# Galerkin projection

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 June 5, 2011, 10:57 Galerkin projection #1 New Member   sara Join Date: Mar 2011 Posts: 7 Rep Power: 0 Sponsored Links Hi every one. thank you for reading my thread. I am working on galerkin projection to make a reduced order model by proper orthogonal modes, but i don't understand why my galerkin projection dosen't work properly. I've used general coordinates to calculate spatial derivatives. I have checked all the steps but I don't understand why it doesn't work. here is my code ... every term is a part of projection... ns= number of modes nn=number of grids in direction mm=number of grids in direction vm=mean velocity in y direction um=mean velocity in x direction Q = temporal coefficients for ROM thank you. !------------------------------------------ !================================ CONVECTION TERM =========================== !================================ THE FIRST TERM =========================== DO K=1,NS DO I=1,MM DO J=1,NN T1 =PHI_U(I,J,K)*(UM(I,J)*UM_DX(I,J)+VM(I,J)*UM_DY(I, J))& +PHI_V(I,J,K)*(UM(I,J)*VM_DX(I,J)+VM(I,J)*VM_DY(I, J)) TERM_1(k)=T1+TERM_1(k) END DO END DO END DO !================================== THE SECOND TERM ========================== DO K=1,NS DO M=1,NS DO I=1,MM DO J=1,NN T2 =PHI_U(I,J,K)*(UM(I,J)*PHI_UDX(I,J,M)+VM(I,J)*PHI_ UDY(I,J,M))& +PHI_V(I,J,K)*(UM(I,J)*PHI_VDX(I,J,M)+VM(I,J)*PHI_ VDY(I,J,M)) TERM_2(k,M)=TERM_2(K,M)+T2 END DO END DO END DO END DO !=================================== THE THIRD TERM ========================== DO K=1,NS DO M=1,NS DO I=1,MM DO J=1,NN T3 =PHI_U(I,J,K)*(PHI_U(I,J,M)*UM_DX(I,J)+PHI_V(I,J,M )*UM_DY(I,J))& +PHI_V(I,J,K)*(PHI_U(I,J,M)*VM_DX(I,J)+PHI_V(I,J,M )*VM_DY(I,J)) TERM_3(K,M)=TERM_3(K,M)+T3 END DO END DO END DO END DO !=================================== THE FORTH TERM ========================== !=================================== FORTHE-FIRST =========================== DO K=1,NS DO M=1,NS DO N=1,NS DO I=1,MM DO J=1,NN T4_1 =PHI_U(I,J,K)*(PHI_U(I,J,N)*PHI_UDX(I,J,M)+PHI_V(I ,J,N)*PHI_UDY(I,J,M)) TERM4_1(K,M,N)=TERM4_1(K,M,N)+T4_1 END DO END DO END DO END DO END DO !=================================== FORTHE-SECOND ============================ DO K=1,NS DO M=1,NS DO N=1,NS DO I=1,MM DO J=1,NN T4_2 =PHI_V(I,J,K)*(PHI_U(I,J,N)*PHI_VDX(I,J,M)+PHI_V(I ,J,N)*PHI_VDY(I,J,M)) TERM4_2(K,M,N)=TERM4_2(K,M,N)+T4_2 END DO END DO END DO END DO END DO !==================== SUM OF FIRST TERM AND THE SECOND ONE ==================== DO K=1,NS DO M=1,NS DO N=1,NS TERM_4(K,M,N)=TERM4_1(K,M,N)+TERM4_2(K,M,N) !*Q1(M)*Q1(N) END DO END DO END DO !================================================= ============================= ! THE PRESSURE TERM IS ZERO AND IT HAS NO CORPORATION TO THE SET OF ODES !================================================= ============================= !================================== THE DIFFUSION TERM ============================ DO K=1,NS DO I=1,MM DO J=1,NN TERM5_1(K)=TERM5_1(K)+PHI_U(I,J,K)*(UM_DX2(I,J)+UM _DY2(I,J))+PHI_V(I,J,K)*(VM_DX2(I,J)+VM_DY2(I,J)) END DO END DO END DO !==================================== FIFTH-SECOND ============================= DO K=1,NS DO M=1,NS DO I=1,MM DO J=1,NN T5_2=PHI_U(I,J,K)*(PHI_UDX2(I,J,M)+PHI_UDY2(I,J,M) )+PHI_V(I,J,K)*(PHI_VDX2(I,J,M)+PHI_VDY2(I,J,M)) TERM5_2(K,M)=TERM5_2(K,M)+T5_2 END DO END DO END DO END DO !================================================= ============================= !=========== !=========== !=========== DO K=1,NS A(K) =-TERM_1(K)+TERM5_1(K)/RE END DO ! DO K=1,NS DO M=1,NS B(K,M) =-TERM_2(K,M)-TERM_3(K,M)+TERM5_2(K,M)/RE END DO END DO ! DO K=1,NS DO M=1,NS DO N=1,NS C(K,M,N)=-TERM_4(K,M,N) END DO END DO END DO !================================================= ============================= !====================== !====================== !====================== DO K=1,NS DO M=1,NS BB(K)=BB(K)+B(K,M)*Q1(M) END DO END DO !=============== DO K=1,NS DO M=1,NS DO N=1,NS CC(K)=CC(K)+C(K,M,N)*Q1(M)*Q1(N) END DO END DO END DO !=============== DO K=1,NS F(K)=(A(K)+BB(K)+CC(K)) END DO !=============== !=============== !=============== Q=Q*DT+F

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