A comparison of single-time relaxation lattice Boltzmann schemes with enhanced stability

Tosi, F., Ubertini, S., Succi, S., Chen, H. and Karlin, I.V. (2006) A comparison of single-time relaxation lattice Boltzmann schemes with enhanced stability. International Journal of Modern Physics C, 17 (10), 1375-1390. (doi:10.1142/S0129183106009163).

Abstract

In the recent years the entropic version of the lattice Boltzmann method (ELB) has made proof of significantly enhanced numerical stability as compared to the standard single-time relaxation form of the lattice Boltzmann equation. In this paper, we compare ELB with a more empirical procedure, based on the idea of modifying the value of the relaxation time in such a way as to enforce the positivity of the kinetic distribution function (fix-up method). The stability enhancement due to ELB and fix-up are compared for the case a two-dimensional lid-driven cavity flow. It is shown that ELBM offers higher stability at a moderate price in terms of computational overhead. On the other hand, even the simple fix-up procedure can provide significant savings over the standard single-time relaxation method, virtually cost-free in terms of computational requirements.

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