摘要
We present a new splitting method for time-dependent convention-dominated diffusion problems.The original convention diffusion system is split into two sub-systems:a pure convection system and a diffusion system.At each time step,a convection problem and a diffusion problem are solved successively.A few important features of the scheme lie in the facts that the convection subproblem is solved explicitly and multistep techniques can be used to essentially enlarge the stability region so that the resulting scheme behaves like an unconditionally stable scheme;while the diffusion subproblem is always self-adjoint and coercive so that they can be solved efficiently using many existing optimal preconditioned iterative solvers.The scheme can be extended for solving the Navier-Stokes equations,where the nonlinearity is resolved by a linear explicit multistep scheme at the convection step,while only a generalized Stokes problem is needed to solve at the diffusion step and the major stiffness matrix stays invariant in the time marching process.Numerical simulations are presented to demonstrate the stability,convergence and performance of the single-step and multistep variants of the new scheme.
基金
The work of F.Shi was partially supported by NSFC(Projects 41104039 and 11401563)
Guangdong Natural Science Foundation(Project S201204007760)
Tianyuan Fund for Mathematics of the NSFC(Project 11226314)
the Knowledge Innovation Program of the Chinese Academy of Sciences(China)under KJCX2-EW-L01,and the international cooperation project of Guangdong province(China)under 2011B050400037
J.Zou was substantially supported by Hong Kong RGC grants(Projects 404611 and 405513)。