Namespaces
namespace	detail

Classes
struct	CollocatedNS

struct	CovolumeNS
	The covolume NS solver state: face fluxes u, cell pressure p (from the last projection). More...

struct	DecEdges

struct	FaceMesh

struct	GhostExchange

struct	PolyMesh

struct	PressureSolver

Typedefs
template<class Real >
using	DV = Kokkos::View< Real *, peclet::core::MemSpace >

Functions
template<class Real >
void	perotTranspose (const FaceMesh< Real > &m, const DV< Real > &acell, const DV< Real > &out)
	Transpose of the Perot reconstruction: face-normal tendency from cell tendencies (3N).

template<class Real >
void	cellTendency (const FaceMesh< Real > &m, const DV< Real > &u, const DV< Real > &U, Real nu, const DV< Real > &out, const DV< Real > &force=DV< Real >{}, Real convScale=Real(1), const DV< Real > &Uwall=DV< Real >{}, const DV< Real > &wallGrad=DV< Real >{})

template<class Real >
DecEdges< Real >	buildDecEdges (const TessellationView< Real > &view, const FaceMesh< Real > &m)
	Build the DEC edge structure. `facetOfFace`-style inverse maps are built here from the mesh.

template<class Real >
void	decLaplacian (const FaceMesh< Real > &m, const DecEdges< Real > &d, const DV< Real > &u, const DV< Real > &divScratch, const DV< Real > &out)

template<class Real >
FaceMesh< Real >	buildFaceMesh (const TessellationView< Real > &view, const AuxMaps< Real > &aux, int nOwned=-1)

template<class Real >
void	divergence (const FaceMesh< Real > &m, const DV< Real > &u, const DV< Real > &out)
	(div u)_i from face-normal fluxes u (nFaces; boundary faces included, along the outward normal).

template<class Real >
void	faceGradient (const FaceMesh< Real > &m, const DV< Real > &p, const DV< Real > &out, const DV< Real > &pb=DV< Real >{})

template<class Real >
void	laplacian (const FaceMesh< Real > &m, const DV< Real > &p, const DV< Real > &out, DV< Real > &scratchFace, const DV< Real > &pb=DV< Real >{})
	L p = div(grad p): the two-point Laplacian (Neumann on boundary faces unless `pb` is given).

template<class Real >
void	greenGaussGradient (const FaceMesh< Real > &m, const DV< Real > &p, const DV< Real > &out)
	Green–Gauss cell gradient (3N): distance-weighted face values, boundary faces use p_A.

template<class Real >
void	perotVelocity (const FaceMesh< Real > &m, const DV< Real > &u, const DV< Real > &out)
	Perot reconstruction of the cell velocity (3N) from face-normal fluxes.

template<class Real >
KOKKOS_INLINE_FUNCTION void	cellSkewInverse (const FaceMesh< Real > &m, int i, Real R[9])

template<class Real >
void	vectorGreenGauss (const FaceMesh< Real > &m, const DV< Real > &U, const DV< Real > &out, const DV< Real > &Uwall=DV< Real >{})

template<class Real >
void	projectToFaces (const FaceMesh< Real > &m, const DV< Real > &ucell, const DV< Real > &out, const DV< Real > &gradU=DV< Real >{}, const DV< Real > &ub=DV< Real >{})

template<class Real >
Real	dotCells (const FaceMesh< Real > &m, const DV< Real > &a, const DV< Real > &b)

template<class Real >
Real	dotFaces (const FaceMesh< Real > &m, const DV< Real > &a, const DV< Real > &b)

template<class Real >
void	faceInterpTranspose (const FaceMesh< Real > &m, const DV< Real > &g, const DV< Real > &out, bool skew=false, const DV< Real > &scratch9=DV< Real >{}, bool wallPrescribed=false, const std::function< void(const DV< Real > &, int)> &exchange={})

template<class Real >
void	wallGradientLS (const FaceMesh< Real > &m, const DV< Real > &U, const DV< Real > &gradU, const DV< Real > &Uwall, const DV< Real > &out)

template<class Real >
int	poissonCG (const FaceMesh< Real > &m, const DV< Real > &f, const DV< Real > &p, Real tol, int maxIter, Real &resOut)

template<class Real >
int	mergeWallVertices (PolyMesh< Real > &m, const Real L[3], Real tol)

template<class Real , int MAXP, int MAXT>
PolyMesh< Real >	buildPolyMesh (const TopologyStore< MAXP, MAXT > &store, const Kokkos::View< Real , peclet::core::MemSpace > &pos, int N, const Real L[3], WallStore< Real > wall={}, Kokkos::View< Real , peclet::core::MemSpace > xRef={}, Real quantum=Real(1e-9))
	Assemble the polyhedral mesh of a store at positions `posHost` (3N, world, in [0,L)).

template<class Real >
bool	writeVtu (const std::string &path, const PolyMesh< Real > &m, const std::vector< Real > cellScalar=nullptr, const char scalarName="scalar")

Typedef Documentation

◆ DV

template<class Real >

using peclet::voro::fv::DV = typedef Kokkos::View<Real*, peclet::core::MemSpace>

Function Documentation

◆ buildDecEdges()

template<class Real >

DecEdges< Real > peclet::voro::fv::buildDecEdges	(	const TessellationView< Real > &	view,
		const FaceMesh< Real > &	m
	)

Build the DEC edge structure. facetOfFace-style inverse maps are built here from the mesh.

◆ buildFaceMesh()

template<class Real >

FaceMesh< Real > peclet::voro::fv::buildFaceMesh	(	const TessellationView< Real > &	view,
		const AuxMaps< Real > &	aux,
		int	nOwned = `-1`
	)

Build the face mesh. aux = buildAuxMaps(view). Interior faces are owned by the facet with the lower index of the reciprocal pair; wall facets (facetNbr == kBoundaryFacet) and box facets (−1) become boundary faces. Distributed (rung C5): nOwned ≥ 0 marks cells [0, nOwned) as this rank's owned cells (the tessellation was built for them only, ghosts [nOwned, N) are candidates without facets); a facet toward a ghost is an INTERFACE face owned here (B = the ghost's combined index; the other rank owns its own copy of the same face and computes the same flux from the exchanged fields).

◆ buildPolyMesh()

template<class Real , int MAXP, int MAXT>

PolyMesh< Real > peclet::voro::fv::buildPolyMesh	(	const TopologyStore< MAXP, MAXT > &	store,
		const Kokkos::View< Real *, peclet::core::MemSpace > &	pos,
		int	N,
		const Real	L[3],
		WallStore< Real >	wall = `{}`,
		Kokkos::View< Real *, peclet::core::MemSpace >	xRef = `{}`,
		Real	quantum = `Real(1e-9)`
	)

Assemble the polyhedral mesh of a store at positions posHost (3N, world, in [0,L)).

◆ cellSkewInverse()

template<class Real >

KOKKOS_INLINE_FUNCTION void peclet::voro::fv::cellSkewInverse	(	const FaceMesh< Real > &	m,
		int	i,
		Real	R[9]
	)

Skewness correction of the Green–Gauss gradient. For a LINEAR field the plain Green–Gauss gradient (face values at the connector foot) is (I − S) ∇p with the geometric tensor S = (1/V) Σ_f s_f A_f t_f ⊗ n_f (t_f = the face centroid's tangential offset from the connector; Gauss: Σ_f A_f c_f ⊗ n_f = V I). R = (I − S)⁻¹ makes it exact for linear fields on any polyhedral cell; zero on a lattice / centroidal-symmetric cell.

◆ cellTendency()

template<class Real >

void peclet::voro::fv::cellTendency	(	const FaceMesh< Real > &	m,
		const DV< Real > &	u,
		const DV< Real > &	U,
		Real	nu,
		const DV< Real > &	out,
		const DV< Real > &	force = `DV<Real>{}`,
		Real	convScale = `Real(1)`,
		const DV< Real > &	Uwall = `DV<Real>{}`,
		const DV< Real > &	wallGrad = `DV<Real>{}`
	)

Cell-centred tendency of the reconstructed velocity U (3N) under the face flux u: a_i = −(1/V_i) Σ_f s_if u_f A_f ½(U_i + U_j) + (ν/V_i) Σ_f A_f/d_f (U_j − U_i) + F_i Boundary faces (walls, C3): the face velocity is the prescribed Uwall (3 × nBoundary; zero = no-slip when not given) at distance h_A — two-point wall flux ν A_f (U_wall − U_i)/h_A, and the convective flux F_f carries U_wall (F_f = 0 on an impermeable wall). force (3N) optional.

◆ decLaplacian()

template<class Real >

void peclet::voro::fv::decLaplacian	(	const FaceMesh< Real > &	m,
		const DecEdges< Real > &	d,
		const DV< Real > &	u,
		const DV< Real > &	divScratch,
		const DV< Real > &	out
	)

The DEC Laplacian of the face flux u (interior faces): out_f = grad_f(div u) − (curl curl u)_f, with grad div through the C1 operators; divScratch (nCells). Faces with a skipped edge get only the grad-div part (flagged by weight 0 — the caller decides how to treat them).

◆ divergence()

template<class Real >

void peclet::voro::fv::divergence	(	const FaceMesh< Real > &	m,
		const DV< Real > &	u,
		const DV< Real > &	out
	)

(div u)_i from face-normal fluxes u (nFaces; boundary faces included, along the outward normal).

◆ dotCells()

template<class Real >

Real peclet::voro::fv::dotCells	(	const FaceMesh< Real > &	m,
		const DV< Real > &	a,
		const DV< Real > &	b
	)

◆ dotFaces()

template<class Real >

Real peclet::voro::fv::dotFaces	(	const FaceMesh< Real > &	m,
		const DV< Real > &	a,
		const DV< Real > &	b
	)

◆ faceGradient()

template<class Real >

void peclet::voro::fv::faceGradient	(	const FaceMesh< Real > &	m,
		const DV< Real > &	p,
		const DV< Real > &	out,
		const DV< Real > &	pb = `DV<Real>{}`
	)

Two-point normal gradient on faces. Boundary faces: Dirichlet value pb(f − nInterior) if pb is sized, else zero flux (Neumann).

◆ faceInterpTranspose()

template<class Real >

void peclet::voro::fv::faceInterpTranspose	(	const FaceMesh< Real > &	m,
		const DV< Real > &	g,
		const DV< Real > &	out,
		bool	skew = `false`,
		const DV< Real > &	scratch9 = `DV<Real>{}`,
		bool	wallPrescribed = `false`,
		const std::function< void(const DV< Real > &, int)> &	exchange = `{}`
	)

Transpose of the constraint interpolation T (projectToFaces) in the inner products ⟨·,·⟩_V / ⟨·,·⟩_F: ⟨T U, g⟩_F = ⟨U, Tᵀ g⟩_V for every cell field U and face field g. Plain part: (T₀ᵀ g)_i = (1/V_i) Σ_{f∈i} A_f d_f w_if g_f n_f (w_if = the interpolation weight of cell i on f; on a cubic lattice this IS the central difference = Green–Gauss). With skew the transpose of the centroid correction T₁ ∘ GG is added (two passes: the per-cell moment M_i,ck = Σ_f A_f d_f w_if g_f n_fc t_fk, then the Green–Gauss transpose through the faces). Applied to g = the two-point face gradient of φ this is the cell pressure gradient that makes the ABC cell correction the exact adjoint of the face constraint — flow's gauge-exact gradient (gpCenterGrad, the transpose of centerToFace) on the Voronoi mesh: the pressure does no work on the constraint manifold. scratch9 (9N) is needed for the skew part.

◆ greenGaussGradient()

template<class Real >

void peclet::voro::fv::greenGaussGradient	(	const FaceMesh< Real > &	m,
		const DV< Real > &	p,
		const DV< Real > &	out
	)

Green–Gauss cell gradient (3N): distance-weighted face values, boundary faces use p_A.

◆ laplacian()

template<class Real >

void peclet::voro::fv::laplacian	(	const FaceMesh< Real > &	m,
		const DV< Real > &	p,
		const DV< Real > &	out,
		DV< Real > &	scratchFace,
		const DV< Real > &	pb = `DV<Real>{}`
	)

L p = div(grad p): the two-point Laplacian (Neumann on boundary faces unless pb is given).

◆ mergeWallVertices()

template<class Real >

int peclet::voro::fv::mergeWallVertices	(	PolyMesh< Real > &	m,
		const Real	L[3],
		Real	tol
	)

Conforming wall faces (rung B3 follow-up): every wall cell clips its wall-adjacent faces with ITS OWN tangent plane of a curved wall, so the two copies of a shared edge's wall endpoint (one per cell) differ by the tangent-plane mismatch (~the sagitta, O(h²/R)). This post-pass merges wall vertices closer than tol (union–find on a hash grid, periodic min-image distances) into their mean, rewrites the face polygons, drops repeated vertices and degenerate (< 3-vertex) faces. MEASURED (2026-09-04, test_polymesh): it does NOT make the wall layer conforming — the mismatch is topological (the two cells' copies of a shared interface face are clipped by different tangent planes into polygons of different shape), 106 of 108 non-conforming wall cells keep failing Euler. Conforming walls need one wall plane per wall EDGE inside the clipper. Kept as a coincident-vertex cleanup. Returns the number of vertices merged away.

◆ perotTranspose()

template<class Real >

void peclet::voro::fv::perotTranspose	(	const FaceMesh< Real > &	m,
		const DV< Real > &	acell,
		const DV< Real > &	out
	)

Transpose of the Perot reconstruction: face-normal tendency from cell tendencies (3N).

◆ perotVelocity()

template<class Real >

void peclet::voro::fv::perotVelocity	(	const FaceMesh< Real > &	m,
		const DV< Real > &	u,
		const DV< Real > &	out
	)

Perot reconstruction of the cell velocity (3N) from face-normal fluxes.

◆ poissonCG()

template<class Real >

int peclet::voro::fv::poissonCG	(	const FaceMesh< Real > &	m,
		const DV< Real > &	f,
		const DV< Real > &	p,
		Real	tol,
		int	maxIter,
		Real &	resOut
	)

Conjugate gradients on −L p = f (matrix-free, Neumann/periodic: the mean of f is removed and the mean of p pinned to zero — L is symmetric negative semi-definite with the constant null space). Returns the iteration count; resOut the final relative residual. Unpreconditioned: the coarse-grid / AMG preconditioner is track C2.

◆ projectToFaces()

template<class Real >

void peclet::voro::fv::projectToFaces	(	const FaceMesh< Real > &	m,
		const DV< Real > &	ucell,
		const DV< Real > &	out,
		const DV< Real > &	gradU = `DV<Real>{}`,
		const DV< Real > &	ub = `DV<Real>{}`
	)

The centre→face CONSTRAINT interpolation T: u_f = U_f·n_f with U_f the distance-weighted average of the two cell velocities (exact at the connector foot for linear fields). With gradU (9N, vectorGreenGauss) the SKEW correction adds each cell's gradient times the tangential offset t_f = c_f − h_A n_f of the face centroid from the connector, so U_f is the value AT THE FACE CENTROID (second order on skewed faces). Boundary faces: U(A)·n.

◆ vectorGreenGauss()

template<class Real >

void peclet::voro::fv::vectorGreenGauss	(	const FaceMesh< Real > &	m,
		const DV< Real > &	U,
		const DV< Real > &	out,
		const DV< Real > &	Uwall = `DV<Real>{}`
	)

Skew-corrected Green–Gauss gradient of a cell VECTOR field (3N → 9N, (∂_k U_c)_i at 9i + 3c + k): the plain distance-weighted Green–Gauss gradient times R = (I − S)⁻¹ (cellSkewInverse) — exact for linear fields on every cell; boundary faces use the cell value.

◆ wallGradientLS()

template<class Real >

void peclet::voro::fv::wallGradientLS	(	const FaceMesh< Real > &	m,
		const DV< Real > &	U,
		const DV< Real > &	gradU,
		const DV< Real > &	Uwall,
		const DV< Real > &	out
	)

Second-order wall gradient (3 × nBoundary): for each boundary face f of cell i, the normal derivative AT THE WALL of the wall-anchored quadratic u(s) = U_wall + a s + b s² (s = distance from the wall plane) least-squares fitted to the cell value and its interior neighbours, each sample corrected for the tangential variation with the cell gradient gradU (9N; may be empty). The two-point flux (U_i − U_wall)/h_A is the derivative at s = h_A/2 (the half-cell O(h) wall shear that limits the sphere drag, C4); this is flow's wall-anchored quadratic (centerToFaceWallAware) on the unstructured mesh. On a lattice wall cell the fit passes through (wall, U_i, U_above) exactly, so Poiseuille is reproduced to round-off.

◆ writeVtu()

template<class Real >

bool peclet::voro::fv::writeVtu	(	const std::string &	path,
		const PolyMesh< Real > &	m,
		const std::vector< Real > *	cellScalar = `nullptr`,
		const char *	scalarName = `"scalar"`
	)

Write the mesh as an ASCII VTU of VTK_POLYHEDRON cells (with per-cell volume and, if given, a per-cell scalar), readable by ParaView / pyvista.

Namespaces

Classes

Typedefs

Functions

Typedef Documentation

◆ DV

Function Documentation

◆ buildDecEdges()

◆ buildFaceMesh()

◆ buildPolyMesh()

◆ cellSkewInverse()

◆ cellTendency()

◆ decLaplacian()

◆ divergence()

◆ dotCells()

◆ dotFaces()

◆ faceGradient()

◆ faceInterpTranspose()

◆ greenGaussGradient()

◆ laplacian()

◆ mergeWallVertices()

◆ perotTranspose()

◆ perotVelocity()

◆ poissonCG()

◆ projectToFaces()

◆ vectorGreenGauss()

◆ wallGradientLS()

◆ writeVtu()