Conservative arbitrary order finite difference schemes for shallow-water flows

Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows

Many geophysical flows are merely perturbations of some fundamental equilibrium state. If a numerical scheme shall capture such flows efficiently, it should be able to preserve the unperturbed equilibrium state at the discrete level. Here we present a class of schemes of any desired order of accuracy which preserve the lake at rest perfectly. These schemes should have an impact for studying imp...

Fully Conservative Higher Order Finite Difference Schemes for Incompressible Flow

Conservation properties of the mass, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discrete equations. Existing finite difference schemes in regular and staggered grid systems are checked for violations of the conservation requirements and a few important discrepancies are pointed out. In particular, it is found that ...

Conservative high-order finite-difference schemes for low-Mach number flows

High-order finite difference schemes for incompressible flows

This paper presents a new high order approach to the numerical solution of the incompressible Stokes and Navier-Stokes equations. The class of schemes developed is based upon a velocity-pressure-pressure gradient formulation which allows: (i) high order finite difference stencils to be applied on nonstaggered grids; (ii) high order pressure gradient approximations to be made using standard Padé...

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...