include/pops/physics/bricks/hyperbolic.hpp Source File

adc_cpp 0.3.0 Model-free C++23 core for coupled hyperbolic-elliptic systems on adaptive (AMR) meshes, with MPI and GPU (Kokkos) backends

• include
• pops
• physics
• bricks

hyperbolic.hpp

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1#pragma once

2

3#include <pops/core/state/state.hpp>

4#include <pops/core/foundation/types.hpp>

5#include <pops/core/state/variables.hpp>

6#include <pops/physics/fluids/euler.hpp> // Euler: reused as the CompressibleFlux hyperbolic brick

7

8#include <cmath>

9

17

18namespace pops {

19

27struct ExBVelocity {

28 static constexpr int n_vars = 1;

29 using State = StateVec<1>;

30 Real B0 = 1;

31 POPS_HD Real velocity(const Aux& a, int dir) const {

32 return (dir == 0) ? (-a.grad_y / B0) : (a.grad_x / B0);

33 }

34 POPS_HD StateVec<1> flux(const StateVec<1>& u, const Aux& a, int dir) const {

35 StateVec<1> f{};

36 f[0] = u[0] * velocity(a, dir);

37 return f;

38 }

39 POPS_HD Real max_wave_speed(const StateVec<1>&, const Aux& a, int dir) const {

40 const Real d = velocity(a, dir);

41 return d < 0 ? -d : d;

42 }

44 POPS_HD StateVec<1> eigenvalues(const StateVec<1>&, const Aux& a, int dir) const {

45 StateVec<1> e{};

46 e[0] = velocity(a, dir);

47 return e;

48 }

49 // Scalar: primitive variables = conservative (transported density).

50 using Prim = StateVec<1>;

51 POPS_HD Prim to_primitive(const StateVec<1>& u) const { return u; }

52 POPS_HD StateVec<1> to_conservative(const Prim& p) const { return p; }

53 static VariableSet conservative_vars() {

54 return {VariableKind::Conservative, {"n"}, 1, {VariableRole::Density}};

55 }

56 static VariableSet primitive_vars() {

57 return {VariableKind::Primitive, {"n"}, 1, {VariableRole::Density}};

58 }

59};

60

81struct ExBVelocityPolar {

82 static constexpr int n_vars = 1;

83 using State = StateVec<1>;

84 Real B0 = 1;

86 POPS_HD Real velocity(const Aux& a, int dir) const {

87 return (dir == 0) ? (-a.grad_y / B0) : (a.grad_x / B0);

88 }

89 POPS_HD StateVec<1> flux(const StateVec<1>& u, const Aux& a, int dir) const {

90 StateVec<1> f{};

91 f[0] = u[0] * velocity(a, dir);

92 return f;

93 }

94 POPS_HD Real max_wave_speed(const StateVec<1>&, const Aux& a, int dir) const {

95 const Real d = velocity(a, dir);

96 return d < 0 ? -d : d;

97 }

99 POPS_HD StateVec<1> eigenvalues(const StateVec<1>&, const Aux& a, int dir) const {

100 StateVec<1> e{};

101 e[0] = velocity(a, dir);

102 return e;

103 }

104 // Scalar: primitive variables = conservative (transported density).

105 using Prim = StateVec<1>;

106 POPS_HD Prim to_primitive(const StateVec<1>& u) const { return u; }

107 POPS_HD StateVec<1> to_conservative(const Prim& p) const { return p; }

108 static VariableSet conservative_vars() {

109 return {VariableKind::Conservative, {"n"}, 1, {VariableRole::Density}};

110 }

111 static VariableSet primitive_vars() {

112 return {VariableKind::Primitive, {"n"}, 1, {VariableRole::Density}};

113 }

114};

115

118using CompressibleFlux = Euler;

119

127struct IsothermalFlux {

128 static constexpr int n_vars = 3;

129 using State = StateVec<3>;

130 using Prim = StateVec<3>;

131 Real cs2 = 1;

138 Real vacuum_floor = 0;

141 POPS_HD Real velocity_rho(Real rho) const {

142 return (vacuum_floor > Real(0) && rho < vacuum_floor) ? vacuum_floor : rho;

143 }

144 POPS_HD StateVec<3> flux(const StateVec<3>& u, const Aux&, int dir) const {

145 const Real rho = u[0];

146 const Real vn = (dir == 0 ? u[1] : u[2]) / velocity_rho(rho);

147 const Real p = cs2 * rho;

148 StateVec<3> f{};

149 f[0] = (dir == 0 ? u[1] : u[2]);

150 f[1] = u[1] * vn + (dir == 0 ? p : Real(0));

151 f[2] = u[2] * vn + (dir == 1 ? p : Real(0));

152 return f;

153 }

156 POPS_HD Prim to_primitive(const StateVec<3>& u) const {

157 Prim p{};

158 p[0] = u[0];

159 const Real rho_v = velocity_rho(u[0]);

160 p[1] = u[1] / rho_v;

161 p[2] = u[2] / rho_v;

162 return p;

163 }

165 POPS_HD StateVec<3> to_conservative(const Prim& p) const {

166 StateVec<3> u{};

167 u[0] = p[0];

168 u[1] = p[0] * p[1];

169 u[2] = p[0] * p[2];

170 return u;

171 }

172 POPS_HD Real max_wave_speed(const StateVec<3>& u, const Aux&, int dir) const {

173 const Prim p = to_primitive(u);

174 const Real vn = (dir == 0 ? p[1] : p[2]);

175 const Real a = vn < 0 ? -vn : vn;

176 return a + std::sqrt(cs2);

177 }

179 POPS_HD StateVec<3> eigenvalues(const StateVec<3>& u, const Aux&, int dir) const {

180 const Prim p = to_primitive(u);

181 const Real vn = (dir == 0 ? p[1] : p[2]);

182 const Real c = std::sqrt(cs2);

183 StateVec<3> e{};

184 e[0] = vn - c;

185 e[1] = vn;

186 e[2] = vn + c;

187 return e;

188 }

190 POPS_HD void wave_speeds(const StateVec<3>& u, const Aux&, int dir, Real& smin, Real& smax) const {

191 const Prim p = to_primitive(u);

192 const Real vn = (dir == 0 ? p[1] : p[2]);

193 const Real c = std::sqrt(cs2);

194 smin = vn - c;

195 smax = vn + c;

196 }

197 static VariableSet conservative_vars() {

198 return {VariableKind::Conservative,

199 {"rho", "rho_u", "rho_v"},

200 3,

201 {VariableRole::Density, VariableRole::MomentumX, VariableRole::MomentumY}};

202 }

203 static VariableSet primitive_vars() {

204 return {VariableKind::Primitive,

205 {"rho", "u", "v"},

206 3,

207 {VariableRole::Density, VariableRole::VelocityX, VariableRole::VelocityY}};

208 }

209};

210

241struct IsothermalFluxPolar : IsothermalFlux {

245 POPS_HD StateVec<3> polar_geom_source(const StateVec<3>& u, Real r) const {

246 const Real rho = u[0];

247 const Real inv_rho =

248 Real(1) / velocity_rho(rho); // quasi-vacuum floored (ADC-77; bit-identical if off)

249 const Real mr = u[1], mth = u[2]; // rho v_r, rho v_theta (local basis (e_r, e_theta))

250 const Real p = cs2 * rho;

251 const Real inv_r = Real(1) / r;

252 StateVec<3> s{};

253 s[0] = Real(0);

254 s[1] = (mth * mth * inv_rho + p) * inv_r; // (rho v_theta^2 + p)/r: centrifugal + pressure

255 s[2] = -(mr * mth * inv_rho) * inv_r; // -(rho v_r v_theta)/r: cross curvature

256 return s;

257 }

258};

259

260} // namespace pops

euler.hpp

2D compressible Euler model (ideal gas): pure HYPERBOLIC brick satisfying the HyperbolicPhysicalModel...

pops

Definition amr_hierarchy.hpp:29

pops::VariableKind::Primitive

@ Primitive

pops::VariableKind::Conservative

@ Conservative

pops::Real

double Real

Definition types.hpp:30

pops::VariableRole::VelocityY

@ VelocityY

pops::VariableRole::VelocityX

@ VelocityX

pops::VariableRole::Density

@ Density

pops::VariableRole::MomentumX

@ MomentumX

pops::VariableRole::MomentumY

@ MomentumY

state.hpp

Pointwise types of the physics layer: StateVec<N> (conserved state) and Aux (auxiliary fields from th...

pops::Aux

POINTWISE auxiliary fields shared with the physics: single coupling channel.

Definition state.hpp:123

pops::Aux::grad_y

Real grad_y

Definition state.hpp:126

pops::Aux::grad_x

Real grad_x

Definition state.hpp:125

pops::Euler

2D compressible Euler for an ideal gas: HYPERBOLIC brick (HyperbolicModel concept).

Definition euler.hpp:34

pops::ExBVelocityPolar

Scalar advection by the E x B drift in POLAR coordinates (r, theta) – "annular polar grid" effort,...

Definition hyperbolic.hpp:81

pops::ExBVelocityPolar::conservative_vars

static VariableSet conservative_vars()

Definition hyperbolic.hpp:108

pops::ExBVelocityPolar::B0

Real B0

Definition hyperbolic.hpp:84

pops::ExBVelocityPolar::eigenvalues

POPS_HD StateVec< 1 > eigenvalues(const StateVec< 1 > &, const Aux &a, int dir) const

Spectrum: one wave, the drift speed in direction dir.

Definition hyperbolic.hpp:99

pops::ExBVelocityPolar::primitive_vars

static VariableSet primitive_vars()

Definition hyperbolic.hpp:111

pops::ExBVelocityPolar::to_conservative

POPS_HD StateVec< 1 > to_conservative(const Prim &p) const

Definition hyperbolic.hpp:107

pops::ExBVelocityPolar::max_wave_speed

POPS_HD Real max_wave_speed(const StateVec< 1 > &, const Aux &a, int dir) const

Definition hyperbolic.hpp:94

pops::ExBVelocityPolar::flux

POPS_HD StateVec< 1 > flux(const StateVec< 1 > &u, const Aux &a, int dir) const

Definition hyperbolic.hpp:89

pops::ExBVelocityPolar::velocity

POPS_HD Real velocity(const Aux &a, int dir) const

PHYSICAL component of the drift velocity in direction index dir (0 = r, 1 = theta).

Definition hyperbolic.hpp:86

pops::ExBVelocityPolar::to_primitive

POPS_HD Prim to_primitive(const StateVec< 1 > &u) const

Definition hyperbolic.hpp:106

pops::ExBVelocityPolar::n_vars

static constexpr int n_vars

Definition hyperbolic.hpp:82

pops::ExBVelocity

Scalar advection by the E x B drift: v = (-d_y phi, d_x phi)/B0 (divergence-free).

Definition hyperbolic.hpp:27

pops::ExBVelocity::primitive_vars

static VariableSet primitive_vars()

Definition hyperbolic.hpp:56

pops::ExBVelocity::velocity

POPS_HD Real velocity(const Aux &a, int dir) const

Definition hyperbolic.hpp:31

pops::ExBVelocity::flux

POPS_HD StateVec< 1 > flux(const StateVec< 1 > &u, const Aux &a, int dir) const

Definition hyperbolic.hpp:34

pops::ExBVelocity::conservative_vars

static VariableSet conservative_vars()

Definition hyperbolic.hpp:53

pops::ExBVelocity::B0

Real B0

Definition hyperbolic.hpp:30

pops::ExBVelocity::max_wave_speed

POPS_HD Real max_wave_speed(const StateVec< 1 > &, const Aux &a, int dir) const

Definition hyperbolic.hpp:39

pops::ExBVelocity::n_vars

static constexpr int n_vars

Definition hyperbolic.hpp:28

pops::ExBVelocity::eigenvalues

POPS_HD StateVec< 1 > eigenvalues(const StateVec< 1 > &, const Aux &a, int dir) const

Spectrum: one wave, the drift speed in direction dir.

Definition hyperbolic.hpp:44

pops::ExBVelocity::to_primitive

POPS_HD Prim to_primitive(const StateVec< 1 > &u) const

Definition hyperbolic.hpp:51

pops::ExBVelocity::to_conservative

POPS_HD StateVec< 1 > to_conservative(const Prim &p) const

Definition hyperbolic.hpp:52

pops::IsothermalFluxPolar

ISOTHERMAL Euler flux in POLAR geometry (ring r, theta), 3 variables (rho, rho v_r,...

Definition hyperbolic.hpp:241

pops::IsothermalFluxPolar::polar_geom_source

POPS_HD StateVec< 3 > polar_geom_source(const StateVec< 3 > &u, Real r) const

Definition hyperbolic.hpp:245

pops::IsothermalFlux

ISOTHERMAL Euler flux (p = cs2 rho), 3 variables (rho, rho u, rho v).

Definition hyperbolic.hpp:127

pops::IsothermalFlux::max_wave_speed

POPS_HD Real max_wave_speed(const StateVec< 3 > &u, const Aux &, int dir) const

Definition hyperbolic.hpp:172

pops::IsothermalFlux::eigenvalues

POPS_HD StateVec< 3 > eigenvalues(const StateVec< 3 > &u, const Aux &, int dir) const

Full spectrum: (v_dir - c, v_dir, v_dir + c), c = sqrt(cs2).

Definition hyperbolic.hpp:179

pops::IsothermalFlux::cs2

Real cs2

Definition hyperbolic.hpp:131

pops::IsothermalFlux::primitive_vars

static VariableSet primitive_vars()

Definition hyperbolic.hpp:203

pops::IsothermalFlux::n_vars

static constexpr int n_vars

Definition hyperbolic.hpp:128

pops::IsothermalFlux::to_conservative

POPS_HD StateVec< 3 > to_conservative(const Prim &p) const

Primitive -> conservative: (rho, u, v) -> (rho, rho u, rho v).

Definition hyperbolic.hpp:165

pops::IsothermalFlux::velocity_rho

POPS_HD Real velocity_rho(Real rho) const

rho clamped from below by vacuum_floor for the velocity division ONLY.

Definition hyperbolic.hpp:141

pops::IsothermalFlux::flux

POPS_HD StateVec< 3 > flux(const StateVec< 3 > &u, const Aux &, int dir) const

Definition hyperbolic.hpp:144

pops::IsothermalFlux::vacuum_floor

Real vacuum_floor

Quasi-vacuum density floor (ADC-77).

Definition hyperbolic.hpp:138

pops::IsothermalFlux::conservative_vars

static VariableSet conservative_vars()

Definition hyperbolic.hpp:197

pops::IsothermalFlux::wave_speeds

POPS_HD void wave_speeds(const StateVec< 3 > &u, const Aux &, int dir, Real &smin, Real &smax) const

Signed speeds (HLL/HLLC): v_dir -+ c_s.

Definition hyperbolic.hpp:190

pops::IsothermalFlux::to_primitive

POPS_HD Prim to_primitive(const StateVec< 3 > &u) const

Conservative -> primitive: (rho, rho u, rho v) -> (rho, u, v).

Definition hyperbolic.hpp:156

pops::StateVec

Conserved state vector of fixed size, known at compile time.

Definition state.hpp:29

pops::VariableSet

A model's variable set: kind (cons/prim), names, size, canonical roles (optional, parallel to names; ...

Definition variables.hpp:58

types.hpp

Base scalar types and the POPS_HD macro (host+device portability).

POPS_HD

#define POPS_HD

Definition types.hpp:25

variables.hpp

Descriptor of a model's variables (Vars).

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