Large Time Step Roe scheme for a common 1D two-fluid model

Large Time-Step Numerical Scheme for the Seven-Equation Model of Compressible Two-Phase Flows

A MUSTA Scheme for a Nonconservative Two-Fluid Model

Abstract. We present a multi-stage centred scheme, of the kind proposed by Toro [Appl. Numer. Math. 56 (2006) 1464], for numerically resolving the simultaneous flow of two fluids through a transport pipeline. This model contains non-conservative terms in both the temporal and spatial derivatives, and an extension of the standard numerical framework for conservation laws is needed. In this paper...

On Large Time Step Godunov Scheme for Hyperbolic Conservation Laws

In this paper we study the large time step (LTS) Godunov scheme proposed by LeVeque for nonlinear hyperbolic conservation laws. As we known, when the Courant number is larger than 1, the linear interactions of the elementary waves in this scheme will be much more complicated than those for Courant number less than 1. In this paper, we will show that for scalar conservation laws, for any fixed C...

On a Large Time - Step High Resolution Scheme

This paper presents a class of new second-order accurate (IK + 3)-point explicit schemes for the computation of weak solutions of hyperbolic conservation laws, that are total-variation-diminishing under a CFL restriction of K. These highly nonlinear schemes are obtained by applying a nonoscillatory first-order accurate (IK + l)-point scheme to a modified flux. The so-derived second-order accura...

A numerical scheme for space-time fractional advection-dispersion equation

In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...