Simulation of Cavity Flows by an Implicit Domain Decomposition Algorithm for the Lattice Boltzmann Equations
In this paper, we develop a fully implicit finite difference scheme for the lattice Boltzmann equations. A parallel, highly scalable Newton–Krylov–RAS algorithm is presented to solve the large sparse nonlinear system of equations arising at each time step. RAS is a restricted additive Schwarz preconditioner built with a cheaper discretization. The accuracy of the proposed method is carefully studied by comparing with other benchmark solutions. We show numerically that the nonlinearly implicit method is scalable on a supercomputer with more than 10,000 processors.
KeywordsTime Step Size Cavity Flow Krylov Subspace Method Particle Distribution Function Lattice Boltzmann Equation
The work was supported in part by NSFC grants 61170075 and 973 grant 2011CB309701.
- 6.X.-C. Cai, W.D. Gropp, D.E. Keyes, M.D. Tidriri, Newton-Krylov-Schwarz methods in CFD, in Notes in Numerical Fluid Mechanics: Proceedings of the International Workshop on the Navier-Stokes Equations, ed. by R. Rannacher. (Vieweg Verlag, Braunschweig, 1994), pp. 123–135Google Scholar
- 10.Z.L. Guo, T.S. Zhao, Explicit finite-difference lattice Boltzmann method for curvilinear coordinates. Phys. Rev. E 67, 066709(12p) (2003)Google Scholar