A parallel domain decomposition-based implicit finite volume lattice Boltzmann method for incompressible thermal convection flows on unstructured grids

Abstract

The double distribution function lattice Boltzmann method is known for its ability to handle various temperature changes and maintain strong numerical stability for incompressible thermal convection flows. However, being an explicit scheme on a Cartesian grid, it necessitates small time step sizes and limits its use in simulating fluid flows with intricate geometries. In this paper, a parallel fully implicit finite volume lattice Boltzmann method for incompressible thermal convection flows on unstructured grids is introduced. The double distribution function lattice Boltzmann equations are discretized by a finite volume method in space and an implicit backward Euler scheme in time. The resulting large sparse nonlinear system of algebraic equations is solved by a highly parallel Schwarz type domain decomposition preconditioned Newton–Krylov algorithm. The effectiveness of the proposed method is validated through five benchmark problems with a wide range of Rayleigh numbers: (a) porous plate problem with a temperature gradient, (b) natural convection in a square cavity, (c) natural convection in a concentric annulus, (d) mixed heat transfer from a heated circular cylinder and (e) nature convection in a sine-walled cavity. The numerical results demonstrate the robustness of the proposed method across all test cases, achieving a linear speedup in solving a problem with almost 40 million degrees of freedom using thousands of processor cores. The corresponding parallel efficiency reaches as high as 91.96% using 4096 processor cores.