A Characteristic Domain Decomposition Algorithm for Two-Phase Flows with Interfaces
H. Wang · 1997
This paper describes a characteristic-based, non-overlapping domain decomposition algorithm for solving the saturation equation in two-phase fluid flows with interfaces. First, with the known saturation at the previous time step one obtains an approximate Dirichlet boundary condition at the outflow domain interface by integrating the Ninth International Conference on Domain Decomposition Methods Editor Petter E. Bjrstad, Magne S. Espedal and David E. Keyes c fl1998 DDM.org 836 WANG & ERSLAND saturation equation (ignoring the capillary pressure term) along characteristics. With the approximate outflow Dirichlet boundary condition at the domain interface and the given boundary condition at the physical inflow boundary one can close the system on the current subdomain and applies the characteristic operator-splitting procedure [DEES90, EE87] to solve the full saturation equation (including the capillary pressure effect). Second, one uses the continuity of capillary pressure across the domain interface to pass the value of saturation as an approximate inflow Dirichlet boundary condition to the next subdomain, one then applies the same characteristic operator-splitting procedure to solve the saturation equation on the current subdomain. Third, according to the overall loss or gain of mass one adjusts the approximate outflow Dirichlet boundary condition at the domain interface to iterate between different subdomains until the algorithm converges. Finally, a mixed method is adopted to solve the pressure equation due to its accurate approximation to the velocity field and its local mass conservation property