Abstract
We present a second order time accurate IMplicit/EXplicit (IMEX) method for solving single and multi-phase flow problems. The algorithm consists of a combination of an explicit and an implicit blocks. The explicit block solves the non-stiff parts of the governing system whereas the implicit block operates on the stiff terms. In our self-consistent IMEX implementation, the explicit part is always executed inside the implicit block as part of the nonlinear functions evaluation making use of the Jacobian-free Newton Krylov (JFNK) method (Knoll and Keyes, J. Comput. Phys. 193:357–397, 2004). This leads to an implicitly balanced algorithm in that all non-linearities due to the coupling of different time terms are consistently converged. In this paper, we present computational results when this IMEX strategy is applied to single/multi-phase incompressible flow models.
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