zbMATH — the first resource for mathematics

Meshless method for conservation laws. (English) Zbl 0982.65102
Summary: This paper is devoted to the presentation of new methods based on the introduction of a new class of approximation for the derivatives. They generalize classical weighted particle methods for conservation laws and converge under less restrictive conditions. We present two schemes and apply them to the Euler equations.

65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
Full Text: DOI
[1] Vila, J.P., Weighted particle methods and smooth particle hydrodynamics, Math. models meth. appl. sci., 9, 2, 161-209, (1999) · Zbl 0938.76090
[2] Benharbit, S.; Chalabi, A.; Vila, J.P., Numerical viscosity, and convergence of finite volume methods for conservation laws with boundary conditions, SIAM J. num. anal., 32, 3, 775-796, (1995) · Zbl 0865.35082
[3] Bicknell, G.V., The equations of motion of particles in smoothed particle hydrodynamics, SIAM J. sci. stat. comput., 12, 5, 1198-1206, (1991) · Zbl 0725.76077
[4] Special issue gridless methods, Comp. Meth. Appl. Mech. Eng. (1996) 139.
[5] Gingold, R.A.; Monaghan, J.J., Shock simulation by the particle method SPH, J. comput. phys., 52, 374-389, (1983) · Zbl 0572.76059
[6] Johnson, G.R.; Beissel, S.R., Normalized smoothing functions for impact computations, Int. J. num. meth. eng., 39, 2725-2741, (1996) · Zbl 0880.73076
[7] Osher, S., Riemann solvers, the entropy condition and difference approximations, SIAM J. num. anal., 21, 2, 217-235, (1984) · Zbl 0592.65069
[8] Randles, R.W.; Libertsky, L.D., Smoothed particle hydrodynamics, some recent improvements and applications, Comp. meth. appl. mech. eng., 139, 375-408, (1996) · Zbl 0896.73075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.