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A time-accurate explicit multi-scale technique for gas dynamics. (English) Zbl 1262.76079
Summary: We present a new time-accurate algorithm for the explicit numerical integration of the compressible Euler equations of gas dynamics. This technique is based on the discrete-event simulation (DES) methodology for nonlinear flux-conservative PDEs [the authors, J. Comput. Phys. 216, No. 1, 179–194 (2006; Zbl 1093.65083)]. DES enables adaptive distribution of CPU resources in accordance with local time scales of the underlying numerical solution. It distinctly stands apart from multiple (local) time-stepping algorithms in that it requires neither selecting a global synchronization time step nor pre-determining a sequence of time-integration operations for individual parts of a heterogeneous numerical system.
In this paper we extend the DES methodology in three important directions: (i) we apply DES to a system of coupled gas dynamics equations discretized via a central-upwind scheme [A. Kurganov and E. Tadmor, J. Comput. Phys. 160, No. 1, 241–282 (2000; Zbl 0987.65085); A. Kurganov, S. Noelle and G. Petrova, SIAM J. Sci. Comput. 23, No. 3, 707–740 (2001; Zbl 0998.65091)]; (ii) we introduce a new Preemptive Event Processing (PEP) technique, which automatically enforces synchronous execution of events with sufficiently close update times; (iii) we significantly improve the accuracy of the previous algorithm [the authors, op. cit.] by applying locally second-order-in-time flux-conserving corrections to the solution obtained with the forward Euler scheme. The performance of the new technique is demonstrated in a series of one-dimensional gas dynamics test problems by comparing numerical solutions obtained in event-driven and equivalent time-stepping simulations.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N15 Gas dynamics (general theory)
35Q31 Euler equations
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