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

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.

arXiv admin note: text overlap with arXiv:1105.1938

References in corpus (3)

• Galilean invariance of lattice Boltzmann models
• Univariate Polynomial Equation Providing Models of Thermal Lattice Boltzmann Theory
• Uniform Polynomial Equations Providing Higher-order Multi-dimensional Models in Lattice Boltzmann Theory

Cited by in corpus (3)

• Parametric Lattice Boltzmann Method
• Minimal number of discrete velocities for a flow description and internal structural evolution of a shock wave
• A decoupled scheme based on the Hermite expansion to construct lattice Boltzmann models for the compressible Navier-Stokes equations with arbitrary specific heat ratio