An efficient implementation of nodal discontinuous Galerkin lattice Boltzmann method and validation for direct numerical simulation of turbulent flows

Abstract

The application of finite element method in solving the lattice Boltzmann equation has been successfully demonstrated by many researchers. However, the computation cost of these methods is much higher than the standard lattice Boltzmann method. In this paper, an efficient implementation of nodal discontinuous Galerkin lattice Boltzmann method is presented. It relies on a simplified nodal discontinuous Galerkin formulation, which makes full use of the possible sparse property of elemental matrices in quadrangles and hexahedrons. Some key points of its implementation in the program are also discussed. Performance tests confirm the superior efficiency of the current program, which exceeds the record of previous researchers. The accuracy of the current method is investigated and compared with the standard lattice Boltzmann method. The high-order discretization can give similar accuracy with lower number of grid points and computational time and the efficiency of the present method is sometimes higher than standard lattice Boltzmann method. Direct numerical simulations of several incompressible turbulence benchmark cases are performed. The present method also shows better accuracy and stability especially in the turbulent pipe flow simulations.