PFVT get pressure
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Revision as of 21:10, 15 March 2013 by Jonas Holdeman (Talk | contribs)
function [P,Px,Py] = GetPres3W(eu,NodXY,Elcon,nn2nft,Q,EBCPr,~) % GetPres3W - Compute continuous simple-cubic pressure from velocity % field on general quadrilateral grid (bilinear geometric mapping) or % quadratic pressure for triangular grid (linear mapping). % This version is restricted to 3-node triangles and 4-node quadrilaterals % P,Px,Py must be reshaped or restructured for use in calling program with % P=reshape(P,NumNx,NumNy), etc. because it assumes that the grid may be % unstructured. % % Usage % P = GetPres3W(eu,NodXY,Elcon,nn2nft,Q,EBCPr); % [P,Px,Py] = GetPres3W(eu,NodXY,Elcon,nn2nft,Q,EBCPr); % % Inputs % eu - velocity class, (eg. ELS3412r, ELS4424r, ELS5424r, ELS2309t ) % NodXY - coordinates of nodes % Elcon - element connectivity, nodes in element % nn2nft - global number and type of (non-pressure) DOF at each node % Q - array of DOFs for velocity elements % EBCp - essential pressure boundary condition structure % EBCp.nodn - node number of fixed pressure node % EBCp.val - value of pressure % Outputs % P,Px,Py - pressure degrees of freedom % Uses % ilu - ilu preconditioner % gmres - to solve the system % Indirectly may use (handle passed by eu): % GQuad2 - function providing 2D rectangle quadrature rules. % TQuad2 - function providing 2D triangle quadrature rules. % ELG3412r - basis function class defining the cubic/pressure elements(Q) % ELG2309t - basis function class defining the quadratic/pressure elements(T) % % Jonas Holdeman, January 2007, revised March 2013 % ------------------- Constants and fixed data --------------------------- nvn = eu.nnodes; % Number of nodes in elements (4) nvd = eu.nndofs; % number of velocity DOFs at nodes (3|4|6); if nvn==4, ep = ELG3412r; % simple cubic voricity class definition (Q) elseif nvn==3, ep=ELG2309t; % quadratic voricity class definition (T) else error(['pressure: ' num2str(nvn) ' nodes not supported']); end npd = ep.nndofs; % Number DOFs in pressure fns (3, simple cubic) ND=1:nvd; % Number DOFs in velocity fns (bicubic-derived) NumEl=size(Elcon,1); % Number of elements NumNod=size(NodXY,1); % Number of global nodes NumPdof=npd*NumNod; % Max number pressure DOFs % Parameters for GMRES solver GM.Tol=1.e-11; GM.MIter=30; GM.MRstrt=8; % parameters for ilu preconditioner % Decrease su.droptol if ilu preconditioner fails su.type='ilutp'; su.droptol=1.e-5; nn2pft = zeros(NumNod,2); for n=1:NumNod nn2pft(n,:)=[(n-1)*npd+1,1]; end % ---------------------- end fixed data ---------------------------------- % Begin essential boundary conditions, allocate space EBCp.Mxdof=NumPdof; % Essential boundary condition for pressure EBCp.dof = nn2pft(EBCPr.nodn(1),1); % Degree-of-freedom index EBCp.val = EBCPr.val; % Pressure Dof value % partion out essential (Dirichlet) dofs p_vec = (1:EBCp.Mxdof)'; % List of all dofs EBCp.p_vec_undo = zeros(1,EBCp.Mxdof); % form a list of non-diri dofs EBCp.ndro = p_vec(~ismember(p_vec, EBCp.dof)); % list of non-diri dofs % calculate p_vec_undo to restore Q to the original dof ordering EBCp.p_vec_undo([EBCp.ndro;EBCp.dof]) = (1:EBCp.Mxdof); %p_vec'; % Allocate space for pressure matrix, velocity data pMat = spalloc(NumPdof,NumPdof,36*NumPdof); % allocate P mass matrix Vdata = zeros(NumPdof,1); % allocate velocity data Vdof = zeros(nvd,nvn); % Nodal velocity DOFs Xe = zeros(2,nvn); % BEGIN GLOBAL MATRIX ASSEMBLY for ne=1:NumEl Xe(1:2,1:nvn)=NodXY(Elcon(ne,1:nvn),1:2)'; % Get stream function and velocities for n=1:nvn Vdof(ND,n)=Q((nn2nft(Elcon(ne,n),1)-1)+ND); % Loop over local nodes end % Pressure "mass" matrix [Emat,Rndx,Cndx] = pMassMat(Xe,Elcon(ne,:),nn2pft,ep); pMat=pMat+sparse(Rndx,Cndx,Emat,NumPdof,NumPdof); % Global mass assembly % Convective data term [CDat,RRndx] = PCDat(Xe,Elcon(ne,:),nn2pft,Vdof,ep,eu); Vdata(RRndx) = Vdata(RRndx)-CDat(:); end; % Loop ne % END GLOBAL MATRIX ASSEMBLY Vdatap=Vdata(EBCp.ndro)-pMat(EBCp.ndro,EBCp.dof)*EBCp.val; pMatr=pMat(EBCp.ndro,EBCp.ndro); %Qs=Qp(EBCp.ndro); % Non-Dirichlet (active) dofs [Lm,Um] = ilu(pMatr,su); % incomplete LU Pr = gmres(pMatr,Vdatap,GM.MIter,GM.Tol,GM.MRstrt,Lm,Um,[]); % GMRES Qp=[Pr;EBCp.val]; % Augment active dofs with esential (Dirichlet) dofs Qp=Qp(EBCp.p_vec_undo); % Restore natural order if (nargout==3) Qp=reshape(Qp,npd,NumNod); P = Qp(1,:); Px = Qp(2,:); Py = Qp(3,:); else P = Qp; end return; % >>>>>>>>>>>>> End pressure recovery <<<<<<<<<<<<< % ********************* function pMassMat ******************************** function [MM,Rndx,Cndx]=pMassMat(Xe,Elcon,nn2nftp,ep) % Simple cubic gradient element "mass" matrix % ep = handle to class of definitions for cubic pressure functions: % ELG3412r (rectangle) or ELG2309t (triangle) % % -------------------- Constants and fixed data -------------------------- npn = ep.nnodes; % number of velocity/vorticity element nodes (4) npd = ep.nndofs; % number of vorticity DOFs at nodes (3); nn = ep.nn; % defines local nodal order [-1 -1; 1 -1; 1 1; -1 1] npdf=npn*npd; NP=1:npd; % ------------------------------------------------------------------------ persistent QQ_prMMp; % quadrature rules if isempty(QQ_prMMp) QRord = (2*ep.mxpowr+1); % quadtature rule order [QQ_prMMp.xa, QQ_prMMp.ya, QQ_prMMp.wt, QQ_prMMp.nq]=ep.hQuad(QRord); end % if isempty... xa = QQ_prMMp.xa; ya = QQ_prMMp.ya; wt = QQ_prMMp.wt; Nq = QQ_prMMp.nq; % ------------------------------------------------------------------------ persistent ZZ_Gpmm; % pressure functions if (isempty(ZZ_Gpmm)||size(ZZ_Gpmm,2)~=Nq) % Evaluate and save/cache the set of shape functions at quadrature pts. ZZ_Gpmm=cell(npn,Nq); for k=1:Nq for m=1:npn ZZ_Gpmm{m,k}=ep.G(nn(m,:),xa(k),ya(k)); end end end % if(isempty(*)) % ------------------------ end fixed data -------------------------------- TGi=cell(npn); for m=1:npn % Loop over corner nodes, GBL is gradient of bilinear fn J=(Xe*ep.Gm(nn(:,:),nn(m,1),nn(m,2)))'; % TGi{m} = blkdiag(1,J); end % Loop m MM=zeros(npdf,npdf); G=zeros(2,npdf); % Preallocate arrays for k=1:Nq % Initialize functions and derivatives at the quadrature point (xa,ya). J=(Xe*ep.Gm(nn(:,:),xa(k),ya(k)))'; % Jacobian at (xa,ya) Det=J(1,1)*J(2,2)-J(1,2)*J(2,1); % Determinant of Jt & J Ji=[J(2,2),-J(1,2); -J(2,1),J(1,1)]/Det; for m=1:npn mm=(m-1)*npd; G(:,mm+NP)=Ji*ZZ_Gpmm{m,k}*TGi{m}; end % loop m MM = MM + G'*G*(wt(k)*Det); end % end loop k (quadrature pts) gf=zeros(npdf,1); % array of global freedoms for n=1:npn % Loop over element nodes m=(n-1)*npd; gf(m+NP)=(nn2nftp(Elcon(n),1)-1)+NP; % Get global freedoms end Rndx=repmat(gf,1,npdf); % Row indices Cndx=Rndx'; % Column indices MM = reshape(MM,1,npdf*npdf); Rndx=reshape(Rndx,1,npdf*npdf); Cndx=reshape(Cndx,1,npdf*npdf); return; % *********************** funnction PCDat ****************************** function [PC,Rndx]=PCDat(Xe,Elcon,nn2nftp,Vdof,ep,eu) % Evaluate convective force data % ep = handle to class of definitions for cubic pressure functions: % ELG3412r (rectangle) or ELG2309t (triangle) % % ----------- Constants and fixed data --------------- nvn = eu.nnodes; % number of velocity element nodes (4) nvd = eu.nndofs; % number of velocity DOFs at nodes (3|4|6); npd = ep.nndofs; % number of vorticity DOFs at nodes (3); nn = eu.nn; % defines local nodal order [-1 -1; 1 -1; 1 1; -1 1] npdf=nvn*npd; nvdf=nvn*nvd; NP=1:npd; NV=1:nvd; % ------------------------------------------------------------------------ persistent QQ_prPCp; % quadrature rules if isempty(QQ_prPCp) QRord = (eu.mxpowr+ep.mxpowr-1); % quadtature rule order [QQ_prPCp.xa, QQ_prPCp.ya, QQ_prPCp.wt, QQ_prPCp.nq]=eu.hQuad(QRord); end % if isempty... xa = QQ_prPCp.xa; ya = QQ_prPCp.ya; wt = QQ_prPCp.wt; Nq = QQ_prPCp.nq; % ------------------------------------------------------------------------ persistent ZZ_Spcd; persistent ZZ_SXpcd; persistent ZZ_SYpcd; persistent ZZ_Gpcd; if (isempty(ZZ_Spcd)||isempty(ZZ_Gpcd)||size(ZZ_Spcd,2)~=Nq) % Evaluate and save/cache the set of shape functions at quadrature pts. ZZ_Spcd=cell(nvn,Nq); ZZ_SXpcd=cell(nvn,Nq); ZZ_SYpcd=cell(nvn,Nq); ZZ_Gpcd=cell(nvn,Nq); for k=1:Nq for m=1:nvn ZZ_Spcd{m,k} =eu.S(nn(m,:),xa(k),ya(k)); [ZZ_SXpcd{m,k},ZZ_SYpcd{m,k}]=eu.DS(nn(m,:),xa(k),ya(k)); ZZ_Gpcd{m,k}=ep.G(nn(m,:),xa(k),ya(k)); end % loop m over nodes end % loop k over Nq end % if(isempty(*)) % ----------------------- end fixed data --------------------------------- Ti=cell(nvn); TGi=cell(nvn); for m=1:nvn % Loop over corner nodes Jt=Xe*eu.Gm(nn(:,:),nn(m,1),nn(m,2)); JtiD=[Jt(2,2),-Jt(1,2); -Jt(2,1),Jt(1,1)]; % det(J)*inv(J) if nvd==3, TT=blkdiag(1,JtiD); elseif nvd==4 TT=blkdiag(1,JtiD,(Jt(1,1)*Jt(2,2)+Jt(1,2)*Jt(2,1)) ); else T2=[Jt(1,1)^2, 2*Jt(1,1)*Jt(2,1), Jt(2,1)^2; ... % alt Jt(1,1)*Jt(1,2), Jt(1,1)*Jt(2,2)+Jt(1,2)*Jt(2,1), Jt(2,1)*Jt(2,2); ... Jt(1,2)^2, 2*Jt(1,2)*Jt(2,2), Jt(2,2)^2]; TT=blkdiag(1,JtiD,T2); Bxy=Xe*eu.DGm(nn(:,:),nn(m,1),nn(m,2)); % Second cross derivatives TT(5,2)= Bxy(2); TT(5,3)=-Bxy(1); end Ti{m}=TT; % % J=[Jt(1,1),Jt(2,1); Jt(1,2),Jt(2,2)]; % evaluate J from transpose TGi{m} = blkdiag(1,Jt'); end % Loop m over corner nodes PC=zeros(npdf,1); S=zeros(2,nvdf); Sx=zeros(2,nvdf); Sy=zeros(2,nvdf); G=zeros(2,npdf); for k=1:Nq % Loop over quadrature points Jt=Xe*eu.Gm(nn(:,:),xa(k),ya(k)); % transpose of Jacobian at (xa,ya) Det=Jt(1,1)*Jt(2,2)-Jt(1,2)*Jt(2,1); % Determinant of Jt & J Jtd=Jt/Det; JtiD=[Jt(2,2),-Jt(1,2); -Jt(2,1),Jt(1,1)]; Jti=JtiD/Det; Ji=[Jti(1,1),Jti(2,1); Jti(1,2),Jti(2,2)]; for m=1:nvn % Loop over element nodes mm=nvd*(m-1); S(:,mm+NV) =Jtd*ZZ_Spcd{m,k}*Ti{m}; Sx(:,mm+NV)=Jtd*(Jti(1,1)*ZZ_SXpcd{m,k}+Jti(2,1)*ZZ_SYpcd{m,k})*Ti{m}; Sy(:,mm+NV)=Jtd*(Jti(1,2)*ZZ_SXpcd{m,k}+Jti(2,2)*ZZ_SYpcd{m,k})*Ti{m}; mm=npd*(m-1); G(:,mm+NP)=Ji*ZZ_Gpcd{m,k}*TGi{m}; end % end loop over element nodes % Compute the fluid velocities at the quadrature point. U = S*Vdof(:); Ux = Sx*Vdof(:); Uy = Sy*Vdof(:); UgU = U(1)*Ux+U(2)*Uy; % U dot grad U PC = PC + G'*UgU*(wt(k)*Det); end % end loop over Nq quadrature points gf=zeros(1,npdf); % array of global freedoms for n=1:nvn % Loop over element nodes m=(n-1)*npd; gf(m+NP)=(nn2nftp(Elcon(n),1)-1)+NP; % Get global freedoms end Rndx=gf; PC = reshape(PC,1,npdf); return;