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...

In this paper, a class of weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving Hamilton–Jacobi equations is presented. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and used in the reconstruction, ...

Weighted essentially non-oscillatory (WENO) schemes are effective numerical methods to compute flows having shocks and steep gradients. WENO schemes are based on the successful essentially non-oscillatory (ENO) schemes introduced in [9] and [10]. The initial WENO scheme is constructed in [6], and further research in WENO can be found in papers such as [2], [4] and [5]. Both ENO and WENO schemes...

In this paper, we further analyze, test, modify and improve the high order WENO (weighted essentially non-oscillatory) nite diierence schemes of Liu, Osher and Chan 9]. It was shown by Liu et al. that WENO schemes constructed from the r th order (in L 1 norm) ENO schemes are (r +1) th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of...

In this paper, a class of fifth-order weighted essentially non-oscillatory (WENO) schemes based on Hermite polynomials, termed HWENO (Hermite WENO) schemes, for solving one-dimensional nonlinear hyperbolic conservation law systems is presented. The construction of HWENO schemes is based on a finite volume formulation, Hermite interpolation, and nonlinearly stable Runge–Kutta methods. The idea o...

In this paper, three versions of WENO schemes WENO-JS (JCP 126, 1996), WENO-M (JCP 207, 2005) and WENO-Z (JCP 227, 2008) are used for one-dimensional detonation wave simulations with fifth order characteristic based spatial flux reconstruction. Numerical schemes for solving the system of hyperbolic conversation laws using the ZND analytical solution as initial condition are presented. Numerical...

or perhaps with a forcing term g(u, x, t) on the right-hand side. Here u 5 (u1 , ..., um), f 5 (f1 , ..., fd), x 5 (x1 , ..., xd) In this paper, we further analyze, test, modify, and improve the high order WENO (weighted essentially non-oscillatory) finite differand t . 0. ence schemes of Liu, Osher, and Chan. It was shown by Liu et al. WENO schemes are based on ENO (essentially nonthat WENO sc...

In this paper, we apply the high order WENO schemes to uniform cylindrical and spherical grid. Many 2-D and 3-D problems can be solved in 1-D equations if they have angular and radial symmetry. The reduced equations will typically involve geometric source terms. Therefore, conventional numerical schemes for Cartesian grid may not work well. We propose several approaches to apply the high order ...

In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy for the solutions is...