We propose a new analysis of particle method with remeshing. We derive a class of high-order finite difference methods. Our analysis is completed by numerical comparisons with Lax–Wendroff schemes for the Burger equation.
On propose dans cette Note une nouvelle analyse des méthodes particulaires utilisant des remaillages. Cette analyse fait apparaître une classe de schémas de différences finis d'ordre élevé. Des illustrations numériques viennent compléter cette analyse et permettent de comparer les schémas particulaires avec le schéma de Lax–Wendroff.
Accepted:
Published online:
Georges-Henri Cottet 1; Lisl Weynans 1, 2
@article{CRMATH_2006__343_1_51_0, author = {Georges-Henri Cottet and Lisl Weynans}, title = {Particle methods revisited: a class of high order finite-difference methods}, journal = {Comptes Rendus. Math\'ematique}, pages = {51--56}, publisher = {Elsevier}, volume = {343}, number = {1}, year = {2006}, doi = {10.1016/j.crma.2006.05.001}, language = {en}, }
Georges-Henri Cottet; Lisl Weynans. Particle methods revisited: a class of high order finite-difference methods. Comptes Rendus. Mathématique, Volume 343 (2006) no. 1, pp. 51-56. doi : 10.1016/j.crma.2006.05.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.05.001/
[1] Vortex Methods, Cambridge University Press, 2000
[2] G.-H. Cottet, B. Rebourcet, L. Weynans, A multilevel adaptive particle-grid method for gas dynamics, in: ECCOMAS Thematic Conference on Meshless Methods, 2005
[3] Smoothed particle hydrodynamics: theory and application to non spherical stars, Mon. Not. R. Astron. Soc., Volume 181 (1977), pp. 375-389
[4] A systematic approach for correcting nonlinear instabilities, Numer. Math., Volume 30 (1978), pp. 429-452
[5] Modified interpolation kernels for treating diffusion and remeshing in vortex methods, J. Comput. Phys., Volume 213 (2006), pp. 239-263
Cited by Sources:
Comments - Policy