Constrained Runs algorithm as a lifting operator for the Boltzmann equation

TL;DR

This paper explores using the Constrained Runs algorithm as a lifting operator to initialize various discretizations of the Boltzmann equation from macroscopic variables, extending its application beyond lattice Boltzmann models.

Contribution

The study demonstrates the application of the Constrained Runs algorithm for different Boltzmann discretizations, including finite volume methods, to accurately map macroscopic variables to distribution functions.

Findings

Effective initialization of Boltzmann models from macroscopic data.

Extension of the Constrained Runs algorithm beyond lattice Boltzmann models.

Potential for improved accuracy in kinetic simulations.

Abstract

Lifting operators play an important role in starting a kinetic Boltzmann model from given macroscopic information. The macroscopic variables need to be mapped to the distribution functions, mesoscopic variables of the Boltzmann model. A well-known numerical method for the initialization of Boltzmann models is the Constrained Runs algorithm. This algorithm is used in literature for the initialization of lattice Boltzmann models, special discretizations of the Boltzmann equation. It is based on the attraction of the dynamics toward the slow manifold and uses lattice Boltzmann steps to converge to the desired dynamics on the slow manifold. We focus on applying the Constrained Runs algorithm to map density, average flow velocity, and temperature, the macroscopic variables, to distribution functions. Furthermore, we do not consider only lattice Boltzmann models. We want to perform the algorithm for different discretizations of the Boltzmann equation and consider a standard finite volume discretization.