A nodal discontinuous Galerkin lattice Boltzmann method for fluid flow problems

• A nodal discontinuous Galerkin lattice Boltzmann method is proposed.
• Space discretization is performed using unstructured grids with triangular elements.
• Time marching is done by the low-storage fourth-order, five-stage Runge–Kutta method.
• The method is used to simulate fluid flows at relatively high Reynolds numbers.
• The method is used to evaluate the permeability of a porous medium.

We present a new application of the nodal discontinuous Galerkin method in solving the lattice Boltzmann equation. By splitting the collision and the streaming operators of the lattice Boltzmann equation, the nodal discontinuous Galerkin method is implemented to solve the resulting advection equation. Space discretization is performed using unstructured grids with triangular elements, while time marching is carried out by applying the low-storage fourth-order, five-stage Runge–Kutta method. To validate the results, two well-known benchmark problems are simulated. The lid-driven square cavity at Reynolds numbers of 1000 and 5000 and Mach number of 0.1 and the impulsively started cylinder at Reynolds numbers of 550 and 9500 with Mach numbers of 0.1 and 0.05, respectively. The results show excellent agreement between the present study and the existing results in the literature. The method is then used to simulate flow in a porous medium. It is shown that the present method requires significantly lower number of grid points compared to the standard lattice Boltzmann method for the simulation of the porous medium flow.