double evaluate_q (const NumberArray<NDIM, RawScalar>& xyz)
{
typedef DualNumber<RawScalar, NumberArray<NDIM, RawScalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberArray<NDIM, FirstDerivType> > SecondDerivType;
typedef DualNumber<SecondDerivType, NumberArray<NDIM, SecondDerivType> > ThirdDerivType;
typedef ThirdDerivType ADScalar;
// Treat velocity as a vector
NumberArray<NDIM, ADScalar> U;
ADScalar x = ADScalar(xyz[0],NumberArrayUnitVector<NDIM, 0, RawScalar>::value());
ADScalar y = ADScalar(xyz[1],NumberArrayUnitVector<NDIM, 1, RawScalar>::value());
ADScalar z = ADScalar(xyz[2],NumberArrayUnitVector<NDIM, 2, RawScalar>::value());
// Arbitrary manufactured solutions
U[0] = a * helper_f(x) + helper_g(y).derivatives()[1] + helper_h(z).derivatives()[2];
U[1] = b * helper_f(x).derivatives()[0] + helper_g(y) + helper_h(z).derivatives()[2];
U[2] = c * helper_f(x).derivatives()[0] + helper_g(y).derivatives()[1] + helper_h(z);
ADScalar P = d * helper_f(x) + helper_gt(y) + helper_h(z);
// NS equation residuals
NumberArray<NDIM, RawScalar> Q_rho_u =
raw_value(
// convective term
divergence(U.outerproduct(U))
// pressure
- P.derivatives()
// dissipation
+ nu * divergence(gradient(U)));
return raw_value(Q_rho_u[0]);
}
Scalar MASA::navierstokes_3d_incompressible<Scalar>::eval_q_u(Scalar x1, Scalar y1, Scalar z1)
{
typedef DualNumber<Scalar, NumberArray<NDIM, Scalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberArray<NDIM, FirstDerivType> > SecondDerivType;
typedef DualNumber<SecondDerivType, NumberArray<NDIM, SecondDerivType> > ThirdDerivType;
typedef ThirdDerivType ADScalar;
// Treat velocity as a vector
NumberArray<NDIM, ADScalar> U;
ADScalar x = ADScalar(x1,NumberArrayUnitVector<NDIM, 0, Scalar>::value());
ADScalar y = ADScalar(y1,NumberArrayUnitVector<NDIM, 1, Scalar>::value());
ADScalar z = ADScalar(z1,NumberArrayUnitVector<NDIM, 2, Scalar>::value());
// Arbitrary manufactured solutions
U[0] = a * helper_f(beta,kx,x) * helper_g(y).derivatives()[1] * helper_h(gamma,kz,z).derivatives()[2];
U[1] = b * helper_f(beta,kx,x).derivatives()[0] * helper_g(y) * helper_h(gamma,kz,z).derivatives()[2];
U[2] = c * helper_f(beta,kx,x).derivatives()[0] * helper_g(y).derivatives()[1] * helper_h(gamma,kz,z);
ADScalar P = d * helper_f(beta,kx,x) * helper_gt(y) * helper_h(gamma,kz,z);
// NS equation residuals
NumberArray<NDIM, Scalar> Q_rho_u =
raw_value(
// convective term
divergence(U.outerproduct(U))
// pressure
- P.derivatives()
// dissipation
+ nu * divergence(gradient(U)));
return -Q_rho_u[0];
}
Scalar MASA::ad_cns_3d_crossterms<Scalar>::eval_q_e(Scalar x1, Scalar y1, Scalar z1) const
{
using std::cos;
typedef DualNumber<Scalar, NumberArray<NDIM, Scalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberArray<NDIM, FirstDerivType> > SecondDerivType;
typedef SecondDerivType ADScalar;
// Treat velocity as a vector
NumberArray<NDIM, ADScalar> U;
const ADScalar x = ADScalar(x1,NumberArrayUnitVector<NDIM, 0, Scalar>::value());
const ADScalar y = ADScalar(y1,NumberArrayUnitVector<NDIM, 1, Scalar>::value());
const ADScalar z = ADScalar(z1,NumberArrayUnitVector<NDIM, 2, Scalar>::value());
// Arbitrary manufactured solution
U[0] = u_0 + u_x * cos(a_ux * PI * x / L) * u_y * cos(a_uy * PI * y / L) * cos(a_uy * PI * z / L);
U[1] = v_0 + v_x * cos(a_vx * PI * x / L) * v_y * cos(a_vy * PI * y / L) * cos(a_vy * PI * z / L);
U[2] = w_0 + w_x * cos(a_wx * PI * x / L) * w_y * cos(a_wy * PI * y / L) * cos(a_wy * PI * z / L);
ADScalar RHO = rho_0 + rho_x * cos(a_rhox * PI * x / L) * rho_y * cos(a_rhoy * PI * y / L) * cos(a_rhoz * PI * z / L);
ADScalar P = p_0 + p_x * cos(a_px * PI * x / L) * p_y * cos(a_py * PI * y / L) * cos(a_pz * PI * z / L);
// Temperature
ADScalar T = P / RHO / R;
// Perfect gas energies
ADScalar E = 1./(Gamma-1.)*P/RHO;
ADScalar ET = E + .5 * U.dot(U);
// The shear strain tensor
NumberArray<NDIM, typename ADScalar::derivatives_type> GradU = gradient(U);
// The identity tensor I
NumberArray<NDIM, NumberArray<NDIM, Scalar> > Identity =
NumberArray<NDIM, Scalar>::identity();
// The shear stress tensor
NumberArray<NDIM, NumberArray<NDIM, ADScalar> > Tau = mu * (GradU + transpose(GradU) - 2./3.*divergence(U)*Identity);
// Temperature flux
NumberArray<NDIM, ADScalar> q = -k * T.derivatives();
// Euler equation residuals
// Scalar Q_rho = raw_value(divergence(RHO*U));
// NumberArray<NDIM, Scalar> Q_rho_u =
// raw_value(divergence(RHO*U.outerproduct(U) - Tau) + P.derivatives());
// energy equation
Scalar Q_rho_e = raw_value(divergence((RHO*ET+P)*U + q - Tau.dot(U)));
return Q_rho_e;
}
bool link_det_lu(
size_t size ,
size_t repeat ,
CppAD::vector<double> &matrix ,
CppAD::vector<double> &gradient )
{
// speed test global option values
if( global_onetape || global_atomic )
return false;
if( global_memory || global_optimize )
return false;
// -----------------------------------------------------
// setup
//
// object for computing determinant
typedef fadbad::B<double> ADScalar;
typedef CppAD::vector<ADScalar> ADVector;
CppAD::det_by_lu<ADScalar> Det(size);
size_t i; // temporary index
size_t m = 1; // number of dependent variables
size_t n = size * size; // number of independent variables
ADScalar detA; // AD value of the determinant
ADVector A(n); // AD version of matrix
// ------------------------------------------------------
while(repeat--)
{ // get the next matrix
CppAD::uniform_01(n, matrix);
// set independent variable values
for(i = 0; i < n; i++)
A[i] = matrix[i];
// compute the determinant
detA = Det(A);
// create function object f : A -> detA
detA.diff(0, m); // index 0 of m dependent variables
// evaluate and return gradient using reverse mode
for(i =0; i < n; i++)
gradient[i] = A[i].d(0); // partial detA w.r.t A[i]
}
// ---------------------------------------------------------
return true;
}
bool link_poly(
size_t size ,
size_t repeat ,
CppAD::vector<double> &a , // coefficients of polynomial
CppAD::vector<double> &z , // polynomial argument value
CppAD::vector<double> &ddp ) // second derivative w.r.t z
{
if( global_option["atomic"] )
return false;
if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] )
return false;
// -----------------------------------------------------
// setup
typedef Sacado::Tay::Taylor<double> ADScalar;
CppAD::vector<ADScalar> A(size);
size_t i; // temporary index
ADScalar Z; // domain space AD value
ADScalar P; // range space AD value
unsigned int order = 2; // order of Taylor coefficients
Z.resize(order+1, false);
P.resize(order+1, false);
// choose the polynomial coefficients
CppAD::uniform_01(size, a);
// AD copy of the polynomial coefficients
for(i = 0; i < size; i++)
A[i] = a[i];
// ------------------------------------------------------
while(repeat--)
{ // get the next argument value
CppAD::uniform_01(1, z);
// independent variable value
Z.fastAccessCoeff(0) = z[0]; // argument value
Z.fastAccessCoeff(1) = 1.; // first order coefficient
Z.fastAccessCoeff(2) = 0.; // second order coefficient
// AD computation of the dependent variable
P = CppAD::Poly(0, A, Z);
// second derivative is twice second order Taylor coefficient
ddp[0] = 2. * P.fastAccessCoeff(2);
}
// ------------------------------------------------------
return true;
}
double evaluate_q (const NumberArray<NDIM, ADScalar>& xyz, const int ret)
{
typedef typename RawType<ADScalar>::value_type Scalar;
const Scalar PI = std::acos(Scalar(-1));
const Scalar k = 1.38;
const Scalar u_0 = 200.23;
const Scalar u_x = 1.1;
const Scalar u_y = 1.08;
const Scalar v_0 = 1.2;
const Scalar v_x = 1.6;
const Scalar v_y = .47;
const Scalar rho_0 = 100.02;
const Scalar rho_x = 2.22;
const Scalar rho_y = 0.8;
const Scalar p_0 = 150.2;
const Scalar p_x = .91;
const Scalar p_y = .623;
const Scalar a_px = .165;
const Scalar a_py = .612;
const Scalar a_rhox = 1.0;
const Scalar a_rhoy = 1.0;
const Scalar a_ux = .1987;
const Scalar a_uy = 1.189;
const Scalar a_vx = 1.91;
const Scalar a_vy = 1.0;
const Scalar Gamma = 1.01;
const Scalar mu = .918;
const Scalar L = 3.02;
const ADScalar& x = xyz[0];
const ADScalar& y = xyz[1];
// Treat velocity as a vector
NumberArray<NDIM, ADScalar> U;
// Arbitrary manufactured solution
U[0] = u_0 + u_x * std::sin(a_ux * PI * x / L) + u_y * std::cos(a_uy * PI * y / L);
U[1] = v_0 + v_x * std::cos(a_vx * PI * x / L) + v_y * std::sin(a_vy * PI * y / L);
ADScalar RHO = rho_0 + rho_x * std::sin(a_rhox * PI * x / L) + rho_y * std::cos(a_rhoy * PI * y / L);
ADScalar P = p_0 + p_x * std::cos(a_px * PI * x / L) + p_y * std::sin(a_py * PI * y / L);
// Perfect gas energies
ADScalar E = 1./(Gamma-1.)*P/RHO;
ADScalar ET = E + .5 * U.dot(U);
// Euler equation residuals
Scalar Q_rho = raw_value(divergence(RHO*U));
NumberArray<NDIM, Scalar> Q_rho_u = raw_value(divergence(RHO*U.outerproduct(U)) + P.derivatives());
// energy equation
Scalar Q_rho_e = raw_value(divergence((RHO*ET+P)*U));
// Scalar Q_rho_e = raw_value(divergence((RHO*U*ET)+(P*U)));
switch(ret)
{
// u
case 1:
return Q_rho_u[0];
break;
// v
case 2:
return Q_rho_u[1];
break;
// rho
case 3:
return Q_rho;
break;
// energy
case 4:
return Q_rho_e;
break;
default:
std::cout << "something is wrong!\n";
exit;
}
return 0;
}
double evaluate_q (const NumberArray<NDIM, ADScalar>& xyz, const int ret)
{
typedef typename RawType<ADScalar>::value_type Scalar;
const Scalar PI = std::acos(Scalar(-1));
const Scalar R = masa_get_param("R");
const Scalar u_0 = masa_get_param("u_0");
const Scalar u_x = masa_get_param("u_x");
const Scalar u_y = masa_get_param("u_y");
const Scalar v_0 = masa_get_param("v_0");
const Scalar v_x = masa_get_param("v_x");
const Scalar v_y = masa_get_param("v_y");
const Scalar rho_0 = masa_get_param("rho_0");
const Scalar rho_x = masa_get_param("rho_x");
const Scalar rho_y = masa_get_param("rho_y");
const Scalar p_0 = masa_get_param("p_0");
const Scalar p_x = masa_get_param("p_x");
const Scalar p_y = masa_get_param("p_y");
const Scalar a_px = masa_get_param("a_px");
const Scalar a_py = masa_get_param("a_py");
const Scalar a_rhox = masa_get_param("a_rhox");
const Scalar a_rhoy = masa_get_param("a_rhoy");
const Scalar a_ux = masa_get_param("a_ux");
const Scalar a_uy = masa_get_param("a_uy");
const Scalar a_vx = masa_get_param("a_vx");
const Scalar a_vy = masa_get_param("a_vy");
const Scalar Gamma = masa_get_param("Gamma");
const Scalar L = masa_get_param("L");
const Scalar mu = masa_get_param("mu");
const Scalar k = masa_get_param("k");
const ADScalar& x = xyz[0];
const ADScalar& y = xyz[1];
// Treat velocity as a vector
NumberArray<NDIM, ADScalar> U;
// Arbitrary manufactured solution
U[0] = u_0 + u_x * std::cos(a_ux * PI * x / L) * u_y * std::cos(a_uy * PI * y / L);
U[1] = v_0 + v_x * std::cos(a_vx * PI * x / L) * v_y * std::cos(a_vy * PI * y / L);
ADScalar RHO = rho_0 + rho_x * std::cos(a_rhox * PI * x / L) * rho_y * std::cos(a_rhoy * PI * y / L);
ADScalar P = p_0 + p_x * std::cos(a_px * PI * x / L) * p_y * std::cos(a_py * PI * y / L);
// Temperature
ADScalar T = P / RHO / R;
// Perfect gas energies
ADScalar E = 1./(Gamma-1.)*P/RHO;
ADScalar ET = E + .5 * U.dot(U);
// The shear strain tensor
NumberArray<NDIM, typename ADScalar::derivatives_type> GradU = gradient(U);
// The identity tensor I
NumberArray<NDIM, NumberArray<NDIM, Scalar> > Identity =
NumberArray<NDIM, Scalar>::identity();
// The shear stress tensor
NumberArray<NDIM, NumberArray<NDIM, ADScalar> > Tau = mu * (GradU + transpose(GradU) - 2./3.*divergence(U)*Identity);
// Temperature flux
NumberArray<NDIM, ADScalar> q = -k * T.derivatives();
// Euler equation residuals
Scalar Q_rho = raw_value(divergence(RHO*U));
NumberArray<NDIM, Scalar> Q_rho_u =
raw_value(divergence(RHO*U.outerproduct(U) - Tau) + P.derivatives());
// energy equation
Scalar Q_rho_e = raw_value(divergence((RHO*ET+P)*U + q - Tau.dot(U)));
switch(ret)
{
// u
case 1:
return Q_rho_u[0];
break;
// v
case 2:
return Q_rho_u[1];
break;
// rho
case 3:
return Q_rho;
break;
// energy
case 4:
return Q_rho_e;
break;
default:
std::cout << "something is wrong!\n";
exit(1);
}
}