Cell scalar advection

Namespaces
module	mod_compute_cell_cons_advection_term_exp_rec_schemes
	Explicit reconstruction schemes (wrappers) for the advection equationcompute_cell_cons_advection_term_exp_upwind_generic_rec and compute_cell_cons_advection_term_exp_centered_generic_rec for further details.
module	mod_compute_cell_advection_term_exp_semi_lagrangian
	Explicit semi lagrangian method for the advection equation.
module	mod_compute_cell_cons_advection_term_exp_weno_schemes
	Explicit WENO schemes (wrappers) for the advection equation.
module	mod_compute_cell_cons_advection_term_exp_generic_fast_rec
	Explicit Fast Reconstruction scheme (generic) for the advection equation.
module	mod_compute_cell_cons_advection_term_exp_generic_fast_weno
	Explicit WENO scheme (generic) for the advection equation.
module	mod_compute_cell_cons_advection_term_exp_generic_rec
	Explicit Reconstruction scheme (generic) for the advection equation.
module	mod_compute_cell_cons_advection_term_exp_generic_weno
	Explicit WENO scheme (generic) for the advection equation.
module	mod_compute_cell_cons_advection_term_exp_opt_weno
	Explicit WENO scheme (generic) for the advection equation.
module	mod_integrate_cell_advection_term_explicit_generic
	Integration methods for the advection equation.
module	mod_scalar_advection_tvd_superbee
	Explicit dimensional splitting Lax-Wendroff TVD SuperBee (LW-TVD-SB) scheme for the advection equation.
module	mod_advect_field
	Quick explicit advection method for a scalar field.

Detailed Description

This directory provides a set of routines to discretize a scalar advection equation defined, in a conservative way, on cells such as:

\[ \frac{\partial \phi}{\partial t} = - \nabla \cdot \left( u(\mathbf{x},t) \phi \right) \]

with a given velocity field \( u(\mathbf{x},t) \).

Time discretization

Various schemes are proposed for the computation of the integral of the previous equation between \( t^n \) and \( t^{n+1} \), basicaly Runge-Kutta schemes.

Note

• The canonical first order Euler is the only temporal scheme currently implemented for the explicit dimensional splitting Lax-Wendroff TVD Superbee spatial scheme. Note: RK2 is implemented but Euler should be used until further notice.

Spatial discretization

Various spatial schemes are proposed for the spatial discretization: from the simple first order scheme to more complex WENO schemes. All the methods are implemented in a generic way, thanks to the use of appropriate node level schemes. Also, a classical semi lagrangian method is furnished.