TY - JOUR
T1 - A Parallel Fully Implicit Unstructured Finite Volume Lattice Boltzmann Method for Incompressible Flows
AU - Xu , Lei
AU - Chen , Rongliang
AU - Cai , Xiao-Chuan
JO - Communications in Computational Physics
VL - 2
SP - 547
EP - 574
PY - 2025
DA - 2025/02
SN - 37
DO - http://doi.org/10.4208/cicp.OA-2023-0019
UR - https://global-sci.org/intro/article_detail/cicp/23873.html
KW - Lattice Boltzmann equation, fully implicit method, unstructured grids, Newton-Krylov-Schwarz, parallel computing.
AB - <p style="text-align: justify;">Lattice Boltzmann method is a popular approach in computational fluid dynamics, and it can be used explicitly or implicitly. The explicit methods require small
time step size which is not desirable. In the fully implicit case, existing approaches
either lack a scalable and robust parallel nonlinear solver, or don’t allow the mesh to
be fully unstructured preventing the method to be used for the simulation of fluid
flows in large domains with complex geometry. In this paper, a parallel fully implicit
second-order finite volume lattice Boltzmann method for incompressible flows on unstructured grids is introduced. The lattice Boltzmann equation is 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
proposed method is validated by three benchmark problems with a wide range of
Reynolds 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 obtained
for solving a problem with over ten million degree of freedoms using thousands of
processor cores.</p>