Volume 51, Number 3, May-June 2017
|Page(s)||997 - 1019|
|Published online||02 June 2017|
Blended numerical schemes for the advection equation and conservation laws∗
1 Dipartimento di Matematica, Sapienza – Università di Roma, Rome, Italy
2 Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale delle Ricerche, Rome, Italy
3 Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy
Received: 25 July 2015
Revised: 18 May 2016
Accepted: 23 June 2016
In this paper we propose a method to couple two or more explicit numerical schemes approximating the same time-dependent PDE, aiming at creating a new scheme which inherits advantages of the original ones. We consider both advection equations and nonlinear conservation laws. By coupling a macroscopic (Eulerian) scheme with a microscopic (Lagrangian) scheme, we get a new kind of multiscale numerical method.
Mathematics Subject Classification: 65M12 / 65M99
Key words: Multiscale numerical schemes / hyperbolic problems / conservation laws / advection equation / coupled algorithms / theta methods / filtered schemes / particle level-set method / smoothed-particle hydrodynamics method / particle-in-cell method
© EDP Sciences, SMAI 2017
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