Based on Nessyahu's and Tadmor's nonoscillatory central di erence schemes for one-dimensional hyperbolic conservation laws [14], for higher dimensions, several nite 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 ...

We study the Lax-Friedrichs scheme, approximating the scalar, genuinely nonlinear conservation law u, + fx(u) = 0, where /(h) is, say, strictly convex, /> ¿„ > 0. We show that the divided differences of the numerical solution at time t do not exceed 2(/¿,)-1. This one-sided Lipschitz boundedness is in complete agreement with the corresponding estimate one has in the differential case; in partic...

Fluid-structure interaction (FSI) occurs when the dynamic water hammer forces; cause vibrations in the pipe wall. FSI in pipe systems due to Poisson and junction coupling has been the center of attention in recent years. It causes fluctuations in pressure heads and vibrations in the pipe wall. The governing equations of this phenomenon include a system of first order hyperbolic partial differen...

The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of nonlinear hyperbolic problem to satisfy relevant maximum principles and entropy stability conditions. desired properties are enforced by applying limiter antidiffusive fluxes that represent the difference between high-order baseline scheme property-preserving appro...

Abstract A quasi–second-order scheme is developed to obtain approximate solutions of the two-dimensional shallow water equations (SWEs) with bathymetry. The based on a staggered finite volume space discretization: scalar unknowns are located in discretization cells while vector edges mesh. monotonic upwind-central for conservation laws (MUSCL)-like interpolation discrete convection operators he...

We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+1)dimensional boost-invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of ...

The DFLU numerical flux was introduced in order to solve hyperbolic scalar conservation laws with a flux function discontinuous in space. We show how this flux can be used to solve certain class of systems of conservation laws such as systems modeling polymer flooding in oil reservoir engineering. Furthermore, these results are extended to the case where the flux function is discontinuous in th...