On the Construction, Comparison, and Local Characteristic Decomposition for High-Order Central WENO Schemes

On the Construction, Comparison, and LocalCharacteristic Decomposition for High-OrderCentral WENO Schemes

In this paper, we review and construct fifthand ninth-order central weighted essentially nonoscillatory (WENO) schemes based on a finite volume formulation, staggered mesh, and continuous extension of Runge–Kutta methods for solving nonlinear hyperbolic conservation law systems. Negative linear weights appear in such a formulation and they are treated using the technique recently introduced by ...

High-Order Central WENO Schemes for 1D Hamilton-Jacobi Equations

High-Order Central WENO Schemes for Multidimensional Hamilton-Jacobi Equations

We present new thirdand fifth-order Godunov-type central schemes for approximating solutions of the Hamilton–Jacobi (HJ) equation in an arbitrary number of space dimensions. These are the first central schemes for approximating solutions of the HJ equations with an order of accuracy that is greater than two. In two space dimensions we present two versions for the third-order scheme: one scheme ...

Accelerating high-order WENO schemes using two heterogeneous GPUs

A double-GPU code is developed to accelerate WENO schemes. The test problem is a compressible viscous flow. The convective terms are discretized using third- to ninth-order WENO schemes and the viscous terms are discretized by the standard fourth-order central scheme. The code written in CUDA programming language is developed by modifying a single-GPU code. The OpenMP library is used for parall...

The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws

This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...