A first-order semi-Lagrangian treatment of the implicit BGK collision lets FVDBM replace f_eq^{n+1} with f_eq^n, improving accuracy, cost, and stability in tested cases.
Succi, The Lattice Boltzmann Equation: For Complex States of Flowing Matter, Oxford University Press, 2018
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Semi-Lagrangian implicit Bhatnagar-Gross-Krook collision model for the finite-volume discrete Boltzmann method
A first-order semi-Lagrangian treatment of the implicit BGK collision lets FVDBM replace f_eq^{n+1} with f_eq^n, improving accuracy, cost, and stability in tested cases.