On applying large eddy simulation (LES) to engineering interest, one of the keys is to obtain two-order low-dissipation shock-capturing schemes adapted to LES. Therefore, the preconditioning method for all speed flows is adopted. However, the accuracy of preconditioned schemes is not satisfactory because of the poor performance of stability of preconditioning techniques especially in viscous fl...

The goal of this article is to design a new approximate Riemann solver for the two-layer shallow water system which is fast compared to Roe schemes and accurate compared to Lax-Friedrichs, FORCE, or GFORCE schemes (see [14]). This Riemann solver is based on a suitable decomposition of a Roe matrix (see [27]) by means of a parabolic viscosity matrix (see [16]) that captures some information conc...

This paper presents a robust finite volume shock-capturing scheme based on the rotated approximate Riemann solver. A general framework for constructing the rotated Riemann solver is described and a rotated Roe scheme is discussed in detail. It is found that the robustness of the rotated shock-capturing scheme is closely related to the way in which the direction of upwind differencing is determi...

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...

Through a linear analysis, we show how to modify Godunov type schemes applied to the compressible Euler system to make them accurate at any Mach number. This allows to propose all Mach Godunov type schemes. A linear stability result is proposed and a formal asymptotic analysis justifies the construction in the barotropic case when the Godunov type scheme is a Roe scheme. We also underline that ...

We design energy preserving and energy stable schemes for the shallow water equations. A new explicit energy preserving flux is proposed and is compared with existing energy preserving fluxes. This new flux results in a considerable reduction in the computational cost. We add suitably discretized viscous terms to the energy preserving scheme in order to obtain an energy stable scheme that repli...

Due to improvements in computational resources, interest has recently increased in using implicit scheme for solving flow equations on 3D unstructured grids. However, most of the implicit schemes produce greater numerical diffusion error than their corresponding explicit schemes. This stems from the fact that in linearizing implicit fluxes, it is conventional to replace the Jacobian matrix in t...

A lot of well-balanced schemes have been proposed for discretizing the classical Saint-Venant system for shallow water flows with non-flat bottom. Among them, the hydrostatic reconstruction scheme is a simple and efficient one. It involves the knowledge of an arbitrary solver for the homogeneous problem (for example Godunov, Roe, kinetic. . . ). If this solver is entropy satisfying, then the hy...

A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing RungeKutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-d...

In the present paper, a supersonic wind-tunnel is designed to maintain a flow with Mach number of 3 in a 30cm×30cm test section. An in-house CFD code is developed using the Roe scheme to simulate flow-field and detect location of normal shock in the supersonic wind-tunnel. In the Roe scheme, flow conditions at inner and outer sides of cell faces are determined using an upwind biased algorithm. ...