//---------------------------------------------------------
DMat& NDG2D::Lift2D()
//---------------------------------------------------------
{
// function [LIFT] = Lift2D()
// Purpose : Compute surface to volume lift term for DG formulation
DMat V1D,massEdge1,massEdge2,massEdge3; DVec faceR,faceS;
Index1D J1(1,Nfp), J2(Nfp+1,2*Nfp), J3(2*Nfp+1,3*Nfp);
DMat Emat(Np, Nfaces*Nfp);
// face 1
faceR = r(Fmask(All,1));
V1D = Vandermonde1D(N, faceR);
massEdge1 = inv(V1D*trans(V1D));
Emat(Fmask(All,1), J1) = massEdge1;
// face 2
faceR = r(Fmask(All,2));
V1D = Vandermonde1D(N, faceR);
massEdge2 = inv(V1D*trans(V1D));
Emat(Fmask(All,2), J2) = massEdge2;
// face 3
faceS = s(Fmask(All,3));
V1D = Vandermonde1D(N, faceS);
massEdge3 = inv(V1D*trans(V1D));
Emat(Fmask(All,3), J3) = massEdge3;
// inv(mass matrix)*\I_n (L_i,L_j)_{edge_n}
LIFT = V*(trans(V)*Emat);
return LIFT;
}
//---------------------------------------------------------
void CurvedINS2D::INSLiftDrag2D(double ra)
//---------------------------------------------------------
{
// function [Cd, Cl, dP, sw, stri] = INSLiftDrag2D(Ux, Uy, PR, ra, nu, time, tstep, Nsteps)
// Purpose: compute coefficients of lift, drag and pressure drop at cylinder
static FILE* fid;
static DVec sw1, sw2;
static int Nc=0, stri1=0, stri2=0;
if (1 == tstep) {
char buf[50]; sprintf(buf, "liftdraghistory%d.dat", N);
fid = fopen(buf, "w");
fprintf(fid, "timeCdCldP = [...\n");
// Sample location and weights for pressure drop
// Note: the VolkerCylinder test assumes the 2
// sample points (-ra, 0), (ra, 0), are vertices
// located on the internal cylinder boundary
Sample2D(-ra, 0.0, sw1, stri1);
Sample2D( ra, 0.0, sw2, stri2);
Nc = mapC.size()/Nfp;
}
bool bDo=false;
if (1==tstep || tstep==Nsteps || !umMOD(tstep,10)) { bDo=true; }
else if (time > 3.90 && time < 3.96) { bDo=true; } // catch C_d (3.9362)
else if (time > 5.65 && time < 5.73) { bDo=true; } // catch C_l (5.6925)
else if (time > 7.999) { bDo=true; } // catch dP (8.0)
if (!bDo) return;
DVec PRC, nxC, nyC, wv, tv;
DMat dUxdx,dUxdy, dUydx,dUydy, MM1D, V1D;
DMat dUxdxC,dUxdyC, dUydxC,dUydyC, hforce, vforce, sJC;
double dP=0.0, Cd=0.0, Cl=0.0;
dP = sw1.inner(PR(All,stri1)) - sw2.inner(PR(All,stri2));
// compute derivatives
Grad2D(Ux, dUxdx,dUxdy); dUxdxC=dUxdx(vmapC); dUxdyC=dUxdy(vmapC);
Grad2D(Uy, dUydx,dUydy); dUydxC=dUydx(vmapC); dUydyC=dUydy(vmapC);
PRC=PR(vmapC); nxC=nx(mapC); nyC=ny(mapC); sJC=sJ(mapC);
hforce = -PRC.dm(nxC) + nu*( nxC.dm( 2.0 *dUxdxC) + nyC.dm(dUydxC+dUxdyC) );
vforce = -PRC.dm(nyC) + nu*( nxC.dm(dUydxC+dUxdyC) + nyC.dm( 2.0 *dUydyC) );
hforce.reshape(Nfp, Nc);
vforce.reshape(Nfp, Nc);
sJC .reshape(Nfp, Nc);
// compute weights for integrating (1,hforce) and (1,vforce)
V1D = Vandermonde1D(N, r(Fmask(All,1)));
MM1D = trans(inv(V1D)) / V1D;
wv = MM1D.col_sums();
tv = wv*(sJC.dm(hforce)); Cd=tv.sum(); // Compute drag coefficient
tv = wv*(sJC.dm(vforce)); Cl=tv.sum(); // Compute lift coefficient
// Output answers for plotting
fprintf(fid, "%15.14f %15.14f %15.14f %15.14f;...\n", time, Cd/ra, Cl/ra, dP);
fflush(fid);
// LOG report
if (1==tstep || tstep==Nsteps || !umMOD(tstep,Nreport)) {
umLOG(1, "%7d %6.3lf %9.5lf %10.6lf %9.5lf\n",
tstep, time, Cd/ra, Cl/ra, dP);
}
if (tstep==Nsteps) {
fprintf(fid, "];\n");
fclose(fid); fid=NULL;
}
}
//---------------------------------------------------------
void NDG2D::MakeCylinder2D
(
const IMat& faces,
double ra,
double xo,
double yo
)
//---------------------------------------------------------
{
// Function: MakeCylinder2D(faces, ra, xo, yo)
// Purpose: Use Gordon-Hall blending with an isoparametric
// map to modify a list of faces so they conform
// to a cylinder of radius r centered at (xo,yo)
int NCurveFaces = faces.num_rows();
IVec vflag(VX.size()); IMat VFlag(EToV.num_rows(),EToV.num_cols());
int n=0,k=0,f=0,v1=0,v2=0;
double theta1=0.0,theta2=0.0,x1=0.0,x2=0.0,y1=0.0,y2=0.0;
double newx1=0.0,newx2=0.0,newy1=0.0,newy2=0.0;
DVec vr, fr, theta, fdx,fdy, vdx, vdy, blend,numer,denom;
IVec va,vb,vc, ks, Fm_f, ids; DMat Vface, Vvol;
for (n=1; n<=NCurveFaces; ++n)
{
// move vertices of faces to be curved onto circle
k = faces(n,1); f = faces(n,2);
v1 = EToV(k, f); v2 = EToV(k, umMOD(f,Nfaces)+1);
theta1 = atan2(VY(v1),VX(v1)); theta2 = atan2(VY(v2),VX(v2));
newx1 = xo + ra*cos(theta1); newy1 = yo + ra*sin(theta1);
newx2 = xo + ra*cos(theta2); newy2 = yo + ra*sin(theta2);
// update mesh vertex locations
VX(v1) = newx1; VX(v2) = newx2; VY(v1) = newy1; VY(v2) = newy2;
// store modified vertex numbers
vflag(v1) = 1; vflag(v2) = 1;
}
// map modified vertex flag to each element
//vflag = vflag(EToV);
VFlag.resize(EToV);
VFlag.set_map(EToV, vflag); // (map, values)
// locate elements with at least one modified vertex
//ks = find(sum(vflag,2)>0);
ks = find(VFlag.row_sums(), '>', 0);
// build coordinates of all the corrected nodes
IMat VA=EToV(ks,1), VB=EToV(ks,2), VC=EToV(ks,3);
// FIXME: loading 2D mapped data into 1D vectors
int Nr=VA.num_rows();
va.copy(Nr,VA.data());
vb.copy(Nr,VB.data());
vc.copy(Nr,VC.data());
// Note: outer products of (Vector,MappedRegion1D)
x(All,ks) = 0.5*(-(r+s)*VX(va)+(1.0+r)*VX(vb)+(1.0+s)*VX(vc));
y(All,ks) = 0.5*(-(r+s)*VY(va)+(1.0+r)*VY(vb)+(1.0+s)*VY(vc));
// deform specified faces
for (n=1; n<=NCurveFaces; ++n)
{
k = faces(n,1); f = faces(n,2);
// find vertex locations for this face and tangential coordinate
if (f==1) { v1=EToV(k,1); v2=EToV(k,2); vr=r; }
else if (f==2) { v1=EToV(k,2); v2=EToV(k,3); vr=s; }
else if (f==3) { v1=EToV(k,1); v2=EToV(k,3); vr=s; }
fr = vr(Fmask(All,f));
x1 = VX(v1); y1 = VY(v1); x2 = VX(v2); y2 = VY(v2);
// move vertices at end points of this face to the cylinder
theta1 = atan2(y1-yo, x1-xo); theta2 = atan2(y2-yo, x2-xo);
// check to make sure they are in the same quadrant
if ((theta2 > 0.0) && (theta1 < 0.0)) { theta1 += 2*pi; }
if ((theta1 > 0.0) && (theta2 < 0.0)) { theta2 += 2*pi; }
// distribute N+1 nodes by arc-length along edge
theta = 0.5*theta1*(1.0-fr) + 0.5*theta2*(1.0+fr);
// evaluate deformation of coordinates
fdx = xo + ra*apply(cos,theta) - x(Fmask(All,f),k);
fdy = yo + ra*apply(sin,theta) - y(Fmask(All,f),k);
// build 1D Vandermonde matrix for face nodes and volume nodes
Vface = Vandermonde1D(N, fr); Vvol = Vandermonde1D(N, vr);
// compute unblended volume deformations
vdx = Vvol * (Vface|fdx); vdy = Vvol * (Vface|fdy);
// blend deformation and increment node coordinates
ids = find(abs(1.0-vr), '>', 1e-7); // warp and blend
denom = 1.0-vr(ids);
if (1==f) { numer = -(r(ids)+s(ids)); }
else if (2==f) { numer = (r(ids)+1.0 ); }
else if (3==f) { numer = -(r(ids)+s(ids)); }
blend = numer.dd(denom);
x(ids,k) += (blend.dm(vdx(ids)));
y(ids,k) += (blend.dm(vdy(ids)));
}
// repair other coordinate dependent information
Fx = x(Fmask, All); Fy = y(Fmask, All);
::GeometricFactors2D(x,y,Dr,Ds, rx,sx,ry,sy,J);
Normals2D(); Fscale = sJ.dd(J(Fmask,All));
}
//---------------------------------------------------------
DVec& NDG2D::PoissonIPDGbc2D
(DVec& ubc, //[in]
DVec& qbc //[in]
)
//---------------------------------------------------------
{
// function [OP] = PoissonIPDGbc2D()
// Purpose: Set up the discrete Poisson matrix directly
// using LDG. The operator is set up in the weak form
// build DG derivative matrices
int max_OP = (K*Np*Np*(1+Nfaces));
// initialize parameters
DVec faceR("faceR"), faceS("faceS");
DMat V1D("V1D"), Dx("Dx"),Dy("Dy"), Dn1("Dn1"), mmE_Fm1("mmE(:,Fm1)");
IVec Fm("Fm"), Fm1("Fm1"), fidM("fidM");
double lnx=0.0,lny=0.0,lsJ=0.0,hinv=0.0,gtau=0.0;
int i=0,k1=0,f1=0,id=0;
IVec i1_Nfp = Range(1,Nfp);
double N1N1 = double((N+1)*(N+1));
// build local face matrices
DMat massEdge[4]; // = zeros(Np,Np,Nfaces);
for (i=1; i<=Nfaces; ++i) {
massEdge[i].resize(Np,Np);
}
// face mass matrix 1
Fm = Fmask(All,1); faceR = r(Fm);
V1D = Vandermonde1D(N, faceR);
massEdge[1](Fm,Fm) = inv(V1D*trans(V1D));
// face mass matrix 2
Fm = Fmask(All,2); faceR = r(Fm);
V1D = Vandermonde1D(N, faceR);
massEdge[2](Fm,Fm) = inv(V1D*trans(V1D));
// face mass matrix 3
Fm = Fmask(All,3); faceS = s(Fm);
V1D = Vandermonde1D(N, faceS);
massEdge[3](Fm,Fm) = inv(V1D*trans(V1D));
// build DG right hand side
DVec* pBC = new DVec(Np*K, "bc", OBJ_temp);
DVec& bc = (*pBC); // reference, for syntax
////////////////////////////////////////////////////////////////
umMSG(1, "\n ==> {OP} assembly [bc]: ");
for (k1=1; k1<=K; ++k1)
{
if (! (k1%100)) { umMSG(1, "%d, ",k1); }
// rows1 = outer(Range((k1-1)*Np+1,k1*Np), Ones(NGauss));
// Build element-to-element parts of operator
for (f1=1; f1<=Nfaces; ++f1)
{
if (BCType(k1,f1))
{
////////////////////////added by Kevin ///////////////////////////////
Fm1 = Fmask(All,f1);
fidM = (k1-1)*Nfp*Nfaces + (f1-1)*Nfp + i1_Nfp;
id = 1+(f1-1)*Nfp + (k1-1)*Nfp*Nfaces;
lnx = nx(id); lny = ny(id);
lsJ = sJ(id); hinv = Fscale(id);
Dx = rx(1,k1)*Dr + sx(1,k1)*Ds;
Dy = ry(1,k1)*Dr + sy(1,k1)*Ds;
Dn1 = lnx*Dx + lny*Dy;
//mmE = lsJ*massEdge(:,:,f1);
//bc(All,k1) += (gtau*mmE(All,Fm1) - Dn1'*mmE(All,Fm1))*ubc(fidM);
mmE_Fm1 = massEdge[f1](All,Fm1); mmE_Fm1 *= lsJ;
gtau = 10*N1N1*hinv; // set penalty scaling
//bc(All,k1) += (gtau*mmE_Fm1 - trans(Dn1)*mmE_Fm1) * ubc(fidM);
switch(BCType(k1,f1)){
case BC_Dirichlet:
bc(Np*(k1-1)+Range(1,Np)) += (gtau*mmE_Fm1 - trans(Dn1)*mmE_Fm1)*ubc(fidM);
break;
case BC_Neuman:
bc(Np*(k1-1)+Range(1,Np)) += mmE_Fm1*qbc(fidM);
break;
default:
std::cout<<"warning: boundary condition is incorrect"<<std::endl;
}
}
}
}
return bc;
}
void NDG2D::PoissonIPDGbc2D(
CSd& spOP //[out] sparse operator
)
{
// function [OP] = PoissonIPDGbc2D()
// Purpose: Set up the discrete Poisson matrix directly
// using LDG. The operator is set up in the weak form
// build DG derivative matrices
int max_OP = (K*Np*Np*(1+Nfaces));
//initialize parameters
DVec faceR("faceR"), faceS("faceS");
IVec Fm("Fm"), Fm1("Fm1"), fidM("fidM");
DMat V1D("V1D"); int i=0;
// build local face matrices
DMat massEdge[4]; // = zeros(Np,Np,Nfaces);
for (i=1; i<=Nfaces; ++i) {
massEdge[i].resize(Np,Np);
}
// face mass matrix 1
Fm = Fmask(All,1); faceR = r(Fm);
V1D = Vandermonde1D(N, faceR);
massEdge[1](Fm,Fm) = inv(V1D*trans(V1D));
// face mass matrix 2
Fm = Fmask(All,2); faceR = r(Fm);
V1D = Vandermonde1D(N, faceR);
massEdge[2](Fm,Fm) = inv(V1D*trans(V1D));
// face mass matrix 3
Fm = Fmask(All,3); faceS = s(Fm);
V1D = Vandermonde1D(N, faceS);
massEdge[3](Fm,Fm) = inv(V1D*trans(V1D));
//continue initialize parameters
DMat Dx("Dx"),Dy("Dy"), Dn1("Dn1"), mmE_Fm1("mmE(:,Fm1)");
double lnx=0.0,lny=0.0,lsJ=0.0,hinv=0.0,gtau=0.0;
int k1=0,f1=0,id=0;
IVec i1_Nfp = Range(1,Nfp);
double N1N1 = double((N+1)*(N+1));
// "OP" triplets (i,j,x), extracted to {Ai,Aj,Ax}
IVec OPi(max_OP),OPj(max_OP), Ai,Aj; DVec OPx(max_OP), Ax;
IMat rows1, cols1; Index1D entries; DMat OP11(Np,Nfp, 0.0);
// global node numbering
entries.reset(1,Np*Nfp);
cols1 = outer(Ones(Np), Range(1,Nfp));
umMSG(1, "\n ==> {OP} assembly [bc]: ");
for (k1=1; k1<=K; ++k1)
{
if (! (k1%100)) { umMSG(1, "%d, ",k1); }
rows1 = outer(Range((k1-1)*Np+1,k1*Np), Ones(Nfp));
// Build element-to-element parts of operator
for (f1=1; f1<=Nfaces; ++f1)
{
if (BCType(k1,f1))
{
////////////////////////added by Kevin ///////////////////////////////
Fm1 = Fmask(All,f1);
fidM = (k1-1)*Nfp*Nfaces + (f1-1)*Nfp + i1_Nfp;
id = 1+(f1-1)*Nfp + (k1-1)*Nfp*Nfaces;
lnx = nx(id); lny = ny(id);
lsJ = sJ(id); hinv = Fscale(id);
Dx = rx(1,k1)*Dr + sx(1,k1)*Ds;
Dy = ry(1,k1)*Dr + sy(1,k1)*Ds;
Dn1 = lnx*Dx + lny*Dy;
//mmE = lsJ*massEdge(:,:,f1);
//bc(All,k1) += (gtau*mmE(All,Fm1) - Dn1'*mmE(All,Fm1))*ubc(fidM);
mmE_Fm1 = massEdge[f1](All,Fm1); mmE_Fm1 *= lsJ;
gtau = 10*N1N1*hinv; // set penalty scaling
//bc(All,k1) += (gtau*mmE_Fm1 - trans(Dn1)*mmE_Fm1) * ubc(fidM);
switch(BCType(k1,f1)){
case BC_Dirichlet:
OP11 = gtau*mmE_Fm1 - trans(Dn1)*mmE_Fm1;
break;
case BC_Neuman:
OP11 = mmE_Fm1;
break;
default:
std::cout<<"warning: boundary condition is incorrect"<<std::endl;
}
OPi(entries)=rows1; OPj(entries)=cols1; OPx(entries)=OP11;
entries += (Np*Nfp);
}
cols1 += Nfp;
}
}
umMSG(1, "\n ==> {OPbc} to sparse\n");
entries.reset(1, entries.hi()-(Np*Nfp));
// extract triplets from large buffers
Ai=OPi(entries); Aj=OPj(entries); Ax=OPx(entries);
// These arrays can be HUGE, so force deallocation
OPi.Free(); OPj.Free(); OPx.Free();
// return 0-based sparse result
Ai -= 1; Aj -= 1;
//-------------------------------------------------------
// This operator is not symmetric, and will NOT be
// factorised, only used to create reference RHS's:
//
// refrhsbcPR = spOP1 * bcPR;
// refrhsbcUx = spOP2 * bcUx;
// refrhsbcUy = spOP2 * bcUy;
//
// Load ALL elements (both upper and lower triangles):
//-------------------------------------------------------
spOP.load(Np*K, Nfp*Nfaces*K, Ai,Aj,Ax, sp_All,false, 1e-15,true);
Ai.Free(); Aj.Free(); Ax.Free();
umMSG(1, " ==> {OPbc} ready.\n");
#if (1)
// check on original estimates for nnx
umMSG(1, " ==> max_OP: %12d\n", max_OP);
umMSG(1, " ==> nnz_OP: %12d\n", entries.hi());
#endif
}
startUp1d::startUp1d(int N,int K) {
NODETOL=1e-10;
r = JacobiGL(0,0,N);
Np = N+1;
Nfp = 1;
Nfaces =2;
V = Vandermonde1D(N,r);
Dr = Dmatrix1D(N,r,V);
invV = V.inverse();
MatrixXd Emat(Np,Nfaces*Nfp);
Emat.setZero(Np,2);
Emat(0,0)=1.0;
Emat(Np-1,1)=1.0;
LIFT = V*V.transpose()*Emat;
EToV.setZero(K,2);
VX.setZero(K+1);
EToV = meshGen(0.0,1.0,K,Nv,VX);
ArrayXi va,vb;
va = EToV.col(0);
vb=EToV.col(1);
VectorXd v1(K),v2(K);
{ int temp=0;
for(int i=0; i<K; i++)
{ temp = va(i);
v1(i)= VX(temp-1);
temp = vb(i);
v2(i)= VX(temp-1);
}
}
VectorXd temp1;
temp1.setOnes(N+1,1);
x =temp1*v1.transpose()+ 0.5*((r.array()+1).matrix())*(v2-v1).transpose();
J = Dr*x;
rx = 1.0/J.array();
Fmask.setZero(2);
Fmask(0)=0;
Fmask(1)=Np-1;
std::cout<<"Fx"<<Fmask<<"\n";
Fx.setZero(2,K);
Fx.row(0)=x.row(0);
Fx.row(1)=x.row(Np-1);
std::cout<<"Fx"<<Fx<<"\n";
nx=Normals1D(Nfp,Nfaces,K);
Fscale.setZero(2,K);
Fscale.row(0)=J.row(0);
Fscale.row(1)=J.row(Np-1);
Fscale = 1.0/Fscale.array();
EToEF = Connect1DEToE(EToV);
std::cout<<"Fscale "<<"\n"<<Fscale<<"\n";
std::cout<<"Fscale "<<"\n"<<EToEF<<"\n";
}
