modification of theboundary conditions and Scheme, correction of some bugs (elements)

Src2D2/Boundary_euler.f90

@@ -2,6 +2,7 @@ MODULE boundary
   USE param2d
   USE overloading
   USE PRECISION
+  use init_bc
   IMPLICIT NONE
   PRIVATE
   INTERFACE BC_corrected
@@ -66,8 +67,11 @@ CONTAINS
 
        ALLOCATE (Res(efr%nsommets))
        ALLOCATE(u(efr%nsommets))
+#if (1==0)
+       DO lp=n_theta(DATA%iordret)-1,n_theta(DATA%iordret)-1
+#else
        DO lp=0,n_theta(DATA%iordret)-1
-
+#endif
           u(:)=ua(lp,efr%nu(:))
 
 
@@ -85,12 +89,15 @@ CONTAINS
              STOP
           END SELECT
           DO is=1,efr%nsommets
-             un(is,jt)=un(is, jt)+theta(lp, k-1, DATA%iordret)*res(is)*dt
+#if (1==0)
+            un(is,jt)=un(is, jt)+res(is)*dt
+#else
+            un(is,jt)=un(is, jt)+theta(lp, k-1, DATA%iordret)*res(is)*dt
+#endif
           ENDDO
        ENDDO
        DEALLOCATE(Res,u)
     ENDDO
-
   END SUBROUTINE BC
 
   SUBROUTINE BC_kinetic(Mesh,k,dt,t,ua,un,DATA,alpha,beta,gamma,n_theta,theta)
@@ -159,134 +166,20 @@ CONTAINS
 
   END SUBROUTINE BC_kinetic
 
-  FUNCTION BCs(efr,uloc,x,y,temps,Icas) RESULT(ubord)
+    FUNCTION BCs(efr,uloc,x,y,temps,Icas) RESULT(ubord)
     TYPE(frontiere), INTENT(in) :: efr
     TYPE(PVar),      INTENT(in) :: uloc
     REAL(DP),            INTENT(in) :: x,y
     REAL(DP),            INTENT(in) :: temps
     INTEGER, INTENT(in)              :: Icas
     TYPE(Pvar)                  :: ubord
-    REAL(DP),            PARAMETER:: pi=ACOS(-1.) ! pi
-    REAL(DP)::vel,ro,u,v,p
-    REAL(DP),DIMENSION(2)           ::  nor
-    REAL(DP)                        :: mn
-    SELECT CASE(Icas)
-    CASE(0)
-       !       ubord=uloc
-       ubord%u=(/0.5_dp,1._dp,0._dp,0.125_dp/(gmm-1._dp)+0.5_dp*1._dp/0.5_dp/)
-    CASE(1,8)
-       !Sod/Vortex
-       ubord = uloc
-
-    CASE(10)
-       ! BC for DMR
-       SELECT CASE(efr%bc_tag)! Enable to define the quantity at infty, for logfr=2 or 3
-       CASE(2)
-          IF (x.LE.0_dp) THEN
-             ro=8._dp; u=8.25_dp; v=0._dp; p=116.5_dp
-          ELSE
-             ro=1.4_dp; u=0._dp; v=0._dp; p=1._dp
-          ENDIF
-
-          ! inflow (left horizontal wall)
-          ubord%u(1) = ro
-          ubord%u(2) = ro*u
-          ubord%u(3) = ro*v
-          ubord%u(4) = ubord%eEOS(ro,p)+0.5_dp*ro*(u*u+v*v)
-
-       CASE(1)
-          ! outflow (right horizontal wall)
-          ubord = uloc
-
-       CASE(3)
-          ! wall (horizontal). COMPUTE THE state with symmetry
-          nor=efr%n/SQRT(SUM(efr%n**2))
-          mn= SUM(uloc%u(2:3)*nor)
-
-          ubord%u(1) = uloc%u(1)
-          ubord%u(2:3) = uloc%u(2:3)- 2._dp*mn*nor
-          ubord%u(4) = uloc%u(4)
-
-
-
-       CASE default
-          PRINT*, 'Wrong BC type in BC_Data, efr%bc_tag = ', efr%bc_tag
-          STOP
-       END SELECT
-
-    CASE(11)
-       ! BC for Step
-       SELECT CASE(efr%bc_tag)
-       CASE(2)
-          ! outflow (right horizontal wall)
-          ubord = uloc
-
-!!$       CASE(1,2,3,5)
-!!$          ! wall (horizontal). COMPUTE THE state with symmetry
-!!$          nor=efr%n/SQRT(SUM(efr%n**2))
-!!$          mn= SUM(uloc%u(2:3)*nor)
-!!$
-!!$          ubord%u(1) = uloc%u(1)
-!!$          ubord%u(2:3) = uloc%u(2:3)- mn*nor
-!!$          ubord%u(4) = uloc%u(4)
-
-
-
-       CASE default
-          PRINT*, 'Wrong BC type in BC_Data, efr%bc_tag = ', efr%bc_tag
-          STOP
-       END SELECT
-    CASE(13)
-       ro=EXP(x**2+y**2)
-       p=ro*0.5_dp
-
-       u=-y; v=x
-
-       ubord%u(1)=ro ! [kg/m^3]
-       ubord%u(2)=ro*u ! [m/s]
-       ubord%u(3)=ro*v ! [m/s]
-       ubord%u(4)= ubord%eEOS(ubord%u(1),p) + 0.5_dp*ro*(u*u+v*v)
-    CASE(14)
-       ! contact
-       SELECT CASE(efr%bc_tag)! Enable to define the quantity at infty, for logfr=2 or 3
-       CASE(2)
-          IF (x.LE.0_dp) THEN
-             ro=8._dp; u=1._dp; v=0._dp; p=1._dp
-          ELSE
-             ro=1.4_dp; u=1._dp; v=0._dp; p=1._dp
-          ENDIF
-
-          ! inflow (left horizontal wall)
-          ubord%u(1) = ro
-          ubord%u(2) = ro*u
-          ubord%u(3) = ro*v
-          ubord%u(4) = ubord%eEOS(ro,p)+0.5_dp*ro*(u*u+v*v)
-
-       CASE(1)
-          ! outflow (right horizontal wall)
-          ubord = uloc
-
-       CASE(3)
-          ! wall (horizontal). COMPUTE THE state with symmetry
-          nor=efr%n/SQRT(SUM(efr%n**2))
-          mn= SUM(uloc%u(2:3)*nor)
-
-          ubord%u(1) = uloc%u(1)
-          ubord%u(2:3) = uloc%u(2:3)- 2._dp*mn*nor
-          ubord%u(4) = uloc%u(4)
-
-
-
-       CASE default
-          PRINT*, 'Wrong BC type in BC_Data, efr%bc_tag = ', efr%bc_tag
-          STOP
-       END SELECT
-    CASE default
-       PRINT*, "Wrong test number for BCs, cas= ", Icas
-       STOP
-    END SELECT
+     real(dp),dimension(2):: z
+
+    z(1)=x; z(2)=y
+    ubord=IC(0,z,Icas,temps)
+    end function BCs
+
 
-  END FUNCTION BCs
 
   SUBROUTINE  galerkin_bc2(e,t,u,res,DATA)
     IMPLICIT NONE
@@ -311,12 +204,14 @@ CONTAINS
     REAL(DP), PARAMETER                               :: eps=0._dp
     TYPE(Pvar), DIMENSION(n_dim)                      :: flux
     TYPE(Pvar)                                        :: dphi, prim
+    real(dp), dimension(4,4):: lambda
 
     res=0._dp
     n=-e%n ! interior normal in principle
     DO k=1, e%nsommets
        DO i=1, e%nquad
           y=e%quad(:,i)
+
           x(1)=SUM(y*e%coor(1,1:2))
           x(2)=SUM(y*e%coor(2,1:2))
           DO l=1, e%nsommets
@@ -327,8 +222,8 @@ CONTAINS
           ENDDO
           ubord = BCs(e,uloc,x(1),x(2),t, DATA%icas)
 
-
-          dphi%u(:)=MATMUL( uloc%min_mat(x,eps,n)         , ubord%u(:)-uloc%u(:) )
+          dphi%u(:)=-MATMUL( uloc%max_mat(x,eps,n)         , ubord%u(:)-uloc%u(:) )
+ 
 
           Res(k)%u(:)=Res(k)%u(:) +  dphi%u(:) *e%weight(i)*base(k)
 
@@ -360,6 +255,7 @@ CONTAINS
 
        DO k=1, e%nquad
           y=e%quad(:,i)
+
           x(1)=SUM(y*e%coor(1,1:2))
           x(2)=SUM(y*e%coor(2,1:2))
 

Src2D2/Fortran/quickhull.f90

@@ -33,7 +33,8 @@ MODULE quickhull
   IMPLICIT NONE
   PRIVATE
   PUBLIC:: test_quick
-  REAL(DP), PARAMETER:: tol=-MAX(SQRT(EPSILON(0.0_dp)), 1.e-10_dp)
+  REAL(DP), PARAMETER:: tol=-SQRT(EPSILON(0.0_dp))
+  REAL(dp), PARAMETER:: tol_hull=1.e-4_dp!0._dp!-epsilon(0.0_dp)
 CONTAINS
   SUBROUTINE tri(x,y)
     IMPLICIT NONE
@@ -65,7 +66,6 @@ CONTAINS
     REAL(DP),INTENT(IN) :: v3(2)    !< input vector 3
     !-----------------------------------------------
     ! OUTPUT VARIABLES
-    !    REAL(DP)            :: Cross    !< cross product, normalised
     REAL(DP)            :: w1(2), w2(2)
     !-----------------------------------------------
     ! LOCAL VARIABLES
@@ -78,7 +78,8 @@ CONTAINS
 
   SUBROUTINE ConvHull(nPoints,Points_o,nHull,Hull)!, ilower, Lower, iupper, upper)
     ! IMPLICIT VARIABLE HANDLING
-    IMPLICIT NONE 
+    IMPLICIT NONE
+    CHARACTER(LEN = *), PARAMETER :: mod_name ="ConvHull"
     !------------------------------------------------
     ! INPUT VARIABLES
     INTEGER,INTENT(IN)      :: nPoints
@@ -115,10 +116,10 @@ CONTAINS
        END DO
 
        iUpper = 0
-       Upper  = HUGE(1.)
+       Upper  = HUGE(1._dp)
        DO i=nPoints-1,0,-1
           DO WHILE(iUpper.GE.2.AND.Cross(Upper(:,iUpper-2),Upper(:,iUpper-1),Points(:,i)).LE.0._dp)
-             Upper(:,iUpper) = HUGE(1.)
+             Upper(:,iUpper) = HUGE(1._dp)
              iUpper          = iUpper - 1
           END DO
           Upper(:,iUpper) = Points(:,i)
@@ -129,6 +130,7 @@ CONTAINS
        iUpper = iUpper-1
        nHull  = iLower+iUpper+1
 
+
        ! NOTE: Initialize Hull with zeros
        Hull   = 0._dp
 
@@ -143,11 +145,11 @@ CONTAINS
 
   END SUBROUTINE ConvHull
 
-  LOGICAL FUNCTION is_in (Nhull, Hull, x)
+  LOGICAL FUNCTION is_in (Nhull, Hull, x, lk, jt)
     IMPLICIT NONE
     ! The parameter tol must be negative to be less strict that <0.
-
-    INTEGER, INTENT(in):: Nhull
+    CHARACTER(LEN = *), PARAMETER :: mod_name ="is_in"
+    INTEGER, INTENT(in):: Nhull, lk, jt
     REAL(DP), DIMENSION(2,0:Nhull-1), INTENT(in):: Hull
     REAL(DP), DIMENSION(2), INTENT(in):: x
     REAL(DP), DIMENSION(Nhull-1):: prod
@@ -157,18 +159,19 @@ CONTAINS
        prod(l)=cross(x, hull(:,l-1), hull(:,l))
     ENDDO
 
-    IF (MINVAL(prod)*MAXVAL(prod).LE.tol) THEN
+
+    IF (MINVAL(prod)*MAXVAL(prod).LE.-tol_hull) THEN! this is essential
        is_in=.FALSE.
     ELSE
        is_in=.TRUE.
     ENDIF
-
   END FUNCTION is_in
 
-  LOGICAL FUNCTION test_quick(nPoints,Points,x,n, flag)
+  LOGICAL FUNCTION test_quick(nPoints,Points,x,n,jt, lk, flag)
     IMPLICIT NONE
+    CHARACTER(LEN = *), PARAMETER :: mod_name ="test_quick"
     ! INPUT VARIABLES
-    INTEGER,INTENT(IN)  :: nPoints,n
+    INTEGER,INTENT(IN)  :: nPoints,n, jt, lk
     REAL(DP),INTENT(IN)     :: Points(2,0:nPoints-1)
     REAL(DP), DIMENSION(2,n), INTENT(in):: x
     LOGICAL, INTENT(in), OPTIONAL:: flag
@@ -177,7 +180,9 @@ CONTAINS
     REAL(DP)    :: Hull(2,0:nPoints)
     INTEGER:: i
     LOGICAL:: test
+
     CALL ConvHull(npoints, Points, nHull,Hull)
+
     IF (PRESENT(flag)) THEN
        PRINT*, nhull
        DO i=0, nhull-1
@@ -185,7 +190,8 @@ CONTAINS
        ENDDO
     ENDIF
     DO i=1, n
-       test=is_in(Nhull,Hull,x(:,i))
+       test=is_in(Nhull,Hull,x(:,i),lk, jt)
+
        IF (.NOT.test) THEN
           test_quick=.FALSE.
           RETURN

Src2D2/aretes.f90

@@ -29,7 +29,7 @@ MODULE arete_class
      ! points communs (puisque le maillage est confome)  aux deux elements sur cette face dans chacun des elements jt1 et jt2
      REAL(DP),    DIMENSION(:,:), POINTER :: coor =>NULL() ! il s'agit des coordonnees physique des dofs (communs) sur la face (commune)
      REAL(DP)                             :: volume=0._dp  !
-     REAL(DP)                             :: jump_flag=1.0 ! between 0 and 1 which gives the weight of the edge term
+     REAL(DP)                            :: jump_flag=1.0_dp ! between 0 and 1 which gives the weight of the edge term
      REAL(DP),    DIMENSION(:),   POINTER :: n   =>NULL()     ! normales exterieures
      INTEGER                          :: log    ! logique
 !!!!   quadrature de surface
@@ -87,16 +87,16 @@ CONTAINS
     nullify(e%quad, e%weight)
     ALLOCATE(e%quad(2,e%nquad),e%weight(e%nquad))
 
-    s=SQRT(0.6)
-    e%quad(1,1)=0.5*(1.0 - s)
-    e%quad(2,1)=0.5*(1.0 + s)
-    e%weight(1) = 5.0/18.0
-    e%quad(1,2)=0.5*(1.0 + s)
-    e%quad(2,2)=0.5*(1.0 - s)
-    e%weight(2) = 5.0/18.0
-    e%quad(1,3)=0.5
-    e%quad(2,3)=0.5
-    e%weight(3)=8.0/18.0
+    s=SQRT(0.6_dp)
+    e%quad(1,1)=0.5_dp*(1.0_dp - s)
+    e%quad(2,1)=0.5_dp*(1.0_dp + s)
+    e%weight(1) = 5.0_dp/18.0_dp
+    e%quad(1,2)=0.5_dp*(1.0_dp + s)
+    e%quad(2,2)=0.5_dp*(1.0_dp - s)
+    e%weight(2) = 5.0_dp/18.0_dp
+    e%quad(1,3)=0.5_dp
+    e%quad(2,3)=0.5_dp
+    e%weight(3)=8.0_dp/18.0_dp
 
 
   END SUBROUTINE quadrature_arete

Src2D2/elements.f90

@@ -119,6 +119,8 @@ MODULE element_class
      PROCEDURE, PUBLIC:: eval_coeff   =>eval_coeff_element
      PROCEDURE, PUBLIC:: iso          =>iso_element
      PROCEDURE, PUBLIC:: d_iso          =>d_iso_element
+     PROCEDURE, PUBLIC:: basegradATquad =>basegradATquad_element
+     PROCEDURE, PUBLIC:: baseATquad_edge=>baseATquad_edge_element
      FINAL:: deallocate_element
   END TYPE element
 
@@ -546,9 +548,9 @@ CONTAINS
     CHARACTER(LEN = *), PARAMETER :: mod_name = "gradient_element_ref"
     CLASS(element),             INTENT(in) :: e  ! calling element
     INTEGER,                    INTENT(in) :: k  ! index of basis function
-    REAL(DP), DIMENSION(e%nvertex), INTENT(in) :: x  ! barycentric coordinates
-    REAL(DP), DIMENSION(2)             :: grad
-    REAL(DP)                           :: fx,fy,fz
+    REAL(DP), DIMENSION(:), INTENT(in)     :: x  ! barycentric coordinates
+    REAL(DP), DIMENSION(n_dim)             :: grad
+    REAL(DP)                               :: fx,fy,fz
 
     SELECT CASE(e%nvertex)
 
@@ -654,7 +656,7 @@ CONTAINS
              !base_element = 27.0*x(1)*x(2)*x(3)
              fx = 27.0_dp*x(2)*x(3)
              fy = 27.0_dp*x(1)*x(3)
-             fz = 27.0*x(1)*x(2)
+             fz = 27.0_dp*x(1)*x(2)
           END SELECT
 
        CASE default
@@ -795,13 +797,13 @@ CONTAINS
     CHARACTER(LEN = *), PARAMETER :: mod_name = "gradient_element"
     CLASS(element),             INTENT(in)     :: e  ! calling element
     INTEGER,                    INTENT(in)     :: k  ! index of basis function
-    REAL(DP), DIMENSION(e%nvertex), INTENT(in) :: x  ! barycentric coordinates
-    REAL(DP), DIMENSION(2)                     :: grad
+    REAL(DP), DIMENSION(:), INTENT(in)         :: x  ! barycentric coordinates
+    REAL(DP), DIMENSION(n_dim)                 :: grad
     REAL(DP)                                   :: fx,fy,fz
 
     REAL(DP), DIMENSION(e%nsommets)            :: xx, yy
-    REAL(DP), DIMENSION(2,e%nsommets)          :: grad_ref
-    REAL(DP), DIMENSION(2,2)                   :: Jac, JacInv
+    REAL(DP), DIMENSION(n_dim,e%nsommets)      :: grad_ref
+    REAL(DP), DIMENSION(n_dim,n_dim)           :: Jac, JacInv
     INTEGER                                    :: i
     REAL(DP)                                   :: a,b,c,d
 
@@ -1054,12 +1056,6 @@ CONTAINS
           STOP
        END SELECT
 
-       ! assumes elements with linear shapes
-
-       !       Jac(1,1) = e%coor(1,2) - e%coor(1,1) + x(2)*(e%coor(1,1) - e%coor(1,2) + e%coor(1,3) - e%coor(1,4))
-       !       Jac(1,2) = e%coor(1,4) - e%coor(1,1) + x(1)*(e%coor(1,1) - e%coor(1,2) + e%coor(1,3) - e%coor(1,4))
-       !       Jac(2,1) = e%coor(2,2) - e%coor(2,1) + x(2)*(e%coor(2,1) - e%coor(2,2) + e%coor(2,3) - e%coor(2,4))
-       !       Jac(2,2) = e%coor(2,4) - e%coor(2,1) + x(1)*(e%coor(2,1) - e%coor(2,2) + e%coor(2,3) - e%coor(2,4))
 
        Jac=d_iso_element(e,x)
 
@@ -1632,37 +1628,41 @@ CONTAINS
        STOP
 
     END SELECT
-    NULLIFY(e%base_at_quad, e%grad_at_quad)
-    ALLOCATE(e%base_at_quad(e%nsommets,e%nquad),e%grad_at_quad(n_dim,e%nsommets,e%nquad))
-    CALL basegradATquad()
-
-    NULLIFY(e%base_at_quad_edge, e%grad_at_quad)
-    ALLOCATE(e%base_at_quad_edge(SIZE(e%quad_edge,1), e%nsommets,e%nquad_edge ))
-    CALL baseATquad_edge()
-  CONTAINS
-    SUBROUTINE basegradATquad()
-      INTEGER:: l, iq
-      DO iq=1,e%nquad
-         DO l=1,e%nsommets
-            e%base_at_quad(l  ,iq)=e%base    (l, e%quad(:,iq))
-            e%grad_at_quad(:,l,iq)=e%gradient(l, e%quad(:,iq))
-         ENDDO
-      ENDDO
-    END SUBROUTINE basegradATquad
-
-    SUBROUTINE baseATquad_edge()
-      INTEGER:: l, iq,k
-      DO k=1, SIZE(e%quad_edge,1)
-         DO iq=1,e%nquad_edge
-            DO l=1,e%nsommets!nvertex
-               e%base_at_quad_edge(k,l  ,iq)=e%base    (l, e%quad_edge(k,:,iq))
-            ENDDO
-         ENDDO
-      ENDDO
-    END SUBROUTINE baseATquad_edge
-
   END SUBROUTINE quadrature_element
 
+
+
+  SUBROUTINE basegradATquad_element(e)
+    IMPLICIT NONE
+    CHARACTER(LEN = *), PARAMETER :: mod_name = "basgradATquad"
+    CLASS(element), INTENT(inout)     :: e
+    INTEGER:: l, iq
+
+    DO iq=1,e%nquad
+       DO l=1,e%nsommets
+          e%base_at_quad(l  ,iq)=e%base    (l, e%quad(:,iq))
+          e%grad_at_quad(:,l,iq)=e%gradient(l, e%quad(:,iq))
+       ENDDO
+    ENDDO
+  END SUBROUTINE basegradATquad_element
+
+  SUBROUTINE baseATquad_edge_element(e)
+    IMPLICIT NONE
+    CHARACTER(LEN = *), PARAMETER :: mod_name = "baseATquad_edge"
+    CLASS(element), INTENT(inout)     :: e
+    INTEGER:: l, iq,k
+  
+    DO k=1, SIZE(e%quad_edge,1)
+       DO iq=1,e%nquad_edge
+          DO l=1,e%nsommets!nvertex
+             e%base_at_quad_edge(k,l  ,iq)=e%base    (l, e%quad_edge(k,:,iq))
+          ENDDO
+       ENDDO
+    ENDDO
+  END SUBROUTINE baseATquad_edge_element
+
+
+
   !==================================================================
   ! Interpolation of the function value
   !==================================================================

Src2D2/init_bc_euler.f90

@@ -29,16 +29,19 @@ CONTAINS
   !---------------------------------------
   ! Set initial and boundary conditions
   !---------------------------------------
-  TYPE(Pvar) FUNCTION IC(jt,x,initial_cond) RESULT(Var)
+  TYPE(Pvar) FUNCTION IC(jt,x,initial_cond,time) RESULT(Var)
     IMPLICIT NONE
     CHARACTER(LEN = *), PARAMETER :: mod_name = "init_bc_euler/IC"
     INTEGER, INTENT(in)                :: initial_cond, jt
     REAL(DP), DIMENSION(:), INTENT(in) :: x
+    REAL(dp), INTENT(in), OPTIONAL:: time
     REAL(DP)                               :: alpha
     REAL(DP), DIMENSION(n_dim)             :: y, centre
     REAL(DP) :: r2, vt, cs, r0, epsil, r,beta
     REAL(dp):: uinf, vinf, Tinf, du, dv, deltaT, coeff
     REAL(dp):: ro, u, v, Ma,p, x0, theta
+    REAL(dp):: xc, yc, rc, ro1, u1, v1, p1, ro0, u0, v0, p0
+    REAL(dp):: T, T0, T1,  eps, rap, z(2)
     REAL(DP),            PARAMETER:: dpi=ACOS(-1._dp) ! pi
     !---------------
     ! for Euler
@@ -221,7 +224,8 @@ CONTAINS
        !    Var%u(4) = Var%eEOS(Var%u(1),p)+ 0.5_dp*(Var%u(2)**2+Var%u(3)**2)/Var%u(1)       
     CASE(12)
        beta=5
-       r = SQRT((x(1)- 1._dp)**2+(x(2)- 0._dp)**2)
+       xc=0.25_dp; yc=0.5_dp
+       r = SQRT((x(1)- xc)**2+(x(2)- yc)**2)
        ro=(1-((gmm-1._dp)*beta**2*EXP(1-r**2))/(8*gmm*dpi**2))**(1._dp/(gmm-1._dp))
        p=ro**gmm
        Var%u(1) = ro
@@ -308,8 +312,8 @@ CONTAINS
        Var%u(3)=ro*v ! [m/s]
        Var%u(4)= Var%eEOS(Var%u(1),p) + 0.5_dp*ro*(u*u+v*v)
 
-    case(14)
-              x0=-0.05_dp
+    CASE(14)
+       x0=-0.05_dp
        x0=0._dp
        IF (x(1) .GE. x0) THEN
           ro=1.4_dp; u=1._dp; v=0._dp; p=1._dp
@@ -320,8 +324,69 @@ CONTAINS
        Var%u(2)=ro*u ! [m/s]
        Var%u(3)=ro*v ! [m/s]
        Var%u(4)= Var%eEOS(Var%u(1),p) + 0.5_dp*ro*(u*u+v*v)
+    CASE(15) ! moving vortex
+       xc=0.25_dp; yc=0.5_dp
+       alpha=0.204_dp; rc=0.05; eps=0.3_dp
+       ! shock parameters
+       Ma=1.1
+       ! before shock
+       ro0=1._dp
+       u0=Ma*SQRT(gmm); v0=0._dp; p0=1._dp
+       T0=p0/ro0
+       z(1)=x(1)-xc-u0*t; z(2)=x(2)-yc-v0*t; z=z/rc
+       ! superposition
+       !       IF (x(1).GE.0.5_dp) THEN
+       !          ro=ro1;u=u1;v=0._dp;p=p1
+       !       ELSE
+       !!          ro=ro0; u=u0;v=v0; p=p0
+       R2=z(1)**2+z(2)**2
+       coeff=EXP(alpha*(1._dp-R2))
+       u=u0+eps* z(2)*coeff
+       v=v0-eps* z(1)*coeff
+       T=1._dp-(gmm-1._dp)/(4._dp*alpha*gmm)*eps*eps*coeff*coeff
+       ro= ro0*( T/T0)**(1._dp/gmm)
+       p=ro*T
+       !       ENDIF
+       Var%u(1)=ro
+       Var%u(2)=ro*u
+       Var%u(3)=ro*v
+       Var%u(4)=Var%eEOS(ro,p)+0.5_dp*ro*(u*u+v*v)
+    CASE(16) ! shock vortex interaction
+       xc=0.25_dp; yc=0.5_dp
+       alpha=0.204_dp; rc=0.05; eps=0.3_dp
+       ! shock parameters
+       Ma=1.1
+       ! before shock
+       ro0=1._dp
+       u0=Ma*SQRT(gmm); v0=0._dp; p0=1._dp
+       ! before shock
+       rap=(gmm-1._dp)/(gmm+1._dp)+2._dp/((gmm+1._dp)*Ma*Ma)
+       ro1=ro0/rap
+       rap=2._dp*gmm/(gmm+1._dp)*Ma*Ma-(gmm-1._dp)/(gmm+1._dp)
+       p1=p0*rap
+       u1=ro0*u0/ro1
+       T0=p0/ro0
+       z(1)=x(1)-xc-u0*t; z(2)=x(2)-yc-v0*t; z=z/rc
+       ! superposition
+       IF (x(1).GE.0.5_dp) THEN
+          ro=ro1;u=u1;v=0._dp;p=p1
+       ELSE
+          R2=z(1)**2+z(2)**2
+          coeff=EXP(alpha*(1._dp-R2))
+          u=u0+eps* z(2)*coeff
+          v=v0-eps* z(1)*coeff
+          T=1._dp-(gmm-1._dp)/(4._dp*alpha*gmm)*eps*eps*coeff*coeff