×

Convergence of SPH method for scalar nonlinear conservation laws. (English) Zbl 0949.65095

The paper is devoted to the study of the convergence of weighted particle approximations by the smooth particle hydrodynamics (SPH) method applied to nonlinear multidimensional conservation laws. The mathematical analysis is performed by connecting this new approach with the finite volume scheme. Convergence of the approximate solution in \(L^p_{\text{loc}}\) \((p<\infty)\) towards the unique weak entropy solution of the Cauchy problem is obtained in the scalar nonlinear case by using uniqueness of measure valued solutions.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M28 Particle methods and lattice-gas methods
76M12 Finite volume methods applied to problems in fluid mechanics
PDFBibTeX XMLCite
Full Text: DOI