Commit d410fc3b authored by Michael Dumbser's avatar Michael Dumbser
Browse files

Added the enforcement of the algebraic constraints

parent 5bf46144

ApplicationExamples/FOCCZ4/FOCCZ4/EinsteinConstraints.f90

0 → 100644
+149 −0
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SUBROUTINE EnforceCCZ4Constraints(luh)

    USE MainVariables, ONLY : nVar  

    IMPLICIT NONE

    ! Argument list

    REAL, INTENT(INOUT)  :: luh(nVar)              ! numerical solution  

    ! Local variables

    INTEGER :: i,j,k,l,iVar,iDim, iter

    REAL    :: Q(nVar) 

    REAL    :: g_cov(3,3), det, g_contr(3,3), Aex(3,3), traceA, phi  

    REAL    :: DD(3,3,3), traceDk 

#if defined(CCZ4EINSTEIN) || defined(CCZ4GRMHD) || defined(CCZ4GRHD) || defined(CCZ4GRGPR) 

    !

            Q = luh(:) 

            ! 

            g_cov(1,1) = Q(1)

            g_cov(1,2) = Q(2)

            g_cov(1,3) = Q(3)

            g_cov(2,1) = Q(2)

            g_cov(2,2) = Q(4)

            g_cov(2,3) = Q(5)

            g_cov(3,1) = Q(3)

            g_cov(3,2) = Q(5)

            g_cov(3,3) = Q(6)

            ! This determinant should be close to unity, since we use the conformal decomposition 

            det = (Q(1)*Q(4)*Q(6)-Q(1)*Q(5)**2-Q(2)**2*Q(6)+2*Q(2)*Q(3)*Q(5)-Q(3)**2*Q(4)) 

            g_contr(1,1) = (Q(4)*Q(6)-Q(5)**2)   / det 

            g_contr(1,2) = -(Q(2)*Q(6)-Q(3)*Q(5))/ det 

            g_contr(1,3) = (Q(2)*Q(5)-Q(3)*Q(4)) / det 

            g_contr(2,1) = -(Q(2)*Q(6)-Q(3)*Q(5))/ det 

            g_contr(2,2) = (Q(1)*Q(6)-Q(3)**2)   / det 

            g_contr(2,3) = -(Q(1)*Q(5)-Q(2)*Q(3))/ det 

            g_contr(3,1) = (Q(2)*Q(5)-Q(3)*Q(4)) / det 

            g_contr(3,2) = -(Q(1)*Q(5)-Q(2)*Q(3))/ det 

            g_contr(3,3) = (Q(1)*Q(4)-Q(2)**2)   / det 

            !

            phi = det**(-1./6.) 

            g_cov = phi**2*g_cov

            det = (g_cov(1,1)*g_cov(2,2)*g_cov(3,3)-g_cov(1,1)*g_cov(2,3)*g_cov(3,2)-g_cov(2,1)*g_cov(1,2)*g_cov(3,3)+g_cov(2,1)*g_cov(1,3)*g_cov(3,2)+g_cov(3,1)*g_cov(1,2)*g_cov(2,3)-g_cov(3,1)*g_cov(1,3)*g_cov(2,2)) 

            g_contr(1,1) =  (g_cov(2,2)*g_cov(3,3)-g_cov(2,3)*g_cov(3,2)) / det 

            g_contr(1,2) = -(g_cov(1,2)*g_cov(3,3)-g_cov(1,3)*g_cov(3,2)) / det

            g_contr(1,3) = -(-g_cov(1,2)*g_cov(2,3)+g_cov(1,3)*g_cov(2,2))/ det 

            g_contr(2,1) = -(g_cov(2,1)*g_cov(3,3)-g_cov(2,3)*g_cov(3,1)) / det 

            g_contr(2,2) = (g_cov(1,1)*g_cov(3,3)-g_cov(1,3)*g_cov(3,1))  / det 

            g_contr(2,3) = -(g_cov(1,1)*g_cov(2,3)-g_cov(1,3)*g_cov(2,1)) / det 

            g_contr(3,1) = -(-g_cov(2,1)*g_cov(3,2)+g_cov(2,2)*g_cov(3,1))/ det 

            g_contr(3,2) = -(g_cov(1,1)*g_cov(3,2)-g_cov(1,2)*g_cov(3,1)) / det 

            g_contr(3,3) = (g_cov(1,1)*g_cov(2,2)-g_cov(1,2)*g_cov(2,1))  / det 

            !

            Aex(1,1) = Q(7) 

            Aex(1,2) = Q(8) 

            Aex(1,3) = Q(9) 

            Aex(2,1) = Q(8) 

            Aex(2,2) = Q(10) 

            Aex(2,3) = Q(11) 

            Aex(3,1) = Q(9) 

            Aex(3,2) = Q(11) 

            Aex(3,3) = Q(12)             

            !

            traceA = SUM(g_contr*Aex) 

            !

            Aex = Aex - 1./3.*g_cov*traceA 

            !

            luh( 1) = g_cov(1,1) 

            luh( 2) = g_cov(1,2) 

            luh( 3) = g_cov(1,3) 

            luh( 4) = g_cov(2,2) 

            luh( 5) = g_cov(2,3) 

            luh( 6) = g_cov(3,3) 

            !

            luh( 7) = Aex(1,1) 

            luh( 8) = Aex(1,2) 

            luh( 9) = Aex(1,3) 

            luh(10) = Aex(2,2) 

            luh(11) = Aex(2,3) 

            luh(12) = Aex(3,3)             

            !

            ! As suggested by our PRD referee, we also enforce the algebraic constraint that results from the first spatial derivative of the constraint

            ! det \tilde{\gamma}_ij = 0, which leads to

            !

            ! \tilde{\gamma}^{ij} D_kij = 0

            !

            ! and is thus a condition of trace-freeness on all submatrices D_kij for k=1,2,3.

            !

            DD(1,1,1)=Q(36)

            DD(1,1,2)=Q(37)

            DD(1,1,3)=Q(38)

            DD(1,2,1)=Q(37)

            DD(1,2,2)=Q(39)

            DD(1,2,3)=Q(40)

            DD(1,3,1)=Q(38)

            DD(1,3,2)=Q(40)

            DD(1,3,3)=Q(41)

            !

            DD(2,1,1)=Q(42)

            DD(2,1,2)=Q(43)

            DD(2,1,3)=Q(44)

            DD(2,2,1)=Q(43)

            DD(2,2,2)=Q(45)

            DD(2,2,3)=Q(46)

            DD(2,3,1)=Q(44)

            DD(2,3,2)=Q(46)

            DD(2,3,3)=Q(47)

            !

            DD(3,1,1)=Q(48)

            DD(3,1,2)=Q(49)

            DD(3,1,3)=Q(50)

            DD(3,2,1)=Q(49)

            DD(3,2,2)=Q(51)

            DD(3,2,3)=Q(52)

            DD(3,3,1)=Q(50)

            DD(3,3,2)=Q(52)

            DD(3,3,3)=Q(53)

            !!

            DO l = 1, 3

                traceDk = SUM(g_contr*DD(l,:,:))

                DD(l,:,:) = DD(l,:,:) - 1./3.*g_cov*traceDk

            ENDDO

            !

            luh(36) = DD(1,1,1)

            luh(37) = DD(1,1,2)

            luh(38) = DD(1,1,3)

            luh(39) = DD(1,2,2)

            luh(40) = DD(1,2,3)

            luh(41) = DD(1,3,3)

            !

            luh(42) = DD(2,1,1)

            luh(43) = DD(2,1,2)

            luh(44) = DD(2,1,3)

            luh(45) = DD(2,2,2)

            luh(46) = DD(2,2,3)

            luh(47) = DD(2,3,3)

            !

            luh(48) = DD(3,1,1)

            luh(49) = DD(3,1,2)

            luh(50) = DD(3,1,3)

            luh(51) = DD(3,2,2)

            luh(52) = DD(3,2,3)

            luh(53) = DD(3,3,3)            

            !

#ifdef CCZ4GRHD 

            !IF( Q(60) < 1e-6) THEN

            !    luh(61:63,i,j,k) = 0.0                  ! in the atmosphere, there is no velocity 

            !ENDIF            

#endif 

            !



#endif 

END SUBROUTINE EnforceCCZ4Constraints

ApplicationExamples/FOCCZ4/FOCCZ4/FOCCZ4Solver_ADERDG.cpp

+4 −0
Original line number Diff line number Diff line
@@ -75,6 +75,10 @@ void FOCCZ4::FOCCZ4Solver_ADERDG::adjustPointSolution(const double* const x,cons 
    

    initialdata_(x_3, &t, Q);

  }

  else

  {

	  enforceccz4constraints_(Q); 

  }

  for(int i = 0; i< 96 ; i++){

    assert(std::isfinite(Q[i]));

  }

ApplicationExamples/FOCCZ4/FOCCZ4/FOCCZ4Solver_FV.cpp

+5 −0
Original line number Diff line number Diff line
@@ -34,6 +34,11 @@ void FOCCZ4::FOCCZ4Solver_FV::adjustSolution(const double* const x,const double 
    

    initialdata_(x_3, &t, Q);

  }

  else

  {

	  enforceccz4constraints_(Q); 

  }

  

  for(int i = 0; i< 96 ; i++){

    assert(std::isfinite(Q[i]));

  }

ApplicationExamples/FOCCZ4/FOCCZ4/PDE.h

+3 −0
Original line number Diff line number Diff line
@@ -38,6 +38,9 @@ void pdecons2prim_(double* V,const double* Q); 
 

void maxhyperboliceigenvaluegrhd_(double* smax, const double* const QR, const double* const QL, double* nv);



void enforceccz4constraints_(double* Q); 





}/* extern "C" */

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