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// Gmsh - Copyright (C) 1997-2021 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// issues on https://gitlab.onelab.info/gmsh/gmsh/issues.
#include "Lambda2.h"
#include "Numeric.h"
StringXNumber Lambda2Options_Number[] = {
{GMSH_FULLRC, "Eigenvalue", nullptr, 2.},
{GMSH_FULLRC, "View", nullptr, -1.}};
extern "C" {
GMSH_Plugin *GMSH_RegisterLambda2Plugin() { return new GMSH_Lambda2Plugin(); }
}
std::string GMSH_Lambda2Plugin::getHelp() const
{
return "Plugin(Lambda2) computes the eigenvalues "
"Lambda(1,2,3) of the tensor (S_ik S_kj + "
"Om_ik Om_kj), where S_ij = 0.5 (ui,j + uj,i) "
"and Om_ij = 0.5 (ui,j - uj,i) are respectively "
"the symmetric and antisymmetric parts of the "
"velocity gradient tensor.\n\n"
"Vortices are well represented by regions where "
"Lambda(2) is negative.\n\n"
"If `View' contains tensor elements, the plugin "
"directly uses the tensors as the values of the "
"velocity gradient tensor; if `View' contains "
"vector elements, the plugin uses them as the "
"velocities from which to derive the velocity "
"gradient tensor.\n\n"
"If `View' < 0, the plugin is run on the current view.\n\n"
"Plugin(Lambda2) creates one new list-based view.";
}
int GMSH_Lambda2Plugin::getNbOptions() const
{
return sizeof(Lambda2Options_Number) / sizeof(StringXNumber);
}
StringXNumber *GMSH_Lambda2Plugin::getOption(int iopt)
{
return &Lambda2Options_Number[iopt];
}
static int inv3x3tran(double mat[3][3], double inv[3][3], double *det)
{
double ud;
*det = det3x3(mat);
if(*det == 0.0) return (0);
ud = 1. / (*det);
inv[0][0] = ud * (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1]);
inv[0][1] = -ud * (mat[1][0] * mat[2][2] - mat[1][2] * mat[2][0]);
inv[0][2] = ud * (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]);
inv[1][0] = -ud * (mat[0][1] * mat[2][2] - mat[0][2] * mat[2][1]);
inv[1][1] = ud * (mat[0][0] * mat[2][2] - mat[0][2] * mat[2][0]);
inv[1][2] = -ud * (mat[0][0] * mat[2][1] - mat[0][1] * mat[2][0]);
inv[2][0] = ud * (mat[0][1] * mat[1][2] - mat[0][2] * mat[1][1]);
inv[2][1] = -ud * (mat[0][0] * mat[1][2] - mat[0][2] * mat[1][0]);
inv[2][2] = ud * (mat[0][0] * mat[1][1] - mat[0][1] * mat[1][0]);
return 1;
}
static void eigen(std::vector<double> &inList, int inNb,
std::vector<double> &outList, int *outNb, int nbTime,
int nbNod, int nbComp, int lam)
{
if(!inNb || (nbComp != 3 && nbComp != 9) || lam < 1 || lam > 3) return;
// loop on elements
int nb = inList.size() / inNb;
for(std::size_t i = 0; i < inList.size(); i += nb) {
// copy node coordinates
for(int j = 0; j < 3 * nbNod; j++) outList.push_back(inList[i + j]);
// loop on time steps
for(int j = 0; j < nbTime; j++) {
double *x = &inList[i];
double *y = &inList[i + nbNod];
double *z = &inList[i + 2 * nbNod];
double GradVel[3][3];
if(nbComp == 9) {
// val is the velocity gradient tensor: we assume that it is
// constant per element
double *v = &inList[i + 3 * nbNod + nbNod * nbComp * j + nbComp * 0];
GradVel[0][0] = v[0];
GradVel[0][1] = v[1];
GradVel[0][2] = v[2];
GradVel[1][0] = v[3];
GradVel[1][1] = v[4];
GradVel[1][2] = v[5];
GradVel[2][0] = v[6];
GradVel[2][1] = v[7];
GradVel[2][2] = v[8];
}
else if(nbComp == 3) {
// FIXME: the following could be greatly simplified and
// generalized by using the classes in shapeFunctions.h
// val contains the velocities: compute the gradient tensor
// from them
const int MAX_NOD = 4;
double val[3][MAX_NOD];
for(int k = 0; k < nbNod; k++) {
double *v = &inList[i + 3 * nbNod + nbNod * nbComp * j + nbComp * k];
for(int l = 0; l < 3; l++) { val[l][k] = v[l]; }
}
// compute gradient of shape functions
double GradPhi_x[MAX_NOD][3];
double GradPhi_ksi[MAX_NOD][3];
double dx_dksi[3][3];
double dksi_dx[3][3];
double det;
if(nbNod == 3) { // triangles
double a[3], b[3], cross[3];
a[0] = x[1] - x[0];
a[1] = y[1] - y[0];
a[2] = z[1] - z[0];
b[0] = x[2] - x[0];
b[1] = y[2] - y[0];
b[2] = z[2] - z[0];
prodve(a, b, cross);
dx_dksi[0][0] = x[1] - x[0];
dx_dksi[0][1] = x[2] - x[0];
dx_dksi[0][2] = cross[0];
dx_dksi[1][0] = y[1] - y[0];
dx_dksi[1][1] = y[2] - y[0];
dx_dksi[1][2] = cross[1];
dx_dksi[2][0] = z[1] - z[0];
dx_dksi[2][1] = z[2] - z[0];
dx_dksi[2][2] = cross[2];
inv3x3tran(dx_dksi, dksi_dx, &det);
GradPhi_ksi[0][0] = -1;
GradPhi_ksi[0][1] = -1;
GradPhi_ksi[0][2] = 0;
GradPhi_ksi[1][0] = 1;
GradPhi_ksi[1][1] = 0;
GradPhi_ksi[1][2] = 0;
GradPhi_ksi[2][0] = 0;
GradPhi_ksi[2][1] = 1;
GradPhi_ksi[2][2] = 0;
}
else if(nbNod == 4) { // tetrahedra
dx_dksi[0][0] = x[1] - x[0];
dx_dksi[0][1] = x[2] - x[0];
dx_dksi[0][2] = x[3] - x[0];
dx_dksi[1][0] = y[1] - y[0];
dx_dksi[1][1] = y[2] - y[0];
dx_dksi[1][2] = y[3] - y[0];
dx_dksi[2][0] = z[1] - z[0];
dx_dksi[2][1] = z[2] - z[0];
dx_dksi[2][2] = z[3] - z[0];
inv3x3tran(dx_dksi, dksi_dx, &det);
GradPhi_ksi[0][0] = -1;
GradPhi_ksi[0][1] = -1;
GradPhi_ksi[0][2] = -1;
GradPhi_ksi[1][0] = 1;
GradPhi_ksi[1][1] = 0;
GradPhi_ksi[1][2] = 0;
GradPhi_ksi[2][0] = 0;
GradPhi_ksi[2][1] = 1;
GradPhi_ksi[2][2] = 0;
GradPhi_ksi[3][0] = 0;
GradPhi_ksi[3][1] = 0;
GradPhi_ksi[3][2] = 1;
}
else {
Msg::Error("Lambda2 not ready for this type of element");
return;
}
for(int k = 0; k < nbNod; k++) {
for(int l = 0; l < 3; l++) {
GradPhi_x[k][l] = 0.0;
for(int m = 0; m < 3; m++) {
GradPhi_x[k][l] += GradPhi_ksi[k][m] * dksi_dx[l][m];
}
}
}
// compute gradient of velocities
for(int k = 0; k < 3; k++) {
for(int l = 0; l < 3; l++) {
GradVel[k][l] = 0.0;
for(int m = 0; m < nbNod; m++) {
GradVel[k][l] += val[k][m] * GradPhi_x[m][l];
}
}
}
}
else
for(int k = 0; k < 3; k++)
for(int l = 0; l < 3; l++) GradVel[k][l] = 0.0;
// compute the sym and antisymetric parts
double sym[3][3];
double asym[3][3];
for(int m = 0; m < 3; m++) {
for(int n = 0; n < 3; n++) {
sym[m][n] = 0.5 * (GradVel[m][n] + GradVel[n][m]);
asym[m][n] = 0.5 * (GradVel[m][n] - GradVel[n][m]);
}
}
double a[3][3];
for(int m = 0; m < 3; m++) {
for(int n = 0; n < 3; n++) {
a[m][n] = 0.0;
for(int l = 0; l < 3; l++)
a[m][n] += sym[m][l] * sym[l][n] + asym[m][l] * asym[l][n];
}
}
// compute the eigenvalues
double lambda[3];
eigenvalue(a, lambda);
for(int k = 0; k < nbNod; k++) outList.push_back(lambda[lam - 1]);
}
(*outNb)++;
}
}
PView *GMSH_Lambda2Plugin::execute(PView *v)
{
int ev = (int)Lambda2Options_Number[0].def;
int iView = (int)Lambda2Options_Number[1].def;
PView *v1 = getView(iView, v);
if(!v1) return v;
PViewDataList *data1 = getDataList(v1);
if(!data1) return v;
PView *v2 = new PView();
PViewDataList *data2 = getDataList(v2);
if(!data2) return v;
// assume that the tensors contain the velocity gradient tensor
int nts = data1->getNumTimeSteps();
eigen(data1->TP, data1->NbTP, data2->SP, &data2->NbSP, nts, 1, 9, ev);
eigen(data1->TL, data1->NbTL, data2->SL, &data2->NbSL, nts, 2, 9, ev);
eigen(data1->TT, data1->NbTT, data2->ST, &data2->NbST, nts, 3, 9, ev);
eigen(data1->TQ, data1->NbTQ, data2->SQ, &data2->NbSQ, nts, 4, 9, ev);
eigen(data1->TS, data1->NbTS, data2->SS, &data2->NbSS, nts, 4, 9, ev);
eigen(data1->TH, data1->NbTH, data2->SH, &data2->NbSH, nts, 8, 9, ev);
eigen(data1->TI, data1->NbTI, data2->SI, &data2->NbSI, nts, 6, 9, ev);
eigen(data1->TY, data1->NbTY, data2->SY, &data2->NbSY, nts, 5, 9, ev);
// assume that the vectors contain the velocities
// FIXME: only implemented for tri/tet at the moment
// eigen(data1->VP, data1->NbVP, data2->SP, &data2->NbSP, nts, 1, 3, ev);
// eigen(data1->VL, data1->NbVL, data2->SL, &data2->NbSL, nts, 2, 3, ev);
eigen(data1->VT, data1->NbVT, data2->ST, &data2->NbST, nts, 3, 3, ev);
// eigen(data1->VQ, data1->NbVQ, data2->SQ, &data2->NbSQ, nts, 4, 3, ev);
eigen(data1->VS, data1->NbVS, data2->SS, &data2->NbSS, nts, 4, 3, ev);
// eigen(data1->VH, data1->NbVH, data2->SH, &data2->NbSH, nts, 8, 3, ev);
// eigen(data1->VI, data1->NbVI, data2->SI, &data2->NbSI, nts, 6, 3, ev);
// eigen(data1->VY, data1->NbVY, data2->SY, &data2->NbSY, nts, 5, 3, ev);
data2->Time = data1->Time;
data2->setName(data1->getName() + "_Lambda2");
data2->setFileName(data1->getName() + "_Lambda2.pos");
data2->finalize();
return v2;
}
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