viscous_flux.h File Reference

Viscous (diffusive) flux functor for the Navier-Stokes equations. More...

#include <Kokkos_Core.hpp>
#include "common.h"
#include "boundary.h"
#include "physics.h"

Go to the source code of this file.

Classes
struct	ViscousFluxFunctor
	Integrates the viscous stress and heat flux over every face (one-point rule) and adds them to face_flux (see ConvectiveFluxFunctor). More...

Functions
KOKKOS_INLINE_FUNCTION void	viscous_traction (const rtype mu, const rtype g[][N_DIM], const rtype *n, rtype *tau_n, const rtype hoop_divergence=0.0_r)
	Viscous traction tau . n of a Newtonian fluid under Stokes' hypothesis, tau = mu (grad u + grad u^T - 2/3 div u I), with g[k][i] = d u_k / d x_i. Axisymmetric flows add the hoop part u_r / r of the divergence.
KOKKOS_INLINE_FUNCTION rtype	hoop_divergence (const rtype r, const rtype *u, const rtype g[][N_DIM])
	u_r / r at radius r for velocity u and gradient g (g[k][i] = d u_k / d x_i), with r = y: its limit d u_r / d r on the axis.
KOKKOS_INLINE_FUNCTION rtype	variance_jump (const Kokkos::View< rtype *[3]> &covariance, const int32_t c0, const int32_t c1, const rtype *d)
	Axisymmetric meshes: jump from cell c0 to c1 of the cells' r-weighted variance along d (Mesh::cell_covariance), divided by |d|^2.
KOKKOS_INLINE_FUNCTION rtype	mean_offset (const rtype *g0, const rtype *g1, const rtype *d, const rtype dvar)
	Part of the jump of two cell averages that comes from the cells' different spreads (variance jump dvar along d, see variance_jump): an average exceeds the value at the center by q_ss var / 2, with the second derivative q_ss along d from the cell gradients g0, g1.
KOKKOS_INLINE_FUNCTION rtype	face_fraction (const Kokkos::View< rtype *[N_DIM]> &face_coords, const Kokkos::View< rtype *[N_DIM]> &cell_coords, const uint32_t f, const int32_t c0, const rtype *d)
	Fraction along d (from the center of cell c0 to that of its neighbor) of the projection of face f's center.

Detailed Description

Viscous (diffusive) flux functor for the Navier-Stokes equations.

Author

Matthew Bonanni (mbona.nosp@m.nni0.nosp@m.01@gm.nosp@m.ail..nosp@m.com)

Version

0.1

Date

2026-10-02

Copyright

Copyright (c) 2026 Matthew Bonanni

Function Documentation

face_fraction()

KOKKOS_INLINE_FUNCTION rtype face_fraction	(	const Kokkos::View< rtype *[N_DIM]> &	face_coords,
		const Kokkos::View< rtype *[N_DIM]> &	cell_coords,
		const uint32_t	f,
		const int32_t	c0,
		const rtype *	d
	)

Fraction along d (from the center of cell c0 to that of its neighbor) of the projection of face f's center.

hoop_divergence()

KOKKOS_INLINE_FUNCTION rtype hoop_divergence	(	const rtype	r,
		const rtype *	u,
		const rtype	g[][N_DIM]
	)

u_r / r at radius r for velocity u and gradient g (g[k][i] = d u_k / d x_i), with r = y: its limit d u_r / d r on the axis.

mean_offset()

KOKKOS_INLINE_FUNCTION rtype mean_offset	(	const rtype *	g0,
		const rtype *	g1,
		const rtype *	d,
		const rtype	dvar
	)

Part of the jump of two cell averages that comes from the cells' different spreads (variance jump dvar along d, see variance_jump): an average exceeds the value at the center by q_ss var / 2, with the second derivative q_ss along d from the cell gradients g0, g1.

variance_jump()

KOKKOS_INLINE_FUNCTION rtype variance_jump	(	const Kokkos::View< rtype *[3]> &	covariance,
		const int32_t	c0,
		const int32_t	c1,
		const rtype *	d
	)

Axisymmetric meshes: jump from cell c0 to c1 of the cells' r-weighted variance along d (Mesh::cell_covariance), divided by |d|^2.

viscous_traction()

KOKKOS_INLINE_FUNCTION void viscous_traction	(	const rtype	mu,
		const rtype	g[][N_DIM],
		const rtype *	n,
		rtype *	tau_n,
		const rtype	hoop_divergence = 0.0_r
	)

Viscous traction tau . n of a Newtonian fluid under Stokes' hypothesis, tau = mu (grad u + grad u^T - 2/3 div u I), with g[k][i] = d u_k / d x_i. Axisymmetric flows add the hoop part u_r / r of the divergence.