![]() ![]() Wee, Modified interpolation kernels for treating diffusion and remeshing in vortex methods. Technical Report, Los Alamos Scientific Laboratory (1956). Harlow, The particle-in-cell method for hydrodynamics calculations. Vanderlinden, A comparison of spectral and vortex methods in three-dimensional incompressible flow. Weynans, Particle methods revisited : a class of high-order finite-difference schemes. Magni, TVD remeshing schemes for particle methods. Cottet, A vortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies. ![]() Application à la turbulence compressible. Berthon, Contribution à l'analyse numérique des équations de Navier-Stokes compressibles à deux entropies spécifiques. Truncation error in meshfree particle methods series#Benz, The Numerical Modelling of Nonlinear Stellar Pulsations, Problems and Prospects, a review, in Smooth Particle Hydrodynamics : NATO ASIS Series (1989) 269-287. Vila, Convergence of SPH methods for scalar nonlinear conservation laws. Then we prove that with these new TVD remeshing schemes the particle methods converge toward the entropy solution of the scalar conservation law. We present numerical results obtained with these new TVD particle methods for the Euler equations in the case of the Sod shock tube. We extend these results to the nonlinear case with arbitrary velocity sign. Cottet and Magni devised recently in and TVD remeshing schemes for particle methods. This allows us to prove the consistency of these methods, and accuracy properties related to the accuracy of interpolation kernels. As in we re-write particle methods with remeshing in the finite-difference formalism. In this paper we analyze the consistency, the accuracy and some entropy properties of particle methods with remeshing in the case of a scalar one-dimensional conservation law. ![]()
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