include/pops/numerics/fv/reconstruction.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
• numerics
• fv

reconstruction.hpp

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1

12

13#pragma once

14

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

16

17#include <cmath>

18

19namespace pops {

20

26struct NoSlope {

27 static constexpr int n_ghost = 1;

28 POPS_HD Real operator()(Real, Real) const { return Real(0); }

29};

30

36struct Minmod {

37 static constexpr int n_ghost = 2;

38 POPS_HD Real operator()(Real a, Real b) const {

39 if (a * b <= Real(0))

40 return Real(0);

41 const Real fa = a < 0 ? -a : a, fb = b < 0 ? -b : b; // |.| device-safe

42 return (fa < fb) ? a : b;

43 }

44};

45

51struct VanLeer {

52 static constexpr int n_ghost = 2;

53 POPS_HD Real operator()(Real a, Real b) const {

54 const Real ab = a * b;

55 if (ab <= Real(0))

56 return Real(0);

57 return Real(2) * ab / (a + b);

58 }

59};

60

70POPS_HD inline Real weno5z(Real vm2, Real vm1, Real v0, Real vp1, Real vp2) {

71 const Real eps = Real(1e-40);

72 // three third-order reconstructions of the +x face of v0

73 const Real q0 = (Real(2) * vm2 - Real(7) * vm1 + Real(11) * v0) / Real(6);

74 const Real q1 = (-vm1 + Real(5) * v0 + Real(2) * vp1) / Real(6);

75 const Real q2 = (Real(2) * v0 + Real(5) * vp1 - vp2) / Real(6);

76 // smoothness indicators (Jiang-Shu)

77 const Real b0 = Real(13) / Real(12) * (vm2 - 2 * vm1 + v0) * (vm2 - 2 * vm1 + v0) +

78 Real(0.25) * (vm2 - 4 * vm1 + 3 * v0) * (vm2 - 4 * vm1 + 3 * v0);

79 const Real b1 = Real(13) / Real(12) * (vm1 - 2 * v0 + vp1) * (vm1 - 2 * v0 + vp1) +

80 Real(0.25) * (vm1 - vp1) * (vm1 - vp1);

81 const Real b2 = Real(13) / Real(12) * (v0 - 2 * vp1 + vp2) * (v0 - 2 * vp1 + vp2) +

82 Real(0.25) * (3 * v0 - 4 * vp1 + vp2) * (3 * v0 - 4 * vp1 + vp2);

83 // WENO-Z weights: alpha_k = d_k (1 + (tau5/(eps+beta_k))^2), tau5 = |beta0 - beta2|

84 const Real tau5 = (b0 - b2 < 0 ? b2 - b0 : b0 - b2);

85 const Real a0 = (Real(1) / Real(10)) * (Real(1) + (tau5 / (eps + b0)) * (tau5 / (eps + b0)));

86 const Real a1 = (Real(6) / Real(10)) * (Real(1) + (tau5 / (eps + b1)) * (tau5 / (eps + b1)));

87 const Real a2 = (Real(3) / Real(10)) * (Real(1) + (tau5 / (eps + b2)) * (tau5 / (eps + b2)));

88 const Real inv = Real(1) / (a0 + a1 + a2);

89 return (a0 * q0 + a1 * q1 + a2 * q2) * inv;

90}

91

98struct Weno5 {

99 static constexpr int n_ghost = 3;

100 POPS_HD Real operator()(Real, Real) const { return Real(0); }

101};

102

103} // namespace pops

pops

Definition amr_hierarchy.hpp:29

pops::Real

double Real

Definition types.hpp:30

pops::weno5z

POPS_HD Real weno5z(Real vm2, Real vm1, Real v0, Real vp1, Real vp2)

weno5z: WENO5-Z reconstruction (Borges 2008) at one interface, on a 5-point stencil.

Definition reconstruction.hpp:70

pops::Minmod

minmod limiter: TVD (Total Variation Diminishing), 2 ghosts, order 2 in smooth regions.

Definition reconstruction.hpp:36

pops::Minmod::n_ghost

static constexpr int n_ghost

Definition reconstruction.hpp:37

pops::Minmod::operator()

POPS_HD Real operator()(Real a, Real b) const

Definition reconstruction.hpp:38

pops::NoSlope

First-order reconstruction (piecewise constant): zero slope, 1 ghost.

Definition reconstruction.hpp:26

pops::NoSlope::operator()

POPS_HD Real operator()(Real, Real) const

Definition reconstruction.hpp:28

pops::NoSlope::n_ghost

static constexpr int n_ghost

Definition reconstruction.hpp:27

pops::VanLeer

van Leer limiter: smooth, 2 ghosts, better order at extrema than Minmod.

Definition reconstruction.hpp:51

pops::VanLeer::operator()

POPS_HD Real operator()(Real a, Real b) const

Definition reconstruction.hpp:53

pops::VanLeer::n_ghost

static constexpr int n_ghost

Definition reconstruction.hpp:52

pops::Weno5

WENO5 tag policy: marks the stencil at 3 ghosts, delegates to weno5z.

Definition reconstruction.hpp:98

pops::Weno5::n_ghost

static constexpr int n_ghost

Definition reconstruction.hpp:99

pops::Weno5::operator()

POPS_HD Real operator()(Real, Real) const

Definition reconstruction.hpp:100

types.hpp

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

POPS_HD

#define POPS_HD

Definition types.hpp:25

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