A New High Resolution TVD Scheme for Unsteady Flows with Shock Waves

A high-resolution scheme of TVD type for the Aw-Rascle-Greenberg model of traffic flow

An approximate Riemann solver for the Aw-Rascle traffic flow model and the extension of Greenberg is constructed on the algebraic level. A discrete diffusion operator is added to the (oscillatory) high-order finite difference/element discretization to enforce a vectorial LED criterion. This yields a nonoscillatory but diffusive low-order scheme. To increase the accuracy an antidiffusion operato...

TVD and ENO Schemes for Multidimensional Steady and Unsteady Flows A Comparative Analysis

This work deals with numerical solution of first order hyperbolic equation or system in 2D or 3D. In the first part, the solution of a 2D linear scalar equation is investigated. Using this model problem, the results of different numerical schemes are compared from the point of view of accuracy and parallel efficiency. The next part describes 2D and 3D steady numerical solutions of the transonic...

High-order TVD shock-capturing schemes for unstructured grid solvers

A total variation diminishing high resolution scheme for nonlinear conservation laws

In this paper we propose a novel high resolution scheme for scalar nonlinear hyperbolic conservation laws. The aim of high resolution schemes is to provide at least second order accuracy in smooth regions and produce sharp solutions near the discontinuities. We prove that the proposed scheme that is derived by utilizing an appropriate flux limiter is nonlinear stable in the sense of total varia...

A pseudo-penalization method for high Reynolds number unsteady flows

A pseudo-penalization method, i.e., an implicit formulation of the standard volume penalization method, is introduced and validated by considering the 2D wake of a cylinder at Reynolds number Re = 200. © 2007 IMACS. Published by Elsevier B.V. All rights reserved. MSC: 76D05; 76D25; 76M22