ABS(mR))/mR
           end if

         m_Mid = mLP+mRN
         

   FLUXJ(1,I,J) = half*m_Mid*(rhoL*aL + rhoR*aR)-half*ABS(m_Mid)&
                  *(rhoR*aR - rhoL*aL)

   FLUXJ(2,I,J) = half*m_Mid*(rhoL*aL*vL + rhoR*aR*vR) - half*ABS(m_Mid)*(rhoR*aR*vR - rhoL*aL*vL)+ (pLP + pRN)*nx

   FLUXJ(3,I,J) = half*m_Mid*(rhoL*aL*vyL + rhoR*aR*vyR) - half*ABS(m_Mid)*(rhoR*aR*vyR - rhoL*aL*vyL)+ (pLP + pRN)*ny
                  
   FLUXJ(4,I,J) = half*m_Mid*(rhoL*aL*hL + rhoR*aR*hR) - half*ABS(m_Mid)*(rhoR*aR*hR - rhoL*aL*hL)

    
12        CONTINUE
      DO 31 J=1,JN-1
      DO 31 I=1,IN-1
        FLUX(1,I,J)=FLUXI(1,I+1,J)*SLNI(I+1,J)-FLUXI(1,I,J)*SLNI(I,J)&
               +FLUXJ(1,I,J+1)*SLNJ(I,J+1)-FLUXJ(1,I,J)*SLNJ(I,J)
        FLUX(2,I,J)=FLUXI(2,I+1,J)*SLNI(I+1,J)-FLUXI(2,I,J)*SLNI(I,J)&
               +FLUXJ(2,I,J+1)*SLNJ(I,J+1)-FLUXJ(2,I,J)*SLNJ(I,J)
        FLUX(3,I,J)=FLUXI(3,I+1,J)*SLNI(I+1,J)-FLUXI(3,I,J)*SLNI(I,J)&
               +FLUXJ(3,I,J+1)*SLNJ(I,J+1)-FLUXJ(3,I,J)*SLNJ(I,J)
        FLUX(4,I,J)=FLUXI(4,I+1,J)*SLNI(I+1,J)-FLUXI(4,I,J)*SLNI(I,J)&
               +FLUXJ(4,I,J+1)*SLNJ(I,J+1)-FLUXJ(4,I,J)*SLNJ(I,J)

31    CONTINUE

[yzeyue]

Hi, how to deal with this problem?

[Krishan.aero]

Hey, I am also trying to implement AUSM in 2D boundary layer problem. Please let me know if anyone knows the answer.