Finite-volume Weno Schemes for Three-dimensional Conservation Laws
نویسندگان
چکیده
The purpose of this paper is twofold. Firstly we carry out an extension of the finite-volume WENO approach to three space dimensions and higher orders of spatial accuracy (up to eleventh order). Secondly, we propose to use three new fluxes as a building block in WENO schemes. These are the one-stage HLLC [29] and FORCE [24] fluxes and a recent multistage MUSTA flux [26]. The numerical results in one, two and three space dimensions suggest the the new centred WENO-FORCE and upwind WENO-HLLC and WENO-MUSTA schemes achieve a uniformly high order of accuracy for smooth solutions and produce essentially nonoscillatory profiles for discontinuities. In particular, the WENO-MUSTA scheme combines the simplicity of the centred non-staggered WENOFORCE scheme and accuracy of the upwind WENO-HLLC scheme with a complete Riemann solver. The advantages of the WENO-MUSTA scheme will be fully realised when solving very complex hyperbolic systems, such as those arising in multi-phase flows, magnetohydrodynamics and general relativity.
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