Fully Implicit Solution of Time-Dependent Partial Differential Equations in Arbitrary Multizone Domains

The alternating direction multizone implicit method is extended to generalized coordinate systems with complex grid-topology cases. The alternating direction multizone implicit method is a novel approach for solving implicitly systems of time-dependent partial differential equations in multizone domains. The method combines alternate direction implicit (or approximate factorization) methods and domain decomposition techniques to yield an efficient time-accurate solution method. Fully implicit solution is possible by defining a separate set of zone for each stage of the alternate direction implicit method. A flexible and simple data structure is developed, so that the alternating direction multizone implicit method serves as a driver that manages data transfers between permanent zones, where the problem is defined and stored, and temporary (sweep) zones, where the calculations are actually performed. The discretization is done only at the level of the sweep zones. Consequently, the alternating direction multizone implicit method can be applied to many existing solvers (that use alternate direction implicit or approximate factorization techniques) without anticipating major programming efforts. Several test cases demonstrate the capabilities of the alternating direction multizone implicit method to solve implicitly problems with complex geometry