A Central Difference Finite Volume Lattice Boltzmann Method for Simulation of 2D Inviscid Compressible Flows on Triangular Meshes

Abstract

In this work, a central difference finite volume lattice Boltzmann method (CDFV-LBM) is developed to compute 2D inviscid compressible flows on triangular meshes. The numerical solution procedure adopted here for solving the lattice Boltzmann equation is nearly the same as the procedure used by Jameson et al. for the solution of the Euler equations. The integral form of the lattice Boltzmann equation using the Gauss divergence theorem is applied on a triangular cell and the numerical fluxes on each edge of the cell are set to the average of their values at the two adjacent cells. Appropriate numerical dissipation terms are added to the discretized lattice Boltzmann equation to have a stable solution. The Boltzmann equation is discretized in time using the fourth-order Runge-Kutta scheme. The computations are performed for three problems, namely, the isentropic vortex and the supersonic flow around a NACA0012 airfoil and over a circular-arc bump. The effect of changing the grid resolution and the dissipation coefficients on the accuracy of the results is also studied. Results obtained by applying the CDFV-LBM are compared with the available numerical results which show good agreement.

Large-eddy lattice-Boltzmann modeling of transonic flows

“…The second test case reproduces the same channel dimensions including a 4% circular bump with a 600 × 200 mesh grid. This configuration is showed here to assess the capability of the method to deal with supersonic flow including shock waves reflection 61,62 . As for the previous test case, the bump is set in the middle of the channel.…”

Numerical Study of Possion Equation in Subsonic and Supersonic Airfoil Flow

“…The wing usually has a complex three-dimensional shape and a variety of airfoils, which will have a complex impact on the aerodynamic performance of the wing surface, so it is sometimes necessary to simplify the problem according to the situation [7]. When the airfoil is very thin, some researchers will use the computational fluid dynamics method to deal with the aerodynamic analysis of the wing as a two-dimensional problem [8,9]. Compared to three-dimensional problems, it can improve efficiency and speed.…”