Quartic Parameters for Acoustic Applications of Lattice Boltzmann Scheme

TL;DR

This paper enhances the lattice Boltzmann method for acoustic applications by deriving quartic parameters that improve accuracy, validated through symbolic solutions and numerical tests.

Contribution

It introduces a fourth order accurate parameter fitting approach for lattice Boltzmann schemes in acoustics, using Taylor expansion and symbolic computation.

Findings

Fourth order accuracy achieved for D3Q27 lattice scheme

Numerical tests confirm improved coherence and precision

Explicit parameter solutions derived for specific lattice configurations

Abstract

Using the Taylor expansion method, we show that it is possible to improve the lattice Boltzmann method for acoustic applications. We derive a formal expansion of the eigenvalues of the discrete approximation and fit the parameters of the scheme to enforce fourth order accuracy. The corresponding discrete equations are solved with the help of symbolic manipulation. The solutions are explicited in the case of D3Q27 lattice Boltzmann scheme. Various numerical tests support the coherence of this approach.