int main() {
int i,j,k;
int mesh=32, cao=5;
double l=10.0;
double alpha;
int mc=1;
int mx,my,mz;
double s1=0.0, s2 = 0.0;
double G_trunc;
double a1, a2, u2;
for(alpha=0.0;alpha<=3.0;alpha+=0.01) {
for(i=-mesh/2;i<=mesh/2;i++)
for(j=-mesh/2;j<=mesh/2;j++)
for(k=-mesh/2;k<=mesh/2;k++) {
a1 = a2 = 0.0;
for(mx=-mc;mx<=mc;mx++)
for(mx=-mc;mx<=mc;mx++)
for(mx=-mc;mx<=mc;mx++) {
u2 = U(i/mesh+mc,j/mesh+my, k/mesh+mz);
a1 += u2;
a2 += K2(i+mesh*mx, j+mesh*my, k+mesh*mz) * u2;
}
}
}
}
static double
strikeyH0 (MagComp component, const fault_params *fault, const magnetic_params *mag, double xi, double et, double qq, double y, double z)
{
double val;
double h = mag->dcurier;
double qd = y * sd + (fault->fdepth - h) * cd;
double K2_val = K2 (component, 1.0, xi, et, qq);
double log_re_val = log_re (component, 1.0, xi, et, qq);
double J2_val = J2 (component, 1.0, xi, et, qq);
// double L2_val = L2 (component, 1.0, xi, et, qq);
double L2_val = L2 (component, 1.0, xi, et, qq) * cd; // todo: check this!
double M2_val = M2 (component, 1.0, xi, et, qq);
double M3_val = M3 (component, 1.0, xi, et, qq);
double M2y_val = M2y (component, 1.0, xi, et, qq);
double M2z_val = M2z (component, 1.0, xi, et, qq);
val = - (2.0 - alpha4) * K2_val
+ alpha4 * log_re_val * sd + alpha3 * J2_val
- alpha3 * (qd * M2_val + (z - h) * L2_val * sd)
- 2.0 * alpha4 * h * (M2_val * cd - L2_val * sd)
- 4.0 * alpha1 * h * L2_val * sd
+ 2.0 * alpha2 * h * M3_val * sd
+ 2.0 * alpha2 * h * ((qd + h * cd) * M2z_val - (z - 2.0 * h) * M2y_val * sd);
return val;
}
Lattice K2 () {
Lattice K2(6,cpx(0,sqrt(3)));
K2.bond(0,1).bond(0,2).bond(1,2).bond(2,3).bond(2,4).bond(3,4).bond(4,5)
.bond(1,0,coo(1,0)).bond(4,3,coo(1,0)).bond(5,3,coo(1,0)).bond(5,1,coo(0,1)).bond(5,0,coo(1,1));
K2.z[0]=0;
K2.z[1]=.5;
K2.z[2]=cpx(.25,.25);
K2.z[3]=cpx(0,.5);
K2.z[4]=cpx(.5,.5);
K2.z[5]=cpx(.75,.75);
return K2;
}
// Private members
std::vector<float> physics::RK2(float t, const std::vector<float>& x)
{
size_t i,max=x.size();
std::vector<float> a,b,ret=x;
a = K1(t,x);
b = K2(t,x,a);
for(i=0;i<max;i++)
{
ret[i]=x[i]+(a[i]*0.5+b[i]*0.5)*h;
}
return ret;
}
static double
strikeyHIII (MagComp component, const fault_params *fault, const magnetic_params *mag, double xi, double et, double qq, double y, double z)
{
double val;
double h = mag->dcurier;
double qd = y * sd + (fault->fdepth - h) * cd;
double K2_val = K2 (component, 1.0, xi, et, qq);
double log_re_val = log_re (component, 1.0, xi, et, qq);
double J2_val = J2 (component, 1.0, xi, et, qq);
double L2_val = L2 (component, 1.0, xi, et, qq);
double M2_val = M2 (component, 1.0, xi, et, qq);
val = - alpha4 * K2_val - alpha4 * log_re_val * sd - alpha3 * J2_val
+ alpha3 * (qd * M2_val + (z - h) * L2_val * sd * cd);
return val;
}
// Runge-Kutta 4 algorithm
void System::RK4(){
vec2dN K1(nObj), K2(nObj), K3(nObj), K4(nObj);
vec2dN L1(nObj), L2(nObj), L3(nObj), L4(nObj);
vec2dN NewR(nObj), NewV(nObj);
if (nObj == 1){ // If only ONE object
K1 = h*derX(vec2dN(nObj));
L1 = h*(SunInf(vec2dN(nObj)));
K2 = h*derX(L1*0.5);
L2 = h*(SunInf(K1*0.5));
K3 = h*derX(L2*0.5);
L3 = h*(SunInf(K2*0.5));
K4 = h*derX(L3);
L4 = h*(SunInf(K3));
} else { // If more than one object
if (!statSun){ // Sun mobile or not pressent
K1 = h*derX(vec2dN(nObj));
L1 = h*derV(vec2dN(nObj));
K2 = h*derX(L1*0.5);
L2 = h*derV(K1*0.5);
K3 = h*derX(L2*0.5);
L3 = h*derV(L2*0.5);
K4 = h*derX(L3);
L4 = h*derV(K4);
} else { // If the sun is stationary
K1 = h*derX(vec2dN(nObj));
L1 = h*(derV(vec2dN(nObj)) + SunInf(vec2dN(nObj)));
K2 = h*derX(L1*0.5);
L2 = h*(derV(K1*0.5) + SunInf(K1*0.5));
K3 = h*derX(L2*0.5);
L3 = h*(derV(K2*0.5) + SunInf(K2*0.5));
K4 = h*derX(L3);
L4 = h*(derV(K3) + SunInf(K3));
}
}
for (int i = 0 ; i < nObj ; i++){
NewR[i] = sys[i].relR + (K1[i] + 2*K2[i] + 2*K3[i] + K4[i])/(double)6;
NewV[i] = sys[i].relV + (L1[i] + 2*L2[i] + 2*L3[i] + L4[i])/(double)6;
}
calc_potential();
for (int i = 0 ; i < nObj ; i++){
sys[i].update(NewR[i], NewV[i], sys[i].relT+h);
}
}
//======================================================================
tensor EightNode_Brick_u_p::getStiffnessTensorH( )
{
int K2_dim[] = {Num_Nodes, Num_Nodes};
tensor K2(2,K2_dim,0.0);
tensor Kk2(2,K2_dim,0.0);
double r = 0.0;
double rw = 0.0;
double s = 0.0;
double sw = 0.0;
double t = 0.0;
double tw = 0.0;
double weight = 0.0;
double det_of_Jacobian = 0.0;
tensor Jacobian;
tensor dhGlobal;
int GP_c_r, GP_c_s, GP_c_t;
for( GP_c_r = 0 ; GP_c_r < Num_IntegrationPts; GP_c_r++ ) {
r = pts[GP_c_r];
rw = wts[GP_c_r];
for( GP_c_s = 0 ; GP_c_s < Num_IntegrationPts; GP_c_s++ ) {
s = pts[GP_c_s];
sw = wts[GP_c_s];
for( GP_c_t = 0 ; GP_c_t < Num_IntegrationPts; GP_c_t++ ) {
t = pts[GP_c_t];
tw = wts[GP_c_t];
Jacobian = this->Jacobian_3D(r,s,t);
det_of_Jacobian = Jacobian.determinant();
weight = rw * sw * tw * det_of_Jacobian ;
dhGlobal = this->dh_Global(r,s,t);
Kk2 = dhGlobal("ai")*perm("ij");
Kk2 = Kk2("aj")*dhGlobal("kj");
K2 += (Kk2*weight);
}
}
}
return K2;
}
ECIES::ECIES (OCTETSTR& M, ECPubKey& pk) {
OCTETSTR P1, P2; // These are 0
ECPrivKey u (pk.dp);
V = ECPubKey(u);
F2M z = ECSVDP_DH (pk.dp, u.s, pk.W);
OCTETSTR Z = FE2OSP (z);
OCTETSTR K = KDF2_SURDOC (Z, 32, P1); // 256 bits
OCTETSTR K1 (16); // 128 bit symmetric encryption key
OCTETSTR K2 (16); // 128 bit MAC key
for (int j=0; j<K1.size();j++) {
K1[j] = K[j];
}
for (int k=0; k<K2.size();k++) {
K2[k] = K[k+K1.size()];
}
C = AES_CBC_IV0_Encrypt (K1, M);
T = MAC1 (K2, C||P2);
}
// Throws ECIES_Err if the tag is invalid
OCTETSTR ECIES::decrypt (ECPrivKey& sk) {
OCTETSTR P1, P2; // These are 0
F2M z = ECSVDP_DH (sk.dp, sk.s, V.W);
OCTETSTR Z = FE2OSP (z);
OCTETSTR K = KDF2_SURDOC (Z, 32, P1); // 256 bits
OCTETSTR K1 (16); // 128 bit symmetric encryption key
OCTETSTR K2 (16); // 128 bit MAC key
for (int j=0; j<K1.size();j++) {
K1[j] = K[j];
}
for (int k=0; k<K2.size();k++) {
K2[k] = K[k+K1.size()];
}
OCTETSTR M = AES_CBC_IV0_Decrypt (K1, C);
if (T != MAC1 (K2, C||P2)) {
throw borzoiException ("ECIES: tag invalid");
}
return M;
}
int R() {
int SG;
int tu;
int b;
int cbnn;
int fJA;
int Ywh;
int Sd3i;
int U;
int FTe;
;
if (AgC9 > + (Y0V(UnE, 791438648 + cK(517618502, + N_ != Ed() != - (Yk(((883538282)), nBa)), sdDM(kC, (1604897559), ! ! 528836364 / (1815076270) / 1477268768), n), psl, - 126855483))) while (om(AZ)) {
int xF;
int yd;
int xEmV;
int vc;
int m9;
while (2044928990) while (- 644557172 + 1573824677 + 1727264726 < TvAP(1980609521, Jy47, C, 953854953, - WyD(RlhU(LY0), + ipA(G, (Vg((1882502790), (1790689388) == 711715734 / (_) != + ! (134548752)))), nk1(((2078180300)) - + - 1230367323 - gD13, pK38 / 1377998756, m4G(1127784867) > u, (QSs()), 1389625403), 929895424, 895835811 < dW) * - 1339857856) / 2045295101) while (pLb) while (+ 1321345616) return ! 708468611;
(J);
return eUY;
continue;
(bRvz = 1838176344);
r(F + ! 196992386, Gg);
if (1419330106) ! (- (uG)) <= ! 996971325;
else T((- ! 2092297653 <= AA >= ! 1494541558 == o((! + v7nD))), 1818433226);
}
else break;
;
;
if (! (! cQ63(1853496451, i(DW9, 988295904 > _Gv, Wlbr, b) / ! ((O(xl))) - - O(+ a_O > 318640956, 1005354893, 167517361) / If, GDD, u, B) * B) + 443946612 + (dN(BFD3(mg <= 1303591176 + hFH2, x) % hch > 1053610009 / RaZ0(ZC7O((720576768)), 124325761, K(! C, 1901412912 * 1202992483, + (+ + e * 389490648), + 1244843051 < (sm = dH), W9(1583501857)), - ! sIs, 1297610228)))) lYAi(1443174874, U8R, + 925787186);
else continue;
continue;
if (+ ! 329152016 + K2()) continue;
else ;
continue;
continue;
}
TEST_F(fisheyeTest, stereoCalibrateFixIntrinsic)
{
const int n_images = 34;
const std::string folder =combine(datasets_repository_path, "calib-3_stereo_from_JY");
std::vector<std::vector<cv::Point2d> > leftPoints(n_images);
std::vector<std::vector<cv::Point2d> > rightPoints(n_images);
std::vector<std::vector<cv::Point3d> > objectPoints(n_images);
cv::FileStorage fs_left(combine(folder, "left.xml"), cv::FileStorage::READ);
CV_Assert(fs_left.isOpened());
for(int i = 0; i < n_images; ++i)
fs_left[cv::format("image_%d", i )] >> leftPoints[i];
fs_left.release();
cv::FileStorage fs_right(combine(folder, "right.xml"), cv::FileStorage::READ);
CV_Assert(fs_right.isOpened());
for(int i = 0; i < n_images; ++i)
fs_right[cv::format("image_%d", i )] >> rightPoints[i];
fs_right.release();
cv::FileStorage fs_object(combine(folder, "object.xml"), cv::FileStorage::READ);
CV_Assert(fs_object.isOpened());
for(int i = 0; i < n_images; ++i)
fs_object[cv::format("image_%d", i )] >> objectPoints[i];
fs_object.release();
cv::Matx33d theR;
cv::Vec3d theT;
int flag = 0;
flag |= cv::fisheye::CALIB_RECOMPUTE_EXTRINSIC;
flag |= cv::fisheye::CALIB_CHECK_COND;
flag |= cv::fisheye::CALIB_FIX_SKEW;
flag |= cv::fisheye::CALIB_FIX_INTRINSIC;
cv::Matx33d K1 (561.195925927249, 0, 621.282400272412,
0, 562.849402029712, 380.555455380889,
0, 0, 1);
cv::Matx33d K2 (560.395452535348, 0, 678.971652040359,
0, 561.90171021422, 380.401340535339,
0, 0, 1);
cv::Vec4d D1 (-7.44253716539556e-05, -0.00702662033932424, 0.00737569823650885, -0.00342230256441771);
cv::Vec4d D2 (-0.0130785435677431, 0.0284434505383497, -0.0360333869900506, 0.0144724062347222);
cv::fisheye::stereoCalibrate(objectPoints, leftPoints, rightPoints,
K1, D1, K2, D2, imageSize, theR, theT, flag,
cv::TermCriteria(3, 12, 0));
cv::Matx33d R_correct( 0.9975587205950972, 0.06953016383322372, 0.006492709911733523,
-0.06956823121068059, 0.9975601387249519, 0.005833595226966235,
-0.006071257768382089, -0.006271040135405457, 0.9999619062167968);
cv::Vec3d T_correct(-0.099402724724121, 0.00270812139265413, 0.00129330292472699);
EXPECT_MAT_NEAR(theR, R_correct, 1e-10);
EXPECT_MAT_NEAR(theT, T_correct, 1e-10);
}
FLOAT_TYPE C(int nx, int ny, int nz, FLOAT_TYPE l, FLOAT_TYPE alpha) {
FLOAT_TYPE k2 = K2(nx, ny, nz,l);
FLOAT_TYPE phi = Phi(nx,ny,nz,l,alpha);
return k2 * SQR(phi);
}
FLOAT_TYPE Phi(int nx, int ny, int nz, FLOAT_TYPE l, FLOAT_TYPE alpha) {
FLOAT_TYPE k2 = K2(nx, ny, nz, l);
return (4*PI/k2) * exp(-k2/(4*alpha*alpha));
}
static double
strikey0 (MagComp component, double xi, double et, double qq)
{
return 2.0 * K2 (component, 1.0, xi, et, qq);
}
vector<SPACETYPE> RungeKutta4::Solve(vector<SPACETYPE> initialValue, TIMETYPE finalTime)
{
// N is the number of spatial gridpoints
int N = initialValue.size();
if (_spatialSolver==NULL)
return initialValue;
//mSolution.push_back(initialValue);
// vector<vector<complex<double> > > mSolution(_timeSteps);
double time=0;
double h = finalTime/(_timeSteps-1);
vector<SPACETYPE> K1(N), K2(N), K3(N), K4(N), Temp(N), Unew(N);
for(int i=1; i<_timeSteps; i++)
{
time+=h;
//K1
K1 = _spatialSolver->GetSpatialSolution(initialValue);
for(int j=0;j<N;j++)
{
K1[j] = h*K1[j];
}
//K2
for(int j=0;j<N;j++)
{
Temp[j] = initialValue[j] + K1[j]/2.0;
}
Temp = _spatialSolver->GetSpatialSolution(Temp);
for(int j=0;j<N;j++)
{
K2[j] = h*Temp[j];
}
//K3
for(int j=0;j<N;j++)
{
Temp[j] = initialValue[j] + K2[j]/2.0;
}
Temp = _spatialSolver->GetSpatialSolution(Temp);
for(int j=0;j<N;j++)
{
K3[j] = h*Temp[j];
}
//K4
for(int j=0;j<N;j++)
{
Temp[j] = initialValue[j] + K3[j];
}
Temp = _spatialSolver->GetSpatialSolution(Temp);
for(int j=0;j<N;j++)
{
K4[j] = h*Temp[j];
}
//New
for(int j=0;j<N;j++)
{
Unew[j] = initialValue[j]+(1/6.0)*(K1[j]+2.0*(K2[j]+K3[j])+K4[j]);
}
//mSolution.push_back(Unew);
initialValue = Unew;
}
return initialValue;
}
void BeamColumnJoint3d::formK(Vector k)
{
// develops the element stiffness matrix
Matrix kSprDiag(13,13);
kSprDiag.Zero();
Matrix kRForce(16,16);
kRForce.Zero();
Matrix kRFT1(4,12);
kRFT1.Zero();
Matrix kRFT2(4,4);
kRFT2.Zero();
Matrix kRFT3(12,4);
kRFT3.Zero();
Matrix I(4,4);
I.Zero();
Matrix kRSTinv(4,4);
kRSTinv.Zero();
Matrix kRF(12,12);
kRF.Zero();
Matrix K2Temp(12,4);
K2Temp.Zero();
Matrix K2(12,12);
K2.Zero();
matDiag(k,kSprDiag);
kRForce.addMatrixTripleProduct(0.0,BCJoint,kSprDiag,1.0); // kRForce = BCJoint'*kSprDiag*BCJoint
kRFT2.Extract(kRForce,12,12,1.0);
kRFT1.Extract(kRForce,12,0,1.0);
kRFT3.Extract(kRForce,0,12,1.0);
kRF.Extract(kRForce,0,0,1.0);
for (int ic=0; ic<4; ic++)
{
I(ic,ic) = 1.0;
}
kRFT2.Solve(I,kRSTinv);
K2Temp.addMatrixProduct(0.0,kRFT3,kRSTinv,1.0);
// done for some idiotic reason
for(int i = 0; i < 12; ++i)
{
for(int j = 0; j < 4; ++j)
{
if(fabs(K2Temp(i,j)) < 1e-15)
K2Temp(i,j) = 0.;
}
}
K2.addMatrixProduct(0.0,K2Temp,kRFT1,1.0); // K2 = kRFT3*kRSTinv*kRFT1
// done for some idiotic reason
for(int i1 = 0; i1 < 12; ++i1)
{
for(int j1 = 0; j1 < 12; ++j1)
{
if(fabs(K2(i1,j1)) < 1e-15)
K2(i1,j1) = 0.;
}
}
kRF.addMatrix(1.0,K2,-1.0); // kRF = kRF - K2
K.addMatrixTripleProduct(0.0,Transf,kRF,1.0); // K = Transf'*kRF*Transf
}
void rk4(
Vector &Xcurrent,
const double t,
const double stepSize,
Vector &Xnext,
orbiterEquationsOfMotion &derivatives )
{
const double h = stepSize;
const int numberOfElements = Xcurrent.size( );
// Evaluate K1 step in RK4 algorithm.
Vector dXdtCurrent( numberOfElements );
Vector K1( numberOfElements );
derivatives( t, Xcurrent, dXdtCurrent );
for( int i = 0; i < numberOfElements; i++ )
{
K1[ i ] = h * dXdtCurrent[ i ];
}
// Evaluate K2 step in RK4 algorithm.
Vector dXdt_K2( numberOfElements );
Vector K2( numberOfElements );
const double t_K2 = t + 0.5 * h;
Vector X_K2( numberOfElements );
for( int i = 0; i < numberOfElements; i++ )
{
X_K2[ i ] = Xcurrent[ i ] + 0.5 * K1[ i ];
}
derivatives( t_K2, X_K2, dXdt_K2 );
for( int i = 0; i < numberOfElements; i++ )
{
K2[ i ] = h * dXdt_K2[ i ];
}
// Evaluate K3 step in RK4 algorithm.
Vector dXdt_K3( numberOfElements );
Vector K3( numberOfElements );
const double t_K3 = t + 0.5 * h;
Vector X_K3( numberOfElements );
for( int i = 0; i < numberOfElements; i++ )
{
X_K3[ i ] = Xcurrent[ i ] + 0.5 * K2[ i ];
}
derivatives( t_K3, X_K3, dXdt_K3 );
for( int i = 0; i < numberOfElements; i++ )
{
K3[ i ] = h * dXdt_K3[ i ];
}
// Evaluate K4 step in RK4 algorithm.
Vector dXdt_K4( numberOfElements );
Vector K4( numberOfElements );
const double t_K4 = t + h;
Vector X_K4( numberOfElements );
for( int i = 0; i < numberOfElements; i++ )
{
X_K4[ i ] = Xcurrent[ i ] + K3[ i ];
}
derivatives( t_K4, X_K4, dXdt_K4 );
for( int i = 0; i < numberOfElements; i++ )
{
K4[ i ] = h * dXdt_K4[ i ];
}
// Final step, evaluate the weighted summation.
for( int i = 0; i < numberOfElements; i++ )
{
Xnext[ i ] = Xcurrent[ i ]
+ ( 1.0 / 6.0 ) * K1[ i ]
+ ( 1.0 / 3.0 ) * K2[ i ]
+ ( 1.0 / 3.0 ) * K3[ i ]
+ ( 1.0 / 6.0 ) * K4[ i ];
}
}
void Foam::kineticTheoryModel::solve(const volTensorField& gradUat)
{
if (!kineticTheory_)
{
return;
}
const scalar sqrtPi = sqrt(constant::mathematical::pi);
surfaceScalarField phi(1.5*rhoa_*phia_*fvc::interpolate(alpha_));
volTensorField dU(gradUat.T()); //fvc::grad(Ua_);
volSymmTensorField D(symm(dU));
// NB, drag = K*alpha*beta,
// (the alpha and beta has been extracted from the drag function for
// numerical reasons)
volScalarField Ur(mag(Ua_ - Ub_));
volScalarField betaPrim(alpha_*(1.0 - alpha_)*draga_.K(Ur));
// Calculating the radial distribution function (solid volume fraction is
// limited close to the packing limit, but this needs improvements)
// The solution is higly unstable close to the packing limit.
gs0_ = radialModel_->g0
(
min(max(alpha_, scalar(1e-6)), alphaMax_ - 0.01),
alphaMax_
);
// particle pressure - coefficient in front of Theta (Eq. 3.22, p. 45)
volScalarField PsCoeff
(
granularPressureModel_->granularPressureCoeff
(
alpha_,
gs0_,
rhoa_,
e_
)
);
// 'thermal' conductivity (Table 3.3, p. 49)
kappa_ = conductivityModel_->kappa(alpha_, Theta_, gs0_, rhoa_, da_, e_);
// particle viscosity (Table 3.2, p.47)
mua_ = viscosityModel_->mua(alpha_, Theta_, gs0_, rhoa_, da_, e_);
dimensionedScalar Tsmall
(
"small",
dimensionSet(0 , 2 ,-2 ,0 , 0, 0, 0),
1.0e-6
);
dimensionedScalar TsmallSqrt = sqrt(Tsmall);
volScalarField ThetaSqrt(sqrt(Theta_));
// dissipation (Eq. 3.24, p.50)
volScalarField gammaCoeff
(
12.0*(1.0 - sqr(e_))*sqr(alpha_)*rhoa_*gs0_*(1.0/da_)*ThetaSqrt/sqrtPi
);
// Eq. 3.25, p. 50 Js = J1 - J2
volScalarField J1(3.0*betaPrim);
volScalarField J2
(
0.25*sqr(betaPrim)*da_*sqr(Ur)
/(max(alpha_, scalar(1e-6))*rhoa_*sqrtPi*(ThetaSqrt + TsmallSqrt))
);
// bulk viscosity p. 45 (Lun et al. 1984).
lambda_ = (4.0/3.0)*sqr(alpha_)*rhoa_*da_*gs0_*(1.0+e_)*ThetaSqrt/sqrtPi;
// stress tensor, Definitions, Table 3.1, p. 43
volSymmTensorField tau(2.0*mua_*D + (lambda_ - (2.0/3.0)*mua_)*tr(D)*I);
if (!equilibrium_)
{
// construct the granular temperature equation (Eq. 3.20, p. 44)
// NB. note that there are two typos in Eq. 3.20
// no grad infront of Ps
// wrong sign infront of laplacian
fvScalarMatrix ThetaEqn
(
fvm::ddt(1.5*alpha_*rhoa_, Theta_)
+ fvm::div(phi, Theta_, "div(phi,Theta)")
==
fvm::SuSp(-((PsCoeff*I) && dU), Theta_)
+ (tau && dU)
+ fvm::laplacian(kappa_, Theta_, "laplacian(kappa,Theta)")
+ fvm::Sp(-gammaCoeff, Theta_)
+ fvm::Sp(-J1, Theta_)
+ fvm::Sp(J2/(Theta_ + Tsmall), Theta_)
);
ThetaEqn.relax();
ThetaEqn.solve();
}
else
{
// equilibrium => dissipation == production
// Eq. 4.14, p.82
volScalarField K1(2.0*(1.0 + e_)*rhoa_*gs0_);
volScalarField K3
(
0.5*da_*rhoa_*
(
(sqrtPi/(3.0*(3.0-e_)))
*(1.0 + 0.4*(1.0 + e_)*(3.0*e_ - 1.0)*alpha_*gs0_)
+1.6*alpha_*gs0_*(1.0 + e_)/sqrtPi
)
);
volScalarField K2
(
4.0*da_*rhoa_*(1.0 + e_)*alpha_*gs0_/(3.0*sqrtPi) - 2.0*K3/3.0
);
volScalarField K4(12.0*(1.0 - sqr(e_))*rhoa_*gs0_/(da_*sqrtPi));
volScalarField trD(tr(D));
volScalarField tr2D(sqr(trD));
volScalarField trD2(tr(D & D));
volScalarField t1(K1*alpha_ + rhoa_);
volScalarField l1(-t1*trD);
volScalarField l2(sqr(t1)*tr2D);
volScalarField l3
(
4.0
*K4
*max(alpha_, scalar(1e-6))
*(2.0*K3*trD2 + K2*tr2D)
);
Theta_ = sqr((l1 + sqrt(l2 + l3))/(2.0*(alpha_ + 1.0e-4)*K4));
}
Theta_.max(1.0e-15);
Theta_.min(1.0e+3);
volScalarField pf
(
frictionalStressModel_->frictionalPressure
(
alpha_,
alphaMinFriction_,
alphaMax_,
Fr_,
eta_,
p_
)
);
PsCoeff += pf/(Theta_+Tsmall);
PsCoeff.min(1.0e+10);
PsCoeff.max(-1.0e+10);
// update particle pressure
pa_ = PsCoeff*Theta_;
// frictional shear stress, Eq. 3.30, p. 52
volScalarField muf
(
frictionalStressModel_->muf
(
alpha_,
alphaMax_,
pf,
D,
phi_
)
);
// add frictional stress
mua_ += muf;
mua_.min(1.0e+2);
mua_.max(0.0);
Info<< "kinTheory: max(Theta) = " << max(Theta_).value() << endl;
volScalarField ktn(mua_/rhoa_);
Info<< "kinTheory: min(nua) = " << min(ktn).value()
<< ", max(nua) = " << max(ktn).value() << endl;
Info<< "kinTheory: min(pa) = " << min(pa_).value()
<< ", max(pa) = " << max(pa_).value() << endl;
}
