High-order central Hermite WENO schemes: Dimension-by-dimension moment-based reconstructions

High-order central Hermite WENO schemes: Dimension-by-dimension moment-based reconstructions

Article history: Received 29 November 2015 Received in revised form 9 April 2016 Accepted 2 May 2016 Available online 6 May 2016

High-order central Hermite WENO schemes on staggered meshes for hyperbolic conservation laws

In this paper, we propose a class of high-order schemes for solving oneand two-dimensional hyperbolic conservation laws. The methods are formulated in a central finite volume framework on staggered meshes, and they involve Hermite WENO (HWENO) reconstructions in space, and Lax-Wendroff type discretizations or the natural continuous extension of Runge-Kutta methods in time. Compared with central...

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...

Very-high-order weno schemes

We study WENO(2r-1) reconstruction [Balsara D., Shu C.W.: J. Comp. Phys. 160 (2000) 405–452], with the mapping (WENOM) procedure of the nonlinear weights [Henrick A.K., Aslam T.D., Powers J.M.: J. Comp. Phys. 207 (2005) 542–567], which we extend up to WENO17 (r = 9). We find by numerical experiment that these procedures are essentially nonoscillatory without any stringent CFL limitation (CFL ∈ ...

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