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...

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...

The goal of this work is to introduce new families shock-capturing high-order numerical methods for systems conservation laws that combine Fast WENO (FWENO) and Optimal (OWENO) reconstructions with Approximate Taylor the time discretization. FWENO are based on smoothness indicators require a lower number calculations than standard ones. OWENO definition nonlinear weights allows one unconditiona...

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...

Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to secondorder by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. Thes...

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...