We prove in this paper the Lax–Wendroff consistency of a general finite volume convection operator acting on discrete functions which are possibly not piecewise-constant over cells mesh and time steps. It yields an extension theorem for colocated or non-colocated schemes. This result is obtained polygonal polyhedral meshes, under assumptions which, usual practical cases, essentially boil down t...

Based on the recent development of Jacobian-free Lax–Wendroff (LW) approaches for solving hyperbolic conservation laws (Zorio et al. in J Sci Comput 71:246–273, 2017, Carrillo and Parés 80:1832–1866, 2019), a novel collection explicit multistage multiderivative solvers is presented this work. In contrast to Taylor time-integration methods, Runge–Kutta (MDRK) techniques achieve higher-order cons...

Abstract We perform a comparative accuracy study of the Rusanov, CABARETM, and WENO5 difference schemes used to compute dam break problem for shallow water theory equations. demonstrate that all three have first order convergence inside region occupied by centered rarefaction wave, Rusanov scheme has second in area constant flow between shock while CABARETM there is no local this area. This due...

This talk is dedicated to multi-dimensional numerical simulation of Euler equations for compressible flow problems. To fulfill the conditions of the Lax-Wendroff theorem, it is required that a numerical scheme conserves the mass, momentum and total energy. Associated with the consistency and the increase of the entropy, these conservation properties are sufficient, in 1D, to ensure that a conve...

We develop a high order finite difference numerical boundary condition for solving hyperbolic conservation laws on a Cartesian mesh. The challenge results from the wide stencil of the interior high order scheme and the fact that the boundary intersects the grids in an arbitrary fashion. Our method is based on an inverse Lax-Wendroff procedure for the inflow boundary conditions. We repeatedly us...

In everyday life human faces shock waves and rarefaction largely in their surroundings. Hence it’s necessary to know the behavior of these protect destructive effects. The aim this work observe propagation various dynamics due solve non-linear hyperbolic inviscid Burgers’ equation numerically. models adopted here two numerical schemes which enable us first order explicit upwind scheme (EUDS) se...

We study the Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion and with monotonically increasing initial data using the Riemann-Hilbert (RH) approach. The solution of the Cauchy problem, in the zero dispersion limit, is obtained using the steepest descent method for oscillatory Riemann-Hilbert problems. The asymptotic solution is completely described by a scalar func...