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...

We describe our experience using NVIDIA’s CUDA (Compute Unified Device Architecture) C programming environment to implement a two-dimensional second-order MUSCL-Hancock ideal magnetohydrodynamics (MHD) solver on a GTX 480 Graphics Processing Unit (GPU). Taking a simple approach in which the MHD variables are stored exclusively in the global memory of the GTX 480 and accessed in a cache-friendly...

Crystallizationmodels with direction-dependent growth rates give rise tomulti-dimensional population balance equations (PBE) that require a high computational cost. We propose a model reduction based on the quadrature method of moments (QMOM). Using this method a two-dimensional population balance is reduced to a system of one-dimensional advection equations. Despite the dimension reduction the...

Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind differencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the field-by-field decomposition which is required in order to identify the “direction of the wind.” Instead, we propose to use as a building block the mor...

A parallel algorithm which has sufficient scalability for time accurate solution of a propagating detonation wavefront is developed. The emphasis is placed on reduction of computational time without compromising accuracy. The flow was assumed to be unsteady, inviscid and non-heat-conducting and coupled with finite-rate chemistry. A finite volume formulation was employed to ensure conservation a...

Two-dimensional simulations of the Richtmyer-Meshkov instability with re-shock are carried out based on the single-mode Mach 1.21 air/SF6 shock tube experiments of Collins and Jacobs. A second-order accurate MUSCL-Hancock scheme and several high-order WENO schemes are used for shock capturing along with a gamma-based model for interface capturing to allow for the stable and accurate representat...

Abstract. The nonoscillatory central difference scheme of Nessyahu and Tadmor is a Godunovtype scheme for one-dimensional hyperbolic conservation laws in which the resolution of Riemann problems at the cell interfaces is bypassed thanks to the use of the staggered Lax–Friedrichs scheme. Piecewise linear MUSCL-type (monotonic upstream-centered scheme for conservation laws) cell interpolants and ...

Sixth-order compact and non-compact filter schemes that were designed for multiscale Navier-Stokes, and ideal and non-ideal magnetohydrodynamics (MHD) systems are employed to simulate a 2-D Rightmyer-Meshkov instability (RMI). The suppression of this RMI in the presence of a magnetic field was investigated by Samtaney (2003) and Wheatley et al. (2005). Numerical results illustrated here exhibit...

The VFRoe scheme has been recently introduced to approximate the solutions of the shallow water equations. One of the main interest of this method is to be easily implemented. As a consequence, such a scheme appears as an interesting alternative to other more sophisticated schemes. The VFRoe methods perform approximate solutions in a good agreement with the expected ones. However, the robustnes...

We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity in the advective fluxes is shifted proportionally to the pressure potential gradient. Using a similar strategy for the potential forces, we show the stabilit...