Convergence of the solution for a domain decomposed, heterogeneously modeled flow past a concave profile problem

The free streamline problem investigated is that of fluid flow past a symme tric truncated concave-shaped profile between walls. An open wake or cavity is formed behind the profile. Conformal mapping techniques are used to sol ve this problem. The problem formulated in the hodograph plane is decompose d into two nonoverlapping domains. Heterogeneous modeling is then used to d escribe the problems, i.e., a different governing differential equation in each domain. In one of these domains, a Baiocchi-type transformation is use d to obtain a fixed domain formulation for the part of the transformed prob lem containing an unknown boundary. In the other domain, the Baiocchi-type transformation is extended across the boundary between the two domains, thu s yielding a different problem formulation. This also assures that the depe ndent variables and their normal derivatives are continuous along this comm on boundary. The numerical solution scheme, a successive over-relaxation ap proach, is applied over the whole problem domain with the use of a projecti on-operation over only the fixed domain formulated part. Numerical results are obtained for the case of a truncated circular profile. These results ar e found to be in good agreement with another published result. The existenc e and uniqueness of the solution to the problem as a variational inequality is shown, and the convergence of the numerical solution using a domain dec omposition method scheme is demonstrated by assuming some convergence prope rty on the common interface of the two subdomains. (C) 2000 John Wiley & So ns, Inc.