teno Namespace Reference

Classes
struct	PackedStencils
	Per-cell stencils of different sizes, stored without padding to the largest one in the mesh. Slot s of a cell's stencil holds the stencil cell, its mirror boundary face (or -1) and width pseudo-inverse entries. Consecutive cells form slices of 2^shift cells; a slice is padded to its largest stencil and interleaves its cells' slots. With single, pinv holds the pseudo-inverse entries as floats, two to an element, at the same indices. More...
struct	SmoothnessTerms
	The terms of the smoothness-indicator matrix (3D): entry e (upper_index(l, m)) is sum_t weight(t) moments(cell, moment(t)) over t in [start(e), start(e + 1)), with products of D^beta factors (whole numbers below 2^16) as weights; term(t) holds weight(t) << 16 | moment(t). More...

Typedefs
using	Moments = Kokkos::View< double **, Kokkos::LayoutRight >
	(cell, k): central moments of each cell, mean of ((x - x_c) / h_c)^a ... (3D).

Functions
KOKKOS_INLINE_FUNCTION constexpr uint8_t	n_dof (const uint8_t r)
	Number of non-constant N_DIM-variate monomials of total degree <= r.
KOKKOS_INLINE_FUNCTION constexpr uint16_t	upper_index (const uint8_t l, const uint8_t m, const uint8_t n)
	Index of entry (l, m), l <= m, of a symmetric n x n matrix stored as its upper triangle, row by row.
KOKKOS_INLINE_FUNCTION void	exponents (const uint8_t l, uint8_t &a, uint8_t &b)
	Exponents (a, b) of the l-th monomial xi^a eta^b, ordered by total degree: (1,0), (0,1), (2,0), (1,1), (0,2), (3,0), ...
KOKKOS_INLINE_FUNCTION void	exponents (const uint8_t l, uint8_t &a, uint8_t &b, uint8_t &c)
	Exponents (a, b, c) of the l-th trivariate monomial xi^a eta^b zeta^c, ordered by total degree, then by decreasing a, then decreasing b: (1,0,0), (0,1,0), (0,0,1), (2,0,0), (1,1,0), (1,0,1), (0,2,0), ...
template<typename T >
KOKKOS_INLINE_FUNCTION T	ipow (const T x, const uint8_t n)
template<typename T >
KOKKOS_INLINE_FUNCTION void	monomials (const uint8_t r, const T xi, const T eta, T *phi)
	Evaluate all monomials of degree 1..r at (xi, eta).
template<typename T >
KOKKOS_INLINE_FUNCTION void	monomial_gradients (const uint8_t r, const T xi, const T eta, T *d_xi, T *d_eta)
	Derivatives with respect to xi and eta of all monomials of degree 1..r at (xi, eta).
template<typename T >
KOKKOS_INLINE_FUNCTION void	monomials (const uint8_t r, const T xi, const T eta, const T zeta, T *phi)
	Evaluate all trivariate monomials of degree 1..r at (xi, eta, zeta).
template<typename T >
KOKKOS_INLINE_FUNCTION void	monomials (const uint8_t r, const T *x, T *phi)
	Monomials at a point x (N_DIM coordinates, already scaled).
KOKKOS_INLINE_FUNCTION void	eigenvectors (const rtype *W, const rtype *n, const rtype gamma, rtype L[N_CONSERVATIVE][N_CONSERVATIVE], rtype R[N_CONSERVATIVE][N_CONSERVATIVE])
	Left (L) and right (R) eigenvectors of the Euler flux Jacobian in direction n for conservative variables, at state W = [rho, u, p]. Characteristic order: u_n - a, u_n (entropy), u_n + a, then one u_n (shear) wave per tangent of tangent_basis(n).
KOKKOS_INLINE_FUNCTION void	primitive_eigenvectors (const rtype *W, const rtype a, const rtype *n, rtype L[N_CONSERVATIVE][N_CONSERVATIVE], rtype R[N_CONSERVATIVE][N_CONSERVATIVE])
	Left (L) and right (R) eigenvectors of the Euler equations in primitive variables W = [rho, u, p] in direction n, for sound speed a: valid for any equation of state. Same characteristic order as eigenvectors(): u_n - a, u_n (entropy, here the density at fixed p and u), u_n + a, then the shear waves.
KOKKOS_INLINE_FUNCTION rtype	adaptive_CT (const rtype sigma, const rtype sigma_L, const rtype sigma_U)
	Adaptive cutoff C_T from the troubled-cell measure sigma (Liang, Shyy & Fu 2025): 1e-10 near sigma_L, 1e-6 above sigma_U.

Variables
constexpr uint8_t	MAX_DEGREE = 5
constexpr uint8_t	MAX_NK = n_dof(MAX_DEGREE)
constexpr uint8_t	NK_SMALL = n_dof(2)
constexpr uint8_t	MAX_FACES = (N_DIM == 2) ? 4 : 6
constexpr uint8_t	MAX_FACE_QUAD = (N_DIM == 2) ? 4 : 9
constexpr uint8_t	SLICE_SHIFT
	log2 of the cells per slice of PackedStencils: 32 on GPUs, so that a warp reads consecutive words, and 1 on the host, where each cell's stencil is then contiguous.

Typedef Documentation

Moments

using teno::Moments = typedef Kokkos::View<double **, Kokkos::LayoutRight>

(cell, k): central moments of each cell, mean of ((x - x_c) / h_c)^a ... (3D).

Function Documentation

adaptive_CT()

KOKKOS_INLINE_FUNCTION rtype teno::adaptive_CT	(	const rtype	sigma,
		const rtype	sigma_L,
		const rtype	sigma_U
	)

Adaptive cutoff C_T from the troubled-cell measure sigma (Liang, Shyy & Fu 2025): 1e-10 near sigma_L, 1e-6 above sigma_U.

eigenvectors()

KOKKOS_INLINE_FUNCTION void teno::eigenvectors	(	const rtype *	W,
		const rtype *	n,
		const rtype	gamma,
		rtype	L[N_CONSERVATIVE][N_CONSERVATIVE],
		rtype	R[N_CONSERVATIVE][N_CONSERVATIVE]
	)

Left (L) and right (R) eigenvectors of the Euler flux Jacobian in direction n for conservative variables, at state W = [rho, u, p]. Characteristic order: u_n - a, u_n (entropy), u_n + a, then one u_n (shear) wave per tangent of tangent_basis(n).

exponents() [1/2]

KOKKOS_INLINE_FUNCTION void teno::exponents	(	const uint8_t	l,
		uint8_t &	a,
		uint8_t &	b
	)

Exponents (a, b) of the l-th monomial xi^a eta^b, ordered by total degree: (1,0), (0,1), (2,0), (1,1), (0,2), (3,0), ...

exponents() [2/2]

KOKKOS_INLINE_FUNCTION void teno::exponents	(	const uint8_t	l,
		uint8_t &	a,
		uint8_t &	b,
		uint8_t &	c
	)

Exponents (a, b, c) of the l-th trivariate monomial xi^a eta^b zeta^c, ordered by total degree, then by decreasing a, then decreasing b: (1,0,0), (0,1,0), (0,0,1), (2,0,0), (1,1,0), (1,0,1), (0,2,0), ...

ipow()

template<typename T >

KOKKOS_INLINE_FUNCTION T teno::ipow	(	const T	x,
		const uint8_t	n
	)

monomial_gradients()

template<typename T >

KOKKOS_INLINE_FUNCTION void teno::monomial_gradients	(	const uint8_t	r,
		const T	xi,
		const T	eta,
		T *	d_xi,
		T *	d_eta
	)

Derivatives with respect to xi and eta of all monomials of degree 1..r at (xi, eta).

monomials() [1/3]

template<typename T >

KOKKOS_INLINE_FUNCTION void teno::monomials	(	const uint8_t	r,
		const T *	x,
		T *	phi
	)

Monomials at a point x (N_DIM coordinates, already scaled).

monomials() [2/3]

template<typename T >

KOKKOS_INLINE_FUNCTION void teno::monomials	(	const uint8_t	r,
		const T	xi,
		const T	eta,
		const T	zeta,
		T *	phi
	)

Evaluate all trivariate monomials of degree 1..r at (xi, eta, zeta).

monomials() [3/3]

template<typename T >

KOKKOS_INLINE_FUNCTION void teno::monomials	(	const uint8_t	r,
		const T	xi,
		const T	eta,
		T *	phi
	)

Evaluate all monomials of degree 1..r at (xi, eta).

n_dof()

KOKKOS_INLINE_FUNCTION constexpr uint8_t teno::n_dof ( const uint8_t  r )

constexpr

Number of non-constant N_DIM-variate monomials of total degree <= r.

primitive_eigenvectors()

KOKKOS_INLINE_FUNCTION void teno::primitive_eigenvectors	(	const rtype *	W,
		const rtype	a,
		const rtype *	n,
		rtype	L[N_CONSERVATIVE][N_CONSERVATIVE],
		rtype	R[N_CONSERVATIVE][N_CONSERVATIVE]
	)

Left (L) and right (R) eigenvectors of the Euler equations in primitive variables W = [rho, u, p] in direction n, for sound speed a: valid for any equation of state. Same characteristic order as eigenvectors(): u_n - a, u_n (entropy, here the density at fixed p and u), u_n + a, then the shear waves.

upper_index()

KOKKOS_INLINE_FUNCTION constexpr uint16_t teno::upper_index ( const uint8_t  l, const uint8_t  m, const uint8_t  n  )

constexpr

Index of entry (l, m), l <= m, of a symmetric n x n matrix stored as its upper triangle, row by row.

Variable Documentation

MAX_DEGREE

constexpr uint8_t teno::MAX_DEGREE = 5

constexpr

MAX_FACE_QUAD

constexpr uint8_t teno::MAX_FACE_QUAD = (N_DIM == 2) ? 4 : 9

constexpr

MAX_FACES

constexpr uint8_t teno::MAX_FACES = (N_DIM == 2) ? 4 : 6

constexpr

MAX_NK

constexpr uint8_t teno::MAX_NK = n_dof(MAX_DEGREE)

constexpr

NK_SMALL

constexpr uint8_t teno::NK_SMALL = n_dof(2)

constexpr

SLICE_SHIFT

constexpr uint8_t teno::SLICE_SHIFT

constexpr

Initial value:

=
    Kokkos::SpaceAccessibility<Kokkos::DefaultExecutionSpace, Kokkos::HostSpace>::accessible ? 0 : 5

log2 of the cells per slice of PackedStencils: 32 on GPUs, so that a warp reads consecutive words, and 1 on the host, where each cell's stencil is then contiguous.