The Evaluation of Interblock Mobility Using a Modified Midpoint Weighting Scheme

ABSTRACT A modified midpoint weighting scheme is a technique which can be used for increasing the accuracy and stability of finite difference numerical simulations. Generally, if midpoint weighting is used to evaluate the transmissibility at an interface between adjacent blocks, explicit methods may not produce the correct solution and implicit methods may lead to an oscillatory behavior. Reasons for this behavior have been investigated and it has been found that these problems occur because of numerical limitations during accumulation of the displacing fluid within the upstream block. A proposed modified version of midpoint weighting appears to eliminate this problem and several linear displacement test runs have indicated that the local truncation errors are comparable to those in the two-point upstream weighting scheme. The overall accuracy of results in areal systems appears to be better than the two-point upstream scheme the use of which is constrained due to its assymetric character. The results were also compared to the single-point upstream weighting method and it was found that the modified midpoint weighting scheme allowed the use of a coarser grid while maintaining similar accuracy. An additional advantage to this new technique is that it can also be used in an implicit formulation.