A Parallel Fully Implicit Unstructured Finite Volume Lattice Boltzmann Method for Incompressible Flows (Communications in Computational Physics, 2025)
Lattice Boltzmann method is a popular approach in computational fluid dynamics, and it can be used explicitly or implicitly. The explicit methods require smalltime step size which is not desirable. In the fully implicit case, existing approacheseither lack a scalable and robust parallel nonlinear solver, or don’t allow the mesh tobe fully unstructured preventing the method to be used for the simulation of fluidflows in large domains with complex geometry. In this paper, a parallel fully implicitsecond-order finite volume lattice Boltzmann method for incompressible flows on unstructured grids is introduced. The lattice Boltzmann equation is discretized by a finitevolume 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 parallelSchwarz type domain decomposition preconditioned Newton-Krylov algorithm. Theproposed method is validated by three benchmark problems with a wide range ofReynolds number: (a) pressure driven Poiseuille flow, (b) lid-driven cavity flows, and(c) viscous flows passing a circular cylinder. The numerical results show that the proposed method is robust for all the test cases and a superlinear speedup is obtainedfor solving a problem with over ten million degree of freedoms using thousands ofprocessor cores.