Convergence of the Smoothed Particle Hydrodynamics Method for a Specific Barotropic Fluid Flow: Constructive Kernel Theory

DOI10.1137/17M1157696zbMath1434.65157MaRDI QIDQ4683904

Tino Franz, Holger Wendland

Publication date: 26 September 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

convergence analysisEuler equationssmooth solutionssmoothed particle hydrodynamicskernel-based approximation

Mathematics Subject Classification ID

Particle methods and lattice-gas methods (76M28) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Approximation by other special function classes (41A30) Euler equations (35Q31) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75)

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On the convergence of the solutions to the integral SPH heat and advection-diffusion equations: theoretical analysis and numerical verification, Convergence of a Lagrangian Discretization for Barotropic Fluids and Porous Media Flow, Dispersion analysis of SPH as a way to understand its order of approximation, Towards pseudo-spectral incompressible smoothed particle hydrodynamics (ISPH), A kernel derivative free SPH method, Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling, Calculating the smoothing error in SPH, An Improved Convergence Result for the Smoothed Particle Hydrodynamics Method

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