Multidimensional On-lattice Higher-order Models in the Thermal Lattice Boltzmann Theory

TL;DR

This paper introduces new multidimensional on-lattice higher-order models for thermal lattice Boltzmann simulations, achieving accurate thermal compressible flow modeling with fewer discrete velocities, demonstrated through stability and accuracy tests.

Contribution

It develops a set of polynomial equations for compact, higher-order lattice Boltzmann models applicable to thermal flows, reducing the number of velocities needed.

Findings

Models accurately simulate thermal compressible flows.

Three-dimensional model shows stability in Riemann problem.

Fewer discrete velocities required compared to existing models.

Abstract

We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory, while keeping compact the number of discrete velocities. As examples, we explicitly derive two- and three-dimensional on-lattice models applicable to describing thermal compressible flows of the accuracy levels of the Navier-Stokes equations with smaller numbers of discrete velocities in comparison to the existing models. We demonstrate the accuracy and stability of the three-dimensional model by using the Riemann problem.