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_w(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;
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());
// Treat velocity as a vector
NumberArray<NDIM, ADScalar> U;
// 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());
return Q_rho_u[2];
}
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);
}
}