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ad_cns_3d_les.cpp
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// -*-c++-*-
//-----------------------------------------------------------------------bl-
//--------------------------------------------------------------------------
//
// MASA - Manufactured Analytical Solutions Abstraction Library
//
// Copyright (C) 2010,2011,2012,2013 The PECOS Development Team
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the Version 2.1 GNU Lesser General
// Public License as published by the Free Software Foundation.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc. 51 Franklin Street, Fifth Floor,
// Boston, MA 02110-1301 USA
//
//-----------------------------------------------------------------------el-
#include <masa_internal.h>
#ifdef HAVE_METAPHYSICL
#include <ad_masa.h>
typedef ShadowNumber<double, long double> RawScalar;
const unsigned int NDIM = 3;
typedef DualNumber<RawScalar, NumberVector<NDIM, RawScalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberVector<NDIM, FirstDerivType> > SecondDerivType;
typedef SecondDerivType ADType;
using namespace MASA;
template <typename Scalar>
MASA::ad_cns_3d_les<Scalar>::ad_cns_3d_les()
{
this->mmsname = "ad_cns_3d_les";
this->dimension = 3;
this->register_var("R",&R);
this->register_var("k",&k);
this->register_var("u_0",&u_0);
this->register_var("u_x",&u_x);
this->register_var("u_y",&u_y);
this->register_var("u_z",&u_z);
this->register_var("v_0",&v_0);
this->register_var("v_x",&v_x);
this->register_var("v_y",&v_y);
this->register_var("v_z",&v_z);
this->register_var("w_0",&w_0);
this->register_var("w_x",&w_x);
this->register_var("w_y",&w_y);
this->register_var("w_z",&w_z);
this->register_var("rho_0",&rho_0);
this->register_var("rho_x",&rho_x);
this->register_var("rho_y",&rho_y);
this->register_var("rho_z",&rho_z);
this->register_var("p_0",&p_0);
this->register_var("p_x",&p_x);
this->register_var("p_y",&p_y);
this->register_var("p_z",&p_z);
this->register_var("a_px",&a_px);
this->register_var("a_py",&a_py);
this->register_var("a_pz",&a_pz);
this->register_var("a_rhox",&a_rhox);
this->register_var("a_rhoy",&a_rhoy);
this->register_var("a_rhoz",&a_rhoz);
this->register_var("a_ux",&a_ux);
this->register_var("a_uy",&a_uy);
this->register_var("a_uz",&a_uz);
this->register_var("a_vx",&a_vx);
this->register_var("a_vy",&a_vy);
this->register_var("a_vz",&a_vz);
this->register_var("a_wx",&a_wx);
this->register_var("a_wy",&a_wy);
this->register_var("a_wz",&a_wz);
this->register_var("Gamma",&Gamma);
this->register_var("mu",&mu);
this->register_var("mu_bulk",&mu_bulk);
this->register_var("L",&L);
this->register_var("Cs",&Cs);
this->register_var("CI",&CI);
this->register_var("PrT",&PrT);
this->register_var("deltabar",&deltabar);
this->init_var();
} // done with constructor
template <typename Scalar>
int MASA::ad_cns_3d_les<Scalar>::init_var()
{
int err = 0;
err += this->set_var("R",1.01);
err += this->set_var("k",1.38);
err += this->set_var("u_0",10.23);
err += this->set_var("u_x",1.1);
err += this->set_var("u_y",.08);
err += this->set_var("u_z",.08);
err += this->set_var("v_0",12);
err += this->set_var("v_x",1.6);
err += this->set_var("v_y",.67);
err += this->set_var("v_z",.67);
err += this->set_var("w_0",12);
err += this->set_var("w_x",1.6);
err += this->set_var("w_y",.67);
err += this->set_var("w_z",.67);
err += this->set_var("rho_0",10.02);
err += this->set_var("rho_x",7.2);
err += this->set_var("rho_y",9.8);
err += this->set_var("rho_z",9.8);
err += this->set_var("p_0",10.2);
err += this->set_var("p_x",.91);
err += this->set_var("p_y",.623);
err += this->set_var("p_z",.623);
err += this->set_var("a_px",.165);
err += this->set_var("a_py",.612);
err += this->set_var("a_pz",.612);
err += this->set_var("a_rhox",.627);
err += this->set_var("a_rhoy",.828);
err += this->set_var("a_rhoz",.828);
err += this->set_var("a_ux",.1987);
err += this->set_var("a_uy",1.189);
err += this->set_var("a_uz",1.189);
err += this->set_var("a_vx",1.91);
err += this->set_var("a_vy",2.901);
err += this->set_var("a_vz",2.901);
err += this->set_var("a_wx",1.91);
err += this->set_var("a_wy",2.901);
err += this->set_var("a_wz",2.901);
err += this->set_var("Gamma",1.01);
err += this->set_var("mu",.918);
err += this->set_var("mu_bulk",.3);
err += this->set_var("L",3.02);
err += this->set_var("Cs",0.16);
err += this->set_var("CI",0.09);
err += this->set_var("PrT",0.7);
err += this->set_var("deltabar",1.0);
return err;
} // done with init_var
// ----------------------------------------
// Source Terms
// ----------------------------------------
// public static method, that can be called from eval_q_t
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_q_rho_u(Scalar x1, Scalar y1, Scalar z1)
{
using std::cos;
using std::sqrt;
typedef DualNumber<Scalar, NumberVector<NDIM, Scalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberVector<NDIM, FirstDerivType> > SecondDerivType;
typedef SecondDerivType ADScalar;
const ADScalar x = ADScalar(x1,NumberVectorUnitVector<NDIM, 0, Scalar>::value());
const ADScalar y = ADScalar(y1,NumberVectorUnitVector<NDIM, 1, Scalar>::value());
const ADScalar z = ADScalar(z1,NumberVectorUnitVector<NDIM, 2, Scalar>::value());
// Treat velocity as a vector
NumberVector<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) * u_z * cos(a_uz * PI * z / L);
U[1] = v_0 + v_x * cos(a_vx * PI * x / L) * v_y * cos(a_vy * PI * y / L) * v_z * cos(a_vz * PI * z / L);
U[2] = w_0 + w_x * cos(a_wx * PI * x / L) * w_y * cos(a_wy * PI * y / L) * w_z * cos(a_wz * PI * z / L);
ADScalar RHO = rho_0 + rho_x * cos(a_rhox * PI * x / L) * rho_y * cos(a_rhoy * PI * y / L) * rho_z * 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) * p_z * cos(a_pz * PI * z / L);
// Temperature
ADScalar T = P / RHO / R;
// Perfect gas energies
ADScalar E = 1./(Gamma-1.)*P;
ADScalar ET = E + .5 * RHO * U.dot(U);
// The shear strain tensor
NumberVector<NDIM, typename ADScalar::derivatives_type> GradU = gradient(U);
// The identity tensor I
NumberVector<NDIM, NumberVector<NDIM, Scalar> > Identity =
NumberVector<NDIM, Scalar>::identity();
// Constant Smagorinsky
NumberVector<NDIM, NumberVector<NDIM, ADScalar> > S = 0.5*(GradU + transpose(GradU));
ADScalar Smag = sqrt(2.0 * (S[0][0]*S[0][0] + S[0][1]*S[0][1] + S[0][2]*S[0][2]
+ S[1][0]*S[1][0] + S[1][1]*S[1][1] + S[1][2]*S[1][2]
+ S[2][0]*S[2][0] + S[2][1]*S[2][1] + S[2][2]*S[2][2]));
ADScalar mut = (Cs*deltabar) * (Cs*deltabar) * RHO * Smag;
ADScalar sigmakk = CI * deltabar*deltabar * RHO * Smag * Smag;
// The shear stress tensor
NumberVector<NDIM, NumberVector<NDIM, ADScalar> > Tau = 2.0 * (mu + mut) * (S - 1./3.*divergence(U)*Identity) + mu_bulk * divergence(U)*Identity - 2./3. * sigmakk * Identity;
// Temperature flux
double Cv = R / (Gamma - 1);
NumberVector<NDIM, ADScalar> q = -(k + Gamma * Cv * mut/PrT) * T.derivatives();
// Momentum equation
NumberVector<NDIM, Scalar> Q_rho_u =
raw_value(divergence(RHO*U.outerproduct(U) - Tau) + P.derivatives());
return Q_rho_u[0];
}
// public, static method
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_q_rho_v(Scalar x1, Scalar y1, Scalar z1)
{
using std::cos;
using std::sqrt;
typedef DualNumber<Scalar, NumberVector<NDIM, Scalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberVector<NDIM, FirstDerivType> > SecondDerivType;
typedef SecondDerivType ADScalar;
const ADScalar x = ADScalar(x1,NumberVectorUnitVector<NDIM, 0, Scalar>::value());
const ADScalar y = ADScalar(y1,NumberVectorUnitVector<NDIM, 1, Scalar>::value());
const ADScalar z = ADScalar(z1,NumberVectorUnitVector<NDIM, 2, Scalar>::value());
// Treat velocity as a vector
NumberVector<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) * u_z * cos(a_uz * PI * z / L);
U[1] = v_0 + v_x * cos(a_vx * PI * x / L) * v_y * cos(a_vy * PI * y / L) * v_z * cos(a_vz * PI * z / L);
U[2] = w_0 + w_x * cos(a_wx * PI * x / L) * w_y * cos(a_wy * PI * y / L) * w_z * cos(a_wz * PI * z / L);
ADScalar RHO = rho_0 + rho_x * cos(a_rhox * PI * x / L) * rho_y * cos(a_rhoy * PI * y / L) * rho_z * 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) * p_z * cos(a_pz * PI * z / L);
// Temperature
ADScalar T = P / RHO / R;
// Perfect gas energies
ADScalar E = 1./(Gamma-1.)*P;
ADScalar ET = E + .5 * RHO * U.dot(U);
// The shear strain tensor
NumberVector<NDIM, typename ADScalar::derivatives_type> GradU = gradient(U);
// The identity tensor I
NumberVector<NDIM, NumberVector<NDIM, Scalar> > Identity =
NumberVector<NDIM, Scalar>::identity();
// Constant Smagorinsky
NumberVector<NDIM, NumberVector<NDIM, ADScalar> > S = 0.5*(GradU + transpose(GradU));
ADScalar Smag = sqrt(2.0 * (S[0][0]*S[0][0] + S[0][1]*S[0][1] + S[0][2]*S[0][2]
+ S[1][0]*S[1][0] + S[1][1]*S[1][1] + S[1][2]*S[1][2]
+ S[2][0]*S[2][0] + S[2][1]*S[2][1] + S[2][2]*S[2][2]));
ADScalar mut = (Cs*deltabar) * (Cs*deltabar) * RHO * Smag;
ADScalar sigmakk = CI * deltabar*deltabar * RHO * Smag * Smag;
// The shear stress tensor
NumberVector<NDIM, NumberVector<NDIM, ADScalar> > Tau = 2.0 * (mu + mut) * (S - 1./3.*divergence(U)*Identity) + mu_bulk * divergence(U)*Identity - 2./3. * sigmakk * Identity;
// Temperature flux
double Cv = R / (Gamma - 1);
NumberVector<NDIM, ADScalar> q = -(k + Gamma * Cv * mut/PrT) * T.derivatives();
// Momentum equation
NumberVector<NDIM, Scalar> Q_rho_u =
raw_value(divergence(RHO*U.outerproduct(U) - Tau) + P.derivatives());
return Q_rho_u[1];
}
// public, static method
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_q_rho_w(Scalar x1, Scalar y1, Scalar z1)
{
using std::cos;
using std::sqrt;
typedef DualNumber<Scalar, NumberVector<NDIM, Scalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberVector<NDIM, FirstDerivType> > SecondDerivType;
typedef SecondDerivType ADScalar;
const ADScalar x = ADScalar(x1,NumberVectorUnitVector<NDIM, 0, Scalar>::value());
const ADScalar y = ADScalar(y1,NumberVectorUnitVector<NDIM, 1, Scalar>::value());
const ADScalar z = ADScalar(z1,NumberVectorUnitVector<NDIM, 2, Scalar>::value());
// Treat velocity as a vector
NumberVector<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) * u_z * cos(a_uz * PI * z / L);
U[1] = v_0 + v_x * cos(a_vx * PI * x / L) * v_y * cos(a_vy * PI * y / L) * v_z * cos(a_vz * PI * z / L);
U[2] = w_0 + w_x * cos(a_wx * PI * x / L) * w_y * cos(a_wy * PI * y / L) * w_z * cos(a_wz * PI * z / L);
ADScalar RHO = rho_0 + rho_x * cos(a_rhox * PI * x / L) * rho_y * cos(a_rhoy * PI * y / L) * rho_z * 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) * p_z * cos(a_pz * PI * z / L);
// Temperature
ADScalar T = P / RHO / R;
// Perfect gas energies
ADScalar E = 1./(Gamma-1.)*P;
ADScalar ET = E + .5 * RHO * U.dot(U);
// The shear strain tensor
NumberVector<NDIM, typename ADScalar::derivatives_type> GradU = gradient(U);
// The identity tensor I
NumberVector<NDIM, NumberVector<NDIM, Scalar> > Identity =
NumberVector<NDIM, Scalar>::identity();
// Constant Smagorinsky
NumberVector<NDIM, NumberVector<NDIM, ADScalar> > S = 0.5*(GradU + transpose(GradU));
ADScalar Smag = sqrt(2.0 * (S[0][0]*S[0][0] + S[0][1]*S[0][1] + S[0][2]*S[0][2]
+ S[1][0]*S[1][0] + S[1][1]*S[1][1] + S[1][2]*S[1][2]
+ S[2][0]*S[2][0] + S[2][1]*S[2][1] + S[2][2]*S[2][2]));
ADScalar mut = (Cs*deltabar) * (Cs*deltabar) * RHO * Smag;
ADScalar sigmakk = CI * deltabar*deltabar * RHO * Smag * Smag;
// The shear stress tensor
NumberVector<NDIM, NumberVector<NDIM, ADScalar> > Tau = 2.0 * (mu + mut) * (S - 1./3.*divergence(U)*Identity) + mu_bulk * divergence(U)*Identity - 2./3. * sigmakk * Identity;
// Temperature flux
double Cv = R / (Gamma - 1);
NumberVector<NDIM, ADScalar> q = -(k + Gamma * Cv * mut/PrT) * T.derivatives();
// Momentum equation
NumberVector<NDIM, Scalar> Q_rho_u =
raw_value(divergence(RHO*U.outerproduct(U) - Tau) + P.derivatives());
return Q_rho_u[2];
}
// public, static method
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_q_rho_e(Scalar x1, Scalar y1, Scalar z1)
{
using std::cos;
using std::sqrt;
typedef DualNumber<Scalar, NumberVector<NDIM, Scalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberVector<NDIM, FirstDerivType> > SecondDerivType;
typedef SecondDerivType ADScalar;
// Treat velocity as a vector
NumberVector<NDIM, ADScalar> U;
const ADScalar x = ADScalar(x1,NumberVectorUnitVector<NDIM, 0, Scalar>::value());
const ADScalar y = ADScalar(y1,NumberVectorUnitVector<NDIM, 1, Scalar>::value());
const ADScalar z = ADScalar(z1,NumberVectorUnitVector<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) * u_z * cos(a_uz * PI * z / L);
U[1] = v_0 + v_x * cos(a_vx * PI * x / L) * v_y * cos(a_vy * PI * y / L) * v_z * cos(a_vz * PI * z / L);
U[2] = w_0 + w_x * cos(a_wx * PI * x / L) * w_y * cos(a_wy * PI * y / L) * w_z * cos(a_wz * PI * z / L);
ADScalar RHO = rho_0 + rho_x * cos(a_rhox * PI * x / L) * rho_y * cos(a_rhoy * PI * y / L) * rho_z * 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) * p_z * cos(a_pz * PI * z / L);
// Temperature
ADScalar T = P / RHO / R;
// Perfect gas energies
ADScalar E = 1./(Gamma-1.)*P;
ADScalar ET = E + .5 * RHO * U.dot(U);
// The shear strain tensor
NumberVector<NDIM, typename ADScalar::derivatives_type> GradU = gradient(U);
// The identity tensor I
NumberVector<NDIM, NumberVector<NDIM, Scalar> > Identity =
NumberVector<NDIM, Scalar>::identity();
// Constant Smagorinsky
NumberVector<NDIM, NumberVector<NDIM, ADScalar> > S = 0.5*(GradU + transpose(GradU));
ADScalar Smag = sqrt(2.0 * (S[0][0]*S[0][0] + S[0][1]*S[0][1] + S[0][2]*S[0][2]
+ S[1][0]*S[1][0] + S[1][1]*S[1][1] + S[1][2]*S[1][2]
+ S[2][0]*S[2][0] + S[2][1]*S[2][1] + S[2][2]*S[2][2]));
ADScalar mut = (Cs*deltabar) * (Cs*deltabar) * RHO * Smag;
ADScalar sigmakk = CI * deltabar*deltabar * RHO * Smag * Smag;
// The shear stress tensor
NumberVector<NDIM, NumberVector<NDIM, ADScalar> > Tau = 2.0 * (mu + mut) * (S - 1./3.*divergence(U)*Identity) + mu_bulk * divergence(U)*Identity - 2./3. * sigmakk * Identity;
// Temperature flux
double Cv = R / (Gamma - 1);
NumberVector<NDIM, ADScalar> q = -(k + Gamma * Cv * mut/PrT) * T.derivatives();
// Energy equation
Scalar Q_rho_e = raw_value(divergence((ET+P)*U + q - Tau.dot(U)));
return Q_rho_e;
}
// public, static method
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_q_rho(Scalar x1, Scalar y1, Scalar z1)
{
using std::cos;
typedef DualNumber<Scalar, NumberVector<NDIM, Scalar> > FirstDerivType;
typedef DualNumber<FirstDerivType, NumberVector<NDIM, FirstDerivType> > SecondDerivType;
typedef SecondDerivType ADScalar;
const ADScalar x = ADScalar(x1,NumberVectorUnitVector<NDIM, 0, Scalar>::value());
const ADScalar y = ADScalar(y1,NumberVectorUnitVector<NDIM, 1, Scalar>::value());
const ADScalar z = ADScalar(z1,NumberVectorUnitVector<NDIM, 2, Scalar>::value());
// Treat velocity as a vector
NumberVector<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) * u_z * cos(a_uz * PI * z / L);
U[1] = v_0 + v_x * cos(a_vx * PI * x / L) * v_y * cos(a_vy * PI * y / L) * v_z * cos(a_vz * PI * z / L);
U[2] = w_0 + w_x * cos(a_wx * PI * x / L) * w_y * cos(a_wy * PI * y / L) * w_z * cos(a_wz * PI * z / L);
ADScalar RHO = rho_0 + rho_x * cos(a_rhox * PI * x / L) * rho_y * cos(a_rhoy * PI * y / L) * rho_z * 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) * p_z * cos(a_pz * PI * z / L);
// Continuity equation
Scalar Q_rho = raw_value(divergence(RHO*U));
return Q_rho;
}
// ----------------------------------------
// Analytical Terms
// ----------------------------------------
// example of a public method called from eval_exact_t
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_exact_u(Scalar x, Scalar y, Scalar z)
{
using std::cos;
Scalar exact_u;
exact_u = u_0 + u_x * cos(a_ux * PI * x / L) * u_y * cos(a_uy * PI * y / L) * u_z * cos(a_uz * PI * z / L);
return exact_u;
}
// public method
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_exact_v(Scalar x, Scalar y, Scalar z)
{
using std::cos;
Scalar exact_v;
exact_v = v_0 + v_x * cos(a_vx * PI * x / L) * v_y * cos(a_vy * PI * y / L) * v_z * cos(a_vz * PI * z / L);
return exact_v;
}
// public method
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_exact_w(Scalar x, Scalar y, Scalar z)
{
using std::cos;
Scalar exact_w;
exact_w = w_0 + w_x * cos(a_wx * PI * x / L) * w_y * cos(a_wy * PI * y / L) * w_z * cos(a_wz * PI * z / L);
return exact_w;
}
// public method
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_exact_p(Scalar x, Scalar y, Scalar z)
{
using std::cos;
Scalar P = p_0 + p_x * cos(a_px * PI * x / L) * p_y * cos(a_py * PI * y / L) * p_z * cos(a_pz * PI * z / L);
return P;
}
// public method
template <typename Scalar>
Scalar MASA::ad_cns_3d_les<Scalar>::eval_exact_rho(Scalar x, Scalar y, Scalar z)
{
using std::cos;
Scalar RHO = rho_0 + rho_x * cos(a_rhox * PI * x / L) * rho_y * cos(a_rhoy * PI * y / L) * rho_z * cos(a_rhoz * PI * z / L);
return RHO;
}
// ----------------------------------------
// Template Instantiation(s)
// ----------------------------------------
MASA_INSTANTIATE_ALL(MASA::ad_cns_3d_les);
#endif // HAVE_METAPHYSICL