TY - JOUR
T1 - Reprint of
T2 - Residual equilibrium schemes for time dependent partial differential equations
AU - Pareschi, Lorenzo
AU - Rey, Thomas
N1 - Publisher Copyright:
© 2018
PY - 2018/6/30
Y1 - 2018/6/30
N2 - Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in particular for high order ones. In this paper, inspired by micro-macro decomposition methods for kinetic equations, we present a class of schemes which are capable to preserve the steady state solution and achieve high order accuracy for a class of time dependent partial differential equations including nonlinear diffusion equations and kinetic equations. Extension to systems of conservation laws with source terms are also discussed.
AB - Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in particular for high order ones. In this paper, inspired by micro-macro decomposition methods for kinetic equations, we present a class of schemes which are capable to preserve the steady state solution and achieve high order accuracy for a class of time dependent partial differential equations including nonlinear diffusion equations and kinetic equations. Extension to systems of conservation laws with source terms are also discussed.
KW - Fokker–Planck equations
KW - Micro-macro decomposition
KW - Shallow-water
KW - Steady-states preserving
KW - Well-balanced schemes
UR - http://www.scopus.com/inward/record.url?scp=85044541209&partnerID=8YFLogxK
U2 - 10.1016/j.compfluid.2018.03.053
DO - 10.1016/j.compfluid.2018.03.053
M3 - Article
AN - SCOPUS:85044541209
SN - 0045-7930
VL - 169
SP - 141
EP - 154
JO - Computers and Fluids
JF - Computers and Fluids
ER -