In this paper, we consider several high-order schemes in one space dimension. In particular, we compare the second-order relaxation ( << 1) or “relaxed” ( = 0) schemes of Jin and Xin [Comm. Pure Appl. Math., 48 (1995), pp. 235–277] with the second-order Lax–Friedrichs scheme of Nessyahu and Tadmor [J. Comp. Phys., 87 (1990), pp. 408–463] and with higher-order essentially nonoscillatory (ENO) an...

This paper is devoted to the construction of numerical fluxes for hyperbolic systems. We first present a GFORCE numerical flux, which is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first order upwind method. Then we incorporate GFORCE in the framework of the...

We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional...

This exploratory work tries to present first results of a novel approach for the numerical approximation of solutions of hyperbolic systems of conservation laws. The objective is to define stable and “reasonably” accurate numerical schemes while being free from any upwind process and from any computation of derivatives or mean Jacobian matrices. That means that we only want to perform flux eval...

The objective of this problem is to study ant foraging lines in one and two dimensions in order to understand their dynamics and examine the fitness of ant colonies. A simple model to describe ant traffic is formulated using conservation laws and a behavioral model. In this work, the behavioral model assumes that the concentration of pheromones is simply proportional to the density of ants. Thi...

A diffusion regulation parameter, which operates based on the jump in the Mach number, is presented for implementation in Euler solvers. This diffusion regulation parameter adjusts itself automatically in different regimes of the flow and leads to the exact capturing of steady contact discontinuities which are aligned with the grid-lines. This diffusion regulator parameter reduces numerical dis...

Currently, the Discontinuous Galerkin Method (DGM) is widely used to solve complex multi-scale problems of mathematical physics that have important applied significance. When implementing it, question choosing a discrete approximation flows for viscous terms Navier-Stokes equation important. It necessary focus on construction limiting functions, selection best approximations diffusion flows, an...

Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the “direction of the wind.” Instead, we propose to use as a building block the mor...

Abstract. The nonoscillatory central difference scheme of Nessyahu and Tadmor is a Godunovtype scheme for one-dimensional hyperbolic conservation laws in which the resolution of Riemann problems at the cell interfaces is bypassed thanks to the use of the staggered Lax–Friedrichs scheme. Piecewise linear MUSCL-type (monotonic upstream-centered scheme for conservation laws) cell interpolants and ...

In this paper, we present a high-order weighted essentially non-oscillatory (WENO) scheme, coupled with a high-order fast sweeping method, for solving a dynamic continuum model for bidirectional flow. We first review the dynamic continuum model for bi-directional flow. This model is composed of a coupled system of a conservation law and an Eikonal equation. Then we present the first-order Lax-F...