| Abstract: | We present a finite volume method for the coupled systems of nonlinear partial differential equations arising in secondary hydrocarbon migration and accumulation processes in basin modeling. We propose a modified alternating direction implicit splitting acceleration technique to solve the scheme in an effective and robust manner. We apply the scheme to simulate model problems with clear physical features and to secondary migration and accumulation problems in real petroleum reservoirs. The numerical experiments show that the scheme is very robust and generates stable and physically reasonable numerical results, even in the extremely long time period that ranges from millions of years to tens of millions of years. This clearly shows the strong potential of the method developed. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 254–270, 2003 |
