We study the relationship between finite volume and mixed finite element methods for the the hyperbolic conservation laws, and the closely related convection-diffusion equations.A general framework is proposed for the derivation and a functional framework is developed which could allow the analysis of relating finite volume (FV) schemes. We show via two nonstandard formulations, that numerous F...

This paper was concerned to simulate both wet and dry bed dam break problems. A high-resolution finite volume method (FVM) was employed to solve the one-dimensional (1D) and two-dimensional (2D) shallowwater equations (SWEs) using an unstructured Voronoi mesh grid. In this attempt, the robust local Lax-Friedrichs (LLxF) scheme was used for the calculating of the numerical flux at cells interfac...

A new form of governing equations is derived from Hamilton’s principle of least action for a constrained Lagrangian, depending on conserved quantities and their derivatives with respect to the time-space. This form yields conservation laws both for non-dispersive case (Lagrangian depends only on conserved quantities) and dispersive case (Lagrangian depends also on their derivatives). For non-di...

The problem of traffic congestion is becoming endemic due to increased levels of populations owning automobiles. In an effort to minimize congestion, an accurate method for modeling the flow of traffic is imperative. While randomized microscopic models can be very accurate, they are computationally much slower than macroscopic models. Furthermore, macroscopic models can be very accurate in mode...

The discontinuous Galerkin (DG) or local discontinuous Galerkin (LDG) method is a spatial discretization procedure for convection-diffusion equations, which employs useful features from high resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. The LaxWendroff time discretization procedure is an alternative method for time d...

The goal of this article is to design robust and simple first order explicit solvers for one-dimensional nonconservative hyperbolic systems. These solvers are intended to be used as the basis for higher order methods for one or multidimensional problems. The starting point for the development of these solvers is the general definition of a Roe linearization introduced by Toumi in 1992 based on ...

We develop a theoretical tool to examine the properties of numerical schemes for advection equations. To magnify the defects of a scheme we consider a convection-reaction equation 0021-9 doi:10. q Th * Co E-m ut þ ðjujq=qÞx 1⁄4 u; u; x 2 R; t 2 Rþ; q > 1: It is shown that, if a numerical scheme for the advection part is performed with a splitting method, the intrinsic properties of the scheme a...

In this paper we present a methodology for constructing accurate and efficient hybrid central-upwind (HCU) type schemes for the numerical resolution of a two-fluid model commonly used by the nuclear and petroleum industry. Particularly, we propose a method which does not make use of any information about the eigenstructure of the Jacobian matrix of the model. The two-fluid model possesses a hig...

Based on Nessyahu and Tadmor’s nonoscillatory central difference schemes for one-dimensional hyperbolic conservation laws [16], for higher dimensions several finite volume extensions and numerical results on structured and unstructured grids have been presented. The experiments show the wide applicability of these multidimensional schemes. The theoretical arguments which support this are some m...