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.
Accepté le :
DOI : 10.1051/m2an/2016047
Mots clés : 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
@article{M2AN_2017__51_3_997_0,
author = {Cacace, Simone and Cristiani, Emiliano and Ferretti, Roberto},
title = {Blended numerical schemes for the advection equation and conservation laws},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {997--1019},
publisher = {EDP-Sciences},
volume = {51},
number = {3},
year = {2017},
doi = {10.1051/m2an/2016047},
mrnumber = {3666654},
zbl = {1369.65098},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2016047/}
}
TY - JOUR AU - Cacace, Simone AU - Cristiani, Emiliano AU - Ferretti, Roberto TI - Blended numerical schemes for the advection equation and conservation laws JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 997 EP - 1019 VL - 51 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2016047/ DO - 10.1051/m2an/2016047 LA - en ID - M2AN_2017__51_3_997_0 ER -
%0 Journal Article %A Cacace, Simone %A Cristiani, Emiliano %A Ferretti, Roberto %T Blended numerical schemes for the advection equation and conservation laws %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 997-1019 %V 51 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2016047/ %R 10.1051/m2an/2016047 %G en %F M2AN_2017__51_3_997_0
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. http://archive.numdam.org/articles/10.1051/m2an/2016047/
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