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://www.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://www.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://www.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://www.numdam.org/articles/10.1051/m2an/2016047/
C.K. Birdsall and A.B. Langdon, Plasma physics via computer simulation. CRC Press, Boca Raton (2004).
, and , A weighted essentially nonoscillatory, large time-step scheme for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 27 (2005) 1071–1091. | DOI | MR | Zbl
, Blending Brownian motion and heat equation. J. Coupled Syst. Multiscale Dyn. 3 (2015) 351–356. | DOI
, and , Multiscale modeling of granular flows with application to crowd dynamics. Multiscale Model. Simul. 9 (2011) 155–182. | DOI | MR | Zbl
W. E, Principles of multiscale modeling. Cambridge University Press (2011). | MR | Zbl
, , and , A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183 (2002) 83–116. | DOI | MR | Zbl
M. Falcone and R. Ferretti, Semi-Lagrangian approximation schemes for linear and Hamilton-Jacobi equations. SIAM (2014). | MR
and , Fast finite difference solvers for singular solutions of the elliptic Monge-Ampère equation. J. Comput. Phys. 230 (2011) 818–834. | DOI | MR | Zbl
and , Convergent filtered schemes for the Monge-Ampère partial differential equation. SIAM J. Numer. Anal. 51 (2013) 423–444. | DOI | MR | Zbl
and , Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181 (1977) 375–389. | DOI | Zbl
, , and , Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys. 71 (1987) 231–303. | DOI | MR | Zbl
, Reformulation of smoothed particle hydrodynamics with Riemann solver. J. Comput. Phys. 179 (2002) 238–267. | DOI | Zbl
R.J. LeVeque, Numerical methods for conservation laws. Birkhäuser (1992). | MR | Zbl
, and , Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115 (1994) 200–212. | DOI | MR | Zbl
, A numerical approach to the testing of the fission hypothesis. Astron. J. 82 (1977) 1013–1024. | DOI
, and , Coupling of Smoothed Particle Hydrodynamics with Finite Volume method for free-surface flows. J. Comput. Phys. 310 (2016) 161–180. | DOI | MR | Zbl
and , Filtered schemes for Hamilton-Jacobi equations: A simple construction of convergent accurate difference schemes. J. Comput. Phys. 284 (2015) 367–388. | DOI | MR | Zbl
and , Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12–49. | DOI | MR | Zbl
and , Approximate Riemann solvers for the Godunov SPH (GSPH). J. Comput. Phys. 270 (2014) 432–458. | DOI | MR | Zbl
C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. NASA/CR-97-206253, ICASE Report No. 97–65 (1997). | MR | Zbl
Cité par Sources :
