In this paper we construct high order weighted essentially non-oscillatory (WENO) schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. We present third order schemes using a combination of linear polynomials, and fourth order schemes using a combination of quadratic polynomials. Numerical examples are shown to demonstrate the accuracies and robustness of ...

Two new formulations of a symmetric WENO method for the direct numerical simulation of compressible turbulence are presented. The schemes are designed to maximize order of accuracy and bandwidth, while minimizing dissipation. The formulations and the corresponding coefficients are introduced. Numerical solutions to canonical flow problems are used to determine the dissipation and bandwidth prop...

In this article, the development of high-order semi-implicit interpolation schemes for convection terms on unstructured grids is presented. It is based on weighted essentially non-oscillatory (WENO) reconstructions which can be applied to the evaluation of any field in finite volumes using its known cell-averaged values. Here, the algorithm handles convex cells in arbitrary three-dimensional me...

Abstract In this paper, we propose a new conservative semi-Lagrangian (SL) finite difference (FD) WENO scheme for linear advection equations, which can serve as a base scheme for the Vlasov equation by Strang splitting [4]. The reconstruction procedure in the proposed SL FD scheme is the same as the one used in the SL finite volume (FV) WENO scheme [3]. However, instead of inputting cell averag...

The present paper describes the use of various high-order schemes in a finite volume formulation for use on structured grids. In particular, WENO and compact upwind schemes as well as central and upwind schemes are investigated. Their efficiency and accuracy are compared to the well-established secondand third-order MUSCL family of schemes. The different schemes are analyzed and tested numerica...

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses onto diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations. These schemes are based on suitable semilinear hyperbolic...

We present a new perspective on the use of weighted essentially nonoscillatory (WENO) reconstructions in high-order methods for scalar hyperbolic conservation laws. The main focus this work is nonlinear stabilization continuous Galerkin (CG) approximations. proposed methodology also provides an interesting alternative to WENO-based limiters discontinuous (DG) methods. Unlike Runge–Kutta DG sche...