Geodesic
Blended numerical schemes for the advection equation and conservation laws
Cacace, Simone1 ; Cristiani, Emiliano2 ; Ferretti, Roberto3 
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
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 997-1019 Cet article a éte moissonné depuis la source Numdam

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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.

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DOI : 10.1051/m2an/2016047
Classification : 65M12, 65M99
Keywords: 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

Cacace, Simone 1 ; Cristiani, Emiliano 2 ; Ferretti, Roberto 3

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 
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     title = {Blended numerical schemes for the advection equation and conservation laws},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {997--1019},
     year = {2017},
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Cacace, Simone; Cristiani, Emiliano; Ferretti, Roberto. Blended numerical schemes for the advection equation and conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 3, pp. 997-1019. doi: 10.1051/m2an/2016047

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