Higher-Order Relaxation Schemes for Hyperbolic Systems of Conservation
Mapundi Banda and Mohammed Seaid
We present a higher order generalisation for relaxation methods in the
framework presented by Jin and Xin. The schemes employ general higher order
integration for spatial discretisation and higher order implicit-explicit
schemes or Total Variation diminishing (TVD) Runge-Kutta schemes for time
integration of relaxed or relaxing schemes, respectively, for time
integration. Numerical experiments are performed on various test problems, in
particular, the Euler equations of inviscid gas dynamics. In addition, uniform
convergence with respect to the relaxation parameter is demonstrated.
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October 4 2001.
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