Interface tracking method for compressible multifluids
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 6, p. 991-1019

This paper is concerned with numerical methods for compressible multicomponent fluids. The fluid components are assumed immiscible, and are separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied by several fluid components require a “mixed-cell” EOS, which may not always be physically meaningful, and often leads to spurious oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell information by solving the Riemann problem between its single-fluid neighboring cells. The resulting algorithm is oscillation-free for isolated material interfaces, conservative, and tends to produce almost perfect jumps across material fronts. The computational framework is general and may be used in conjunction with one's favorite finite-volume method. The robustness of the method is illustrated on shock-interface interaction in one space dimension, oscillating bubbles with radial symmetry and shock-bubble interaction in two space dimensions.

DOI : https://doi.org/10.1051/m2an:2008036
Classification:  76M12,  76N15,  35L65,  35L67
Keywords: compressible Euler equations, multicomponent fluids, material interfaces, finite-volume schemes
@article{M2AN_2008__42_6_991_0,
     author = {Chertock, Alina and Karni, Smadar and Kurganov, Alexander},
     title = {Interface tracking method for compressible multifluids},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {6},
     year = {2008},
     pages = {991-1019},
     doi = {10.1051/m2an:2008036},
     zbl = {pre05370464},
     mrnumber = {2473317},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2008__42_6_991_0}
}
Chertock, Alina; Karni, Smadar; Kurganov, Alexander. Interface tracking method for compressible multifluids. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 6, pp. 991-1019. doi : 10.1051/m2an:2008036. http://www.numdam.org/item/M2AN_2008__42_6_991_0/

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