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@article{Carrillo:2020:10.1137/18M1230050,
author = {Carrillo, de la Plata JA and Kalliadasis, S and Perez, Perez S and Shu, C-W},
doi = {10.1137/18M1230050},
journal = {SIAM: Multiscale Modeling and Simulation},
pages = {502--541},
title = {Well-balanced finite volume schemes for hydrodynamic equations with general free energy},
url = {http://dx.doi.org/10.1137/18M1230050},
volume = {18},
year = {2020}
}

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TY  - JOUR
AB  - Well-balanced  and  free  energy  dissipative  first-  and  second-order  accurate  finite  volume  schemes  are proposed for a general class of hydrodynamic systems with linear and nonlinear damping.  The variation of the natural Liapunov functional of the system,  given by its free energy,  allows,  for a characterization of the stationary states by its  variation.   An  analog  property  at  the  discrete  level  enables  us  to  preserve  stationary  states  at  machine  precision while keeping the dissipation of the discrete free energy.  These schemes can accurately analyse the stability properties of stationary states in challenging problems such as:  phase transitions in collective behavior, generalized Euler-Poisson systems  in  chemotaxis  and  astrophysics,  and  models  in  dynamic  density  functional  theories;  having  done  a  careful validation in a battery of relevant test cases.
AU  - Carrillo,de la Plata JA
AU  - Kalliadasis,S
AU  - Perez,Perez S
AU  - Shu,C-W
DO  - 10.1137/18M1230050
EP  - 541
PY  - 2020///
SN  - 1540-3459
SP  - 502
TI  - Well-balanced finite volume schemes for hydrodynamic equations with general free energy
T2  - SIAM: Multiscale Modeling and Simulation
UR  - http://dx.doi.org/10.1137/18M1230050
UR  - https://epubs.siam.org/doi/abs/10.1137/18M1230050
UR  - http://hdl.handle.net/10044/1/76604
VL  - 18
ER  -

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