In this paper a time-splitting technique for the two dimensional advectiondispersion equation is proposed. A high resolution in space Godunov method for advection is combined with the RT0 Mixed Finite Element for the discretization of the dispersion term. Numerical tests on an analytical one dimensional example ascertain the convergence properties of the scheme. At di erent Peclet numbers, the ...

A macroscopic model describing nonlinear viscoelastic waves is derived in Eulerian formulation, through the introduction of relaxation tensors. It accounts for both constitutive and geometrical nonlinearities. In case small deformations, governing equations recover those linear generalized Zener (GZM) with memory variables, which widely used acoustics seismology. The structure terms implies tha...

The goal of this paper is to provide a theoretical framework allowing to extend some general concepts related to the numerical approximation of 1d conservation laws to the more general case of first order quasi-linear hyperbolic systems. In particular this framework is intended to be useful for the design and the analysis of well-balanced numerical schemes for solving balance laws or coupled sy...

This paper presents a feedback control design for a coordinated ramp metering problem. We design an optimal traffic allocation scheme for ramps based on Godunov’s numerical method and using distributed-diffusive model. Most of the previous work for designing feedback control for ramp metering is based on either the discretized linear methods such as ALINEA or nonlinear methods based on the traf...

We introduce two kinds of explicit solutions to the convection-reaction equation, ut + (|u| /q)x = u, u, x ∈ R, t ∈ R , q > 1, and employ them to test properties of various computational schemes. From this test we observe that computed solutions using Lax-Friedrichs, MacCormack and Lax-Wendroff schemes break down in a finite time. On the other hand some other schemes including WENO, NT and Godu...

This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of hybrid boundary conditions is needed for the problem to be well posed. The boundary conditions are represented by a hybrid automaton with switches between the modes determined by the direction of characteristics of the system at the boundary. The existence ...

High resolution, non-oscillatory, central difference (NOCD) numerical schemes are introduced as alternatives to more traditional artificial viscosity (AV) and Godunov methods for solving the fully general relativistic hydrodynamics equations. These new approaches provide the advantages of Godunov methods in capturing ultra-relativistic flows without the cost and complication of Riemann solvers,...

This paper presents a second-order accurate adaptive Godunov method for twodimensional (2D) compressible multicomponent flows, which is an extension of the previous adaptive moving mesh method of Tang et al. (SIAM J. Numer. Anal. 41:487–515, 2003) to unstructured triangular meshes in place of the structured quadrangular meshes. The current algorithm solves the governing equations of 2D multicom...

In this paper we use the 10-moment description of fluid flow to compute internal nozzle flow and external flow around a micro-airfoil in the continuum-transition regime. The numerical method used is Hancock’s scheme, a second-order non-oscillatory Godunov-type scheme; the numerical flux function incorporated is of the Harten-Lax-van Leer (HLL) type and due to Linde (HLLL). The numerical solutio...

A radiative transfer scheme is presented, based on a moment description of the equation of radiative transfer and the so–called “M1 closure model” for the Eddington tensor. This model features a strictly hyperbolic transport step for radiation : it has been implemented using standard Godunov–like techniques in a new code called ATON. Coupled to simple models of ionization chemistry and photo-he...