Hybrid multiscale methods. I: Hyperbolic relaxation problems. (English) Zbl 1185.65197

Summary: We consider the development of hybrid numerical methods for the solution of hyperbolic relaxation problems with multiple scales. The main ingredients in the schemes are a suitable merging of probabilistic Monte Carlo methods in non-stiff regimes with high resolution shock capturing techniques in stiff ones. The key aspect in the development of the algorithms is the choice of a suitable hybrid representation of the solution. After the introduction of the different schemes the performance of the new methods is tested in the case of the Jin-Xin relaxation system and the Broadwell model.


65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65C05 Monte Carlo methods
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
82D05 Statistical mechanics of gases
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