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The convergence of the SPH method. (English) Zbl 0906.76065

Summary: We prove the convergence of a smooth particle flow to the solution of a regularized version of the Euler equations describing a generic polytropic fluid. This result, combined with a stability property of the Euler equations with respect to suitable regularizations allows to achieve the convergence of the so-called smoothed particle hydrodynamics (SPH) method.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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