Реферат: The numerical stability of the lattice Boltzmann equation (LBE) method in simulations of a fluid described by an equation of state with possible vapor–liquid phase transitions is considered. The Courant–Friedrichs–Lewy number defined by the advection term in the Boltzmann equation is exactly equal to unity in classical LBE models. However, this condition does not ensure the numerical stability of LBE simulations with the equation of state. In our numerical LBE simulations, we find out that instability arises initially in the liquid phase, even if the vapor phase and, consequently, the vapor–liquid interface are absent. We demonstrate both in numerical tests and theoretically that the numerical stability of LBE simulations requires the criterion to be fulfilled for the liquid phase, where is the hydrodynamic Courant number. The hydrodynamic Courant number is proportional to the speed of sound , obtained from an equation of state of a fluid. This criterion is very similar to the well-known criteria of numerical stability of explicit finite difference schemes for a compressible fluid. The critical value of the Courant number depends neither on the temperature , nor on the fluid velocity, nor on the form of the equation of state. This critical value is equal to for the kinetic temperature of LBE pseudo-particles .

Библиографическая ссылка: Kupershtokh A.L.
Criterion of numerical instability of liquid state in LBE simulations
Computers and Mathematics with Applications. 2010. V.59. N7. P.2236-2245. DOI: 10.1016/j.camwa.2009.08.058 WOS Scopus РИНЦ OpenAlex

Идентификаторы БД:

Web of science:	WOS:000277220600009
Scopus:	2-s2.0-77949485817
РИНЦ:	15315272
OpenAlex:	W2086513185

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БД	Цитирований
Web of science	62
Scopus	70
OpenAlex	68
РИНЦ	82

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