Multidimensional flux-vector-splitting and high-resolution characteristic schemes.

*(English)*Zbl 0990.65106
Toro, E. F. (ed.), Godunov methods. Theory and applications. International conference, Oxford, GB, October 1999. New York, NY: Kluwer Academic/ Plenum Publishers. 671-676 (2001).

Summary: The numerical solution of systems of hyperbolic conservation laws is dominated by Riemann-solver based schemes. These one-dimensional schemes are usually extended to several space-dimensions either by using dimensional-splitting on cartesian grids or by the finite-volume approach on unstructured grids.

In this contribution we focus on yet another multi-dimensional approach, M. Fey’s method of transport [J. Comput. Phys. 143, No. 1, 159-180, 181-199 (1998; Zbl 0932.76050; Zbl 0932.76051)], which belongs to the family of flux-vector-splitting schemes. The starting point of Fey’s algorithm is a multi-dimensional wave-model, which leads to a reformulation of the system of conservation laws as a finite set of coupled nonlinear advection equations. At the beginning of each timestep, these coupled nonlinear equations are decomposed into a set of linear scalar advection equations with variable coefficients, which are then solved numerically using characteristic schemes.

For the entire collection see [Zbl 0978.00036].

In this contribution we focus on yet another multi-dimensional approach, M. Fey’s method of transport [J. Comput. Phys. 143, No. 1, 159-180, 181-199 (1998; Zbl 0932.76050; Zbl 0932.76051)], which belongs to the family of flux-vector-splitting schemes. The starting point of Fey’s algorithm is a multi-dimensional wave-model, which leads to a reformulation of the system of conservation laws as a finite set of coupled nonlinear advection equations. At the beginning of each timestep, these coupled nonlinear equations are decomposed into a set of linear scalar advection equations with variable coefficients, which are then solved numerically using characteristic schemes.

For the entire collection see [Zbl 0978.00036].

##### MSC:

65M25 | Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs |

35L65 | Hyperbolic conservation laws |