Low-memory-consumption system with the lattice Boltzmann method based on optional moment definitions including gradient information

This study introduces the lattice Boltzmann method (LBM), composed of optional moment definitions within the second-order moment, and develops a low-memory-consumption system. Since we do not start with kinetic-theory-based moments, we can construct a more flexible moment system. The range of moments within the restricted order enables polynomial expansions of distribution functions using a neighbor discretized particle velocity set, while flexible moment definitions expand the fields of phenomena that the system can simulate. Recent LBM studies have focused on kinetic theory-based distribution function modeling, achieving efficient computation with fewer variables. However, kinetic theory in a continuity particle velocity space requires third-order moments for thermal computation, resulting in the requirement of a large velocity set and more stencils. From this point of view, to expand the range of moment definitions and develop a low-memory-consumption thermal computing system, this study focuses on a discretized velocity space at first and on recovering macroscopic equations from moment definitions in finite particle velocity summation. Because of more free moment definitions, we can construct a thermal flux tensor as a first-order moment and then replace distribution functions for thermal flows with macroscopic variables and their gradients. With low memory consumption, this study computes some benchmarks and shows some validity.