Fundamental Conditions for N-th Order Accurate Lattice Boltzmann Models

TL;DR

This paper establishes fundamental theoretical conditions for designing lattice Boltzmann models that accurately reproduce hydrodynamic moments up to any specified order, enhancing the models' precision and reliability.

Contribution

It provides a set of fundamental, sufficient conditions for discrete velocity sets and weights, enabling the systematic formulation of high-order accurate lattice Boltzmann models.

Findings

Derived fundamental conditions for velocity sets and weights.

Ensured models admit correct hydrodynamic moments up to N-th order.

Facilitated systematic design of high-order lattice Boltzmann models.

Abstract

In this paper, we theoretically prove a set of fundamental conditions pertaining discrete velocity sets and corresponding weights. These conditions provide sufficient conditions for a priori formulation of lattice Boltzmann models that automatically admit correct hydrodynamic moments up to any given N-th order.