#include <cut_cell.hpp>

Classes
struct	Assembled
	The assembled linear operator A as a per-cell diagonal + face CSR: (A u)_i = diag[i]·u_i + Σ_{k∈[start[i],start[i+1])} coef[k]·u[nbr[k]]. More...

Public Types
using	Octree = BlockOctree< 3, Bits >

using	M = typename Octree::M

using	Code = typename Octree::Code

using	Coord = typename Octree::Coord

Public Member Functions
void	init (const Octree &t, Real h0, Vec< 3 > origin=Vec< 3 >{})

Index	numLeaves () const

bool	isFluid (Index i) const

bool	isCut (Index i) const
	True for a cut cell: a fluid cell with at least one solid face neighbour (the row-scaled ξ-overlay band).

Index	neighborOf (Index i, int k) const
	Periodic face neighbour of leaf i in direction k (0=+x,1=-x,2=+y,3=-y,4=+z,5=-z).

double	kappa (Index i) const

double	rhsScale (Index i) const

const AmrPoisson< 3, Bits > &	lap () const
	α=1 C/F ∇² geometry for regular cells

const std::vector< double > &	sdfCRaw () const
	per-cell SDF sample (build Pass 1)

const std::vector< Index > &	nbRaw () const
	n·6 periodic face-neighbour indices

const std::vector< char > &	fluidRaw () const

const std::vector< char > &	cutRaw () const

const std::vector< double > &	acRaw () const

const std::vector< double > &	offRaw () const
	n·6 ξ-overlay off-diagonals

const std::vector< double > &	rscaleRaw () const

double	idiag () const

double	mu () const

double	beta () const
	buildCutStencil's β (= mu_/h0²)

bool	hasAdv () const

const std::vector< double > &	advDiagRaw () const

const std::vector< double > &	advCoefRaw () const

const std::vector< Index > &	advStartRaw () const

const std::vector< Index > &	advNbrRaw () const

template<class SdfFn >
void	build (SdfFn &&sdfFn, double idiag=0.0, double beta=1.0, int nsub=4)
	Build the cut-cell stencils from an SDF callable sdfFn(worldPoint) (>0 fluid, <0 solid).

Assembled	assembleOperator (bool scaleAdvByRscale=false) const
	`scaleAdvByRscale` (default false ⇒ reproduces applyOp/gaussSeidel exactly, for the matvec test): when true, the implicit-FOU advection is multiplied by the cut-cell D_rescale row scale, so the entire cut-cell row (base + advection) is scaled consistently.

FaceCsrOpT< HostArr< double >, HostArr< Index > >	hostOp (const Assembled &A) const
	View a host Assembled as a backend-agnostic FaceCsrOpT for the shared row kernels.

void	applyOp (const std::vector< double > &u, std::vector< double > &out) const
	out = A u, via the shared kernel over the assembled CSR (== device applyMom arithmetic).

double	residual (const std::vector< double > &u, const std::vector< double > &b, std::vector< double > &res) const

void	gaussSeidel (std::vector< double > &u, const std::vector< double > &b, int sweeps) const
	`sweeps` true serial Gauss–Seidel sweeps (ω=1, in place) over the assembled CSR using the shared point-update kernel — the host counterpart of the device multicolour GS, same per-cell formula.

void	applyOpGeometric (const std::vector< double > &u, std::vector< double > &out) const
	Geometric operator apply (walks the octree live) — the INDEPENDENT reference encoding, kept as the test oracle for the assembled CSR (and hence the device kernels).

void	buildAdvectionFou (const std::array< std::vector< double >, 3 > &uadv, double rho, const std::vector< double > &uf, const std::vector< Index > &faceStart, bool useFace)
	Build the implicit first-order-upwind advection operator from a (lagged) advecting velocity field `uadv` (3 components, cell-centred), scaled by `rho`.

std::vector< double >	makeRhs (const std::vector< double > &src, double u_bc) const
	Effective RHS for source `src` (≈ -h^2 f at cell centres) and wall value u_bc: row-scaled by D_rescale and shifted by the inhomogeneous boundary term.

double	residualGeometric (const std::vector< double > &u, const std::vector< double > &b, std::vector< double > &res) const

void	gaussSeidelGeometric (std::vector< double > &u, const std::vector< double > &b, int sweeps) const

double	fouApply (Index i, const std::vector< double > &field) const
	The implicit-FOU advection operator applied to `field` at leaf i: advDiag·field_i + Σ_csr coef·field_nbr (= ρ·∇·(u_adv field) FOU).

bool	hasAdvection () const

Static Public Member Functions
static MORTON_HD void	buildCutStencil (double sdf_c, const double sdf_n[6], double beta, double AC0, double &ACout, double off[6], double &rscaleOut, double &inhomOut)

Static Public Attributes
static constexpr int	Dim = 3

static constexpr int	OPP [6] = {1, 0, 3, 2, 5, 4}

Detailed Description

template<unsigned Bits = 21u>
class peclet::core::amr::AmrCutCell< Bits >

Definition at line 75 of file cut_cell.hpp.

Member Typedef Documentation

◆ Octree

template<unsigned Bits = 21u>

using peclet::core::amr::AmrCutCell< Bits >::Octree = BlockOctree<3, Bits>

Definition at line 78 of file cut_cell.hpp.

◆ M

template<unsigned Bits = 21u>

using peclet::core::amr::AmrCutCell< Bits >::M = typename Octree::M

Definition at line 79 of file cut_cell.hpp.

◆ Code

template<unsigned Bits = 21u>

using peclet::core::amr::AmrCutCell< Bits >::Code = typename Octree::Code

Definition at line 80 of file cut_cell.hpp.

◆ Coord

template<unsigned Bits = 21u>

using peclet::core::amr::AmrCutCell< Bits >::Coord = typename Octree::Coord

Definition at line 81 of file cut_cell.hpp.

Member Function Documentation

◆ init()

template<unsigned Bits = 21u>

void peclet::core::amr::AmrCutCell< Bits >::init	(	const Octree &	t,
		Real	h0,
		Vec< 3 >	origin = `Vec<3>{}`
	)

inline

Definition at line 86 of file cut_cell.hpp.

◆ numLeaves()

template<unsigned Bits = 21u>

Index peclet::core::amr::AmrCutCell< Bits >::numLeaves ( ) const

inline

Definition at line 94 of file cut_cell.hpp.

References peclet::core::amr::BlockOctree< Dim, Bits >::numLeaves().

◆ isFluid()

template<unsigned Bits = 21u>

bool peclet::core::amr::AmrCutCell< Bits >::isFluid ( Index i ) const

inline

Definition at line 95 of file cut_cell.hpp.

◆ isCut()

template<unsigned Bits = 21u>

bool peclet::core::amr::AmrCutCell< Bits >::isCut ( Index i ) const

inline

True for a cut cell: a fluid cell with at least one solid face neighbour (the row-scaled ξ-overlay band).

Its residual is D_rescale-scaled / inconsistent, so it is excluded from the velocity-MG coarse defect (the clean-fluid mask — see VelocityMG).

Definition at line 99 of file cut_cell.hpp.

◆ neighborOf()

template<unsigned Bits = 21u>

Index peclet::core::amr::AmrCutCell< Bits >::neighborOf	(	Index	i,
		int	k
	)		const

inline

Periodic face neighbour of leaf i in direction k (0=+x,1=-x,2=+y,3=-y,4=+z,5=-z).

Definition at line 101 of file cut_cell.hpp.

◆ kappa()

template<unsigned Bits = 21u>

double peclet::core::amr::AmrCutCell< Bits >::kappa ( Index i ) const

inline

Definition at line 102 of file cut_cell.hpp.

◆ rhsScale()

template<unsigned Bits = 21u>

double peclet::core::amr::AmrCutCell< Bits >::rhsScale ( Index i ) const

inline

Definition at line 103 of file cut_cell.hpp.

◆ lap()

template<unsigned Bits = 21u>

const AmrPoisson< 3, Bits > & peclet::core::amr::AmrCutCell< Bits >::lap ( ) const

inline

α=1 C/F ∇² geometry for regular cells

Definition at line 108 of file cut_cell.hpp.

◆ sdfCRaw()

template<unsigned Bits = 21u>

const std::vector< double > & peclet::core::amr::AmrCutCell< Bits >::sdfCRaw ( ) const

inline

per-cell SDF sample (build Pass 1)

Definition at line 111 of file cut_cell.hpp.

◆ nbRaw()

template<unsigned Bits = 21u>

const std::vector< Index > & peclet::core::amr::AmrCutCell< Bits >::nbRaw ( ) const

inline

n·6 periodic face-neighbour indices

Definition at line 114 of file cut_cell.hpp.

◆ fluidRaw()

template<unsigned Bits = 21u>

const std::vector< char > & peclet::core::amr::AmrCutCell< Bits >::fluidRaw ( ) const

inline

Definition at line 115 of file cut_cell.hpp.

◆ cutRaw()

template<unsigned Bits = 21u>

const std::vector< char > & peclet::core::amr::AmrCutCell< Bits >::cutRaw ( ) const

inline

Definition at line 116 of file cut_cell.hpp.

◆ acRaw()

template<unsigned Bits = 21u>

const std::vector< double > & peclet::core::amr::AmrCutCell< Bits >::acRaw ( ) const

inline

Definition at line 117 of file cut_cell.hpp.

◆ offRaw()

template<unsigned Bits = 21u>

const std::vector< double > & peclet::core::amr::AmrCutCell< Bits >::offRaw ( ) const

inline

n·6 ξ-overlay off-diagonals

Definition at line 118 of file cut_cell.hpp.

◆ rscaleRaw()

template<unsigned Bits = 21u>

const std::vector< double > & peclet::core::amr::AmrCutCell< Bits >::rscaleRaw ( ) const

inline

Definition at line 119 of file cut_cell.hpp.

◆ idiag()

template<unsigned Bits = 21u>

double peclet::core::amr::AmrCutCell< Bits >::idiag ( ) const

inline

Definition at line 120 of file cut_cell.hpp.

Referenced by peclet::core::amr::AmrCutCell< Bits >::build().

◆ mu()

template<unsigned Bits = 21u>

double peclet::core::amr::AmrCutCell< Bits >::mu ( ) const

inline

Definition at line 121 of file cut_cell.hpp.

◆ beta()

template<unsigned Bits = 21u>

double peclet::core::amr::AmrCutCell< Bits >::beta ( ) const

inline

buildCutStencil's β (= mu_/h0²)

Definition at line 122 of file cut_cell.hpp.

Referenced by peclet::core::amr::AmrCutCell< Bits >::build(), and peclet::core::amr::AmrCutCell< Bits >::buildCutStencil().

◆ hasAdv()

template<unsigned Bits = 21u>

bool peclet::core::amr::AmrCutCell< Bits >::hasAdv ( ) const

inline

Definition at line 123 of file cut_cell.hpp.

◆ advDiagRaw()

template<unsigned Bits = 21u>

const std::vector< double > & peclet::core::amr::AmrCutCell< Bits >::advDiagRaw ( ) const

inline

Definition at line 124 of file cut_cell.hpp.

◆ advCoefRaw()

template<unsigned Bits = 21u>

const std::vector< double > & peclet::core::amr::AmrCutCell< Bits >::advCoefRaw ( ) const

inline

Definition at line 125 of file cut_cell.hpp.

◆ advStartRaw()

template<unsigned Bits = 21u>

const std::vector< Index > & peclet::core::amr::AmrCutCell< Bits >::advStartRaw ( ) const

inline

Definition at line 126 of file cut_cell.hpp.

◆ advNbrRaw()

template<unsigned Bits = 21u>

const std::vector< Index > & peclet::core::amr::AmrCutCell< Bits >::advNbrRaw ( ) const

inline

Definition at line 127 of file cut_cell.hpp.

◆ build()

template<unsigned Bits = 21u>

template<class SdfFn >

void peclet::core::amr::AmrCutCell< Bits >::build	(	SdfFn &&	sdfFn,
		double	idiag = `0.0`,
		double	beta = `1.0`,
		int	nsub = `4`
	)

inline

Build the cut-cell stencils from an SDF callable sdfFn(worldPoint) (>0 fluid, <0 solid).

Operator A = idiag*I - beta*Laplacian (grid units, dx=1). nsub is the per-axis subsampling for the volume fraction κ.

Definition at line 133 of file cut_cell.hpp.

References peclet::core::amr::AmrCutCell< Bits >::beta(), peclet::core::amr::AmrCutCell< Bits >::buildCutStencil(), peclet::core::amr::AmrCutCell< Bits >::idiag(), peclet::core::amr::AmrPoisson< Dim, Bits >::init(), and peclet::core::amr::AmrCutCell< Bits >::numLeaves().

◆ assembleOperator()

template<unsigned Bits = 21u>

Assembled peclet::core::amr::AmrCutCell< Bits >::assembleOperator ( bool scaleAdvByRscale = false ) const

inline

scaleAdvByRscale (default false ⇒ reproduces applyOp/gaussSeidel exactly, for the matvec test): when true, the implicit-FOU advection is multiplied by the cut-cell D_rescale row scale, so the entire cut-cell row (base + advection) is scaled consistently.

applyOp scales the base + RHS but not the advection — fine for the host serial GS (which gives a bounded approximation) but the inconsistency leaves a (1−rscale)/rscale·FOU amplification in the exact solution that blows up an accurate device solve at thin cut cells. With the advection scaled, the row is the unscaled equation × rscale and the implicit FOU cancels the (rscale-scaled) explicit deferred-correction FOU at steady state. The collocated device flow uses this; regular fluid cells (rscale=1) are unchanged.

Definition at line 218 of file cut_cell.hpp.

References peclet::core::amr::AmrPoisson< Dim, Bits >::cellVolume(), peclet::core::amr::AmrCutCell< Bits >::Assembled::coef, peclet::core::amr::AmrCutCell< Bits >::Assembled::diag, peclet::core::amr::AmrPoisson< Dim, Bits >::forEachFaceNeighbor(), peclet::core::amr::AmrCutCell< Bits >::Assembled::nbr, peclet::core::amr::AmrCutCell< Bits >::numLeaves(), and peclet::core::amr::AmrCutCell< Bits >::Assembled::start.

Referenced by peclet::core::amr::AmrCutCell< Bits >::applyOp(), peclet::core::amr::AmrCutCell< Bits >::gaussSeidel(), and peclet::core::amr::AmrCutCell< Bits >::residual().

◆ hostOp()

template<unsigned Bits = 21u>

FaceCsrOpT< HostArr< double >, HostArr< Index > > peclet::core::amr::AmrCutCell< Bits >::hostOp ( const Assembled & A ) const

inline

View a host Assembled as a backend-agnostic FaceCsrOpT for the shared row kernels.

Definition at line 282 of file cut_cell.hpp.

References peclet::core::amr::AmrCutCell< Bits >::Assembled::coef, peclet::core::amr::AmrCutCell< Bits >::Assembled::diag, peclet::core::amr::AmrCutCell< Bits >::Assembled::nbr, peclet::core::amr::AmrCutCell< Bits >::numLeaves(), and peclet::core::amr::AmrCutCell< Bits >::Assembled::start.

Referenced by peclet::core::amr::AmrCutCell< Bits >::applyOp(), peclet::core::amr::AmrCutCell< Bits >::gaussSeidel(), and peclet::core::amr::AmrCutCell< Bits >::residual().

◆ applyOp()

template<unsigned Bits = 21u>

void peclet::core::amr::AmrCutCell< Bits >::applyOp	(	const std::vector< double > &	u,
		std::vector< double > &	out
	)		const

inline

out = A u, via the shared kernel over the assembled CSR (== device applyMom arithmetic).

Definition at line 294 of file cut_cell.hpp.

References peclet::core::amr::AmrCutCell< Bits >::assembleOperator(), peclet::core::amr::faceCsrApplyRow(), peclet::core::amr::AmrCutCell< Bits >::hostOp(), and peclet::core::amr::AmrCutCell< Bits >::numLeaves().

◆ residual()

template<unsigned Bits = 21u>

double peclet::core::amr::AmrCutCell< Bits >::residual	(	const std::vector< double > &	u,
		const std::vector< double > &	b,
		std::vector< double > &	res
	)		const

inline

Definition at line 304 of file cut_cell.hpp.

References peclet::core::amr::AmrCutCell< Bits >::assembleOperator(), peclet::core::amr::faceCsrApplyRow(), peclet::core::amr::AmrCutCell< Bits >::hostOp(), and peclet::core::amr::AmrCutCell< Bits >::numLeaves().

◆ gaussSeidel()

template<unsigned Bits = 21u>

void peclet::core::amr::AmrCutCell< Bits >::gaussSeidel	(	std::vector< double > &	u,
		const std::vector< double > &	b,
		int	sweeps
	)		const

inline

sweeps true serial Gauss–Seidel sweeps (ω=1, in place) over the assembled CSR using the shared point-update kernel — the host counterpart of the device multicolour GS, same per-cell formula.

Definition at line 324 of file cut_cell.hpp.

References peclet::core::amr::AmrCutCell< Bits >::assembleOperator(), peclet::core::amr::faceCsrOffDiag(), peclet::core::amr::faceCsrPointUpdate(), peclet::core::amr::AmrCutCell< Bits >::hostOp(), and peclet::core::amr::AmrCutCell< Bits >::numLeaves().

◆ applyOpGeometric()

template<unsigned Bits = 21u>

void peclet::core::amr::AmrCutCell< Bits >::applyOpGeometric	(	const std::vector< double > &	u,
		std::vector< double > &	out
	)		const

inline

Geometric operator apply (walks the octree live) — the INDEPENDENT reference encoding, kept as the test oracle for the assembled CSR (and hence the device kernels).

The runtime applyOp below routes through the shared face_csr.hpp kernels instead, so host and device run identical arithmetic; test_amr_cut_cell asserts the two agree. out = A u. A = idiag·I − μ∇² (C/F-aware) on regular fluid cells; the ξ-overlay stencil on cut cells (finest, same-level); identity on solid cells (held at u_bc).

Definition at line 344 of file cut_cell.hpp.

References peclet::core::amr::AmrPoisson< Dim, Bits >::applyLaplacian(), and peclet::core::amr::AmrCutCell< Bits >::numLeaves().

Referenced by peclet::core::amr::AmrCutCell< Bits >::residualGeometric().

◆ buildAdvectionFou()

template<unsigned Bits = 21u>

void peclet::core::amr::AmrCutCell< Bits >::buildAdvectionFou	(	const std::array< std::vector< double >, 3 > &	uadv,
		double	rho,
		const std::vector< double > &	uf,
		const std::vector< Index > &	faceStart,
		bool	useFace
	)

inline

Build the implicit first-order-upwind advection operator from a (lagged) advecting velocity field uadv (3 components, cell-centred), scaled by rho.

C/F-conservative: each face (incl. the 2^(Dim-1) fine sub-faces of a coarse cell, via forEachFaceFull) contributes (1/V)·A·velOut·ρ to the diagonal (outflow) or to a CSR off-diagonal toward the upstream neighbour (inflow); the advecting velocity at a wall (solid neighbour) face is zero (no flow through the immersed boundary). Rebuilt per step. Stable base of the deferred correction. uf/faceStart (+axis face velocity per forEachFaceFull (sub)face, when useFace) is the divergence-free advecting velocity; otherwise the cell average ½(uadv_i+uadv_j) is used (before the first projection has built uf). The implicit FOU and the explicit deferred correction must use the SAME velocity, hence it lives here too — not only in the high-order term.

Definition at line 384 of file cut_cell.hpp.

References peclet::core::amr::AmrPoisson< Dim, Bits >::cellVolume(), peclet::core::amr::AmrPoisson< Dim, Bits >::forEachFaceFull(), and peclet::core::amr::AmrCutCell< Bits >::numLeaves().

◆ makeRhs()

template<unsigned Bits = 21u>

std::vector< double > peclet::core::amr::AmrCutCell< Bits >::makeRhs	(	const std::vector< double > &	src,
		double	u_bc
	)		const

inline

Effective RHS for source src (≈ -h^2 f at cell centres) and wall value u_bc: row-scaled by D_rescale and shifted by the inhomogeneous boundary term.

Definition at line 440 of file cut_cell.hpp.

References peclet::core::amr::AmrCutCell< Bits >::numLeaves().

◆ residualGeometric()

template<unsigned Bits = 21u>

double peclet::core::amr::AmrCutCell< Bits >::residualGeometric	(	const std::vector< double > &	u,
		const std::vector< double > &	b,
		std::vector< double > &	res
	)		const

inline

Definition at line 455 of file cut_cell.hpp.

References peclet::core::amr::AmrCutCell< Bits >::applyOpGeometric(), and peclet::core::amr::AmrCutCell< Bits >::numLeaves().

◆ gaussSeidelGeometric()

template<unsigned Bits = 21u>

void peclet::core::amr::AmrCutCell< Bits >::gaussSeidelGeometric	(	std::vector< double > &	u,
		const std::vector< double > &	b,
		int	sweeps
	)		const

inline

Definition at line 469 of file cut_cell.hpp.

References peclet::core::amr::AmrPoisson< Dim, Bits >::cellVolume(), peclet::core::amr::AmrPoisson< Dim, Bits >::forEachFaceNeighbor(), and peclet::core::amr::AmrCutCell< Bits >::numLeaves().

◆ fouApply()

template<unsigned Bits = 21u>

double peclet::core::amr::AmrCutCell< Bits >::fouApply	(	Index	i,
		const std::vector< double > &	field
	)		const

inline

The implicit-FOU advection operator applied to field at leaf i: advDiag·field_i + Σ_csr coef·field_nbr (= ρ·∇·(u_adv field) FOU).

Used by the flow solver for the explicit deferred-correction term (high-order − this).

Definition at line 516 of file cut_cell.hpp.

◆ hasAdvection()

template<unsigned Bits = 21u>

bool peclet::core::amr::AmrCutCell< Bits >::hasAdvection ( ) const

inline

Definition at line 520 of file cut_cell.hpp.

◆ buildCutStencil()

template<unsigned Bits = 21u>

static MORTON_HD void peclet::core::amr::AmrCutCell< Bits >::buildCutStencil	(	double	sdf_c,
		const double	sdf_n[6],
		double	beta,
		double	AC0,
		double &	ACout,
		double	off[6],
		double &	rscaleOut,
		double &	inhomOut
	)

inlinestatic

Definition at line 536 of file cut_cell.hpp.

References peclet::core::amr::AmrCutCell< Bits >::beta(), peclet::core::amr::cc::poly_abs(), peclet::core::amr::cc::poly_D(), peclet::core::amr::cc::poly_D_sandwich(), peclet::core::amr::cc::poly_N_c_sandwich(), peclet::core::amr::cc::poly_N_nb(), peclet::core::amr::cc::poly_Nbc(), peclet::core::amr::cc::poly_Nbc_mp_sw(), peclet::core::amr::cc::poly_Nbc_pp_sw(), and peclet::core::amr::cc::poly_Nc().

Referenced by peclet::core::amr::AmrCutCell< Bits >::build(), and peclet::core::amr::rebuildCutStencil().

Member Data Documentation

◆ Dim

template<unsigned Bits = 21u>

constexpr int peclet::core::amr::AmrCutCell< Bits >::Dim = 3

staticconstexpr

Definition at line 77 of file cut_cell.hpp.

◆ OPP

template<unsigned Bits = 21u>

constexpr int peclet::core::amr::AmrCutCell< Bits >::OPP[6] = {1, 0, 3, 2, 5, 4}

staticconstexpr

Definition at line 84 of file cut_cell.hpp.

The documentation for this class was generated from the following file:

cut_cell.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ Octree

◆ M

◆ Code

◆ Coord

Member Function Documentation

◆ init()

◆ numLeaves()

◆ isFluid()

◆ isCut()

◆ neighborOf()

◆ kappa()

◆ rhsScale()

◆ lap()

◆ sdfCRaw()

◆ nbRaw()

◆ fluidRaw()

◆ cutRaw()

◆ acRaw()

◆ offRaw()

◆ rscaleRaw()

◆ idiag()

◆ mu()

◆ beta()

◆ hasAdv()

◆ advDiagRaw()

◆ advCoefRaw()

◆ advStartRaw()

◆ advNbrRaw()

◆ build()

◆ assembleOperator()

◆ hostOp()

◆ applyOp()

◆ residual()

◆ gaussSeidel()

◆ applyOpGeometric()

◆ buildAdvectionFou()

◆ makeRhs()

◆ residualGeometric()

◆ gaussSeidelGeometric()

◆ fouApply()

◆ hasAdvection()

◆ buildCutStencil()

Member Data Documentation

◆ Dim

◆ OPP