Compact third-order limiter functions for finite volume methods

Compact third-order limiter functions for finite volume methods

We consider finite volume methods for the numerical solution of conservation laws. In order to achieve high-order accurate numerical approximation to non-linear smooth functions, we introduce a new class of limiter functions for the spatial reconstruction of hyperbolic equations. We therefore employ and generalize the idea of double-logarithmic reconstruction of Artebrant and Schroll [R. Artebr...

High-Order Compact Finite Difference Methods

In this work we present a general approach for developing high-order compact differencing schemes by utilizing the governing differential equation to help approximate truncation error terms. As an illustrative application we consider the stream-function vorticity form of the Navier Stokes equations, and provide driven cavity results. Some extensions to treat non-constant metric coefficients res...

First-, second-, and third-order finite-volume schemes for diffusion

Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system

The subject of the paper is the derivation and analysis of third order nite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the rst order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation ~ U n = RhU n 2 S h from the piecewise constantU 2 S h , to feed into ...

Compact finite difference methods for high order integro-differential equations

High order integro-differential equations (IDE), especially nonlinear, are usually difficult to solve even for approximate solutions. In this paper, we give a high accurate compact finite difference method to efficiently solve integro-differential equations, including high order and nonlinear problems. By numerical experiments, we show that compact finite difference method of integro-differenti...