Chebyshev collocation spectral lattice Boltzmann method in generalized curvilinear coordinates

Abstract

Abstract In this work, the Chebyshev collocation spectral lattice Boltzmann method is implemented in the generalized curvilinear coordinates to provide an accurate and efficient low-speed LB-based flow solver to be capable of handling curved geometries with non-uniform grids. The low-speed form of the D2Q9 and D3Q19 lattice Boltzmann equations is transformed into the generalized curvilinear coordinates and then the spatial derivatives in the resulting equations are discretized by using the Chebyshev collocation spectral method and the temporal term is discretized with the fourth-order Runge–Kutta scheme to provide an accurate and efficient low-speed flow solver. All boundary conditions are implemented based on the solution of the governing equations in the generalized curvilinear coordinates. The accuracy and robustness of the solution methodology presented are demonstrated by computing different benchmark and practical low-speed flow problems that are 2D Couette flow between concentric moving cylinders, 2D flow in a gradual expansion duct, 2D regularized trapezoidal cavity flow, and 3D flow in curved ducts of rectangular cross-sections. Results obtained for these test cases are in good agreement with the existing analytical and numerical results. The computational efficiency of the proposed solution methodology based on the Chebyshev collocation spectral lattice Boltzmann method implemented in the generalized curvilinear coordinates is also examined by comparison with the developed second-order finite-difference lattice Boltzmann method that indicates the proposed method provides more accurate and efficient solutions in terms of the CPU time and memory usage. The study shows the present solution methodology is robust and accurate for solving 2D and 3D low-speed flows over practical geometries. Indications are that the solution algorithm based on the CCSLBM in the generalized curvilinear coordinates does not need any filtering or numerical dissipation for stability considerations and thus high accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the evaluation of other LBM-based flow solvers.