| Abstract: | We present a new splitting method for time-dependent convention-dominated diffusion problems. The original convention diffusion system is split into twosub-systems: a pure convection system and a diffusion system. At each time step, aconvection problem and a diffusion problem are solved successively. A few important features of the scheme lie in the facts that the convection subproblem is solvedexplicitly and multistep techniques can be used to essentially enlarge the stability region so that the resulting scheme behaves like an unconditionally stable scheme; whilethe diffusion subproblem is always self-adjoint and coercive so that they can be solvedefficiently using many existing optimal preconditioned iterative solvers. The schemecan be extended for solving the Navier-Stokes equations, where the nonlinearity isresolved 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 stiffnessmatrix stays invariant in the time marching process. Numerical simulations are presented to demonstrate the stability, convergence and performance of the single-stepand multistep variants of the new scheme. |
