NONSTANDARD FINITE ELEMENT ANALYSIS OF IMMISCIBLE DISPLACEMENT1
John Howard Cushman · Soil Science · 1983
An immiscible displacement problem is examined via nonstandard finite elements. In particular I examine a problem involving water being applied to a one-dimensional horizontal reservoir (of coarse sand or gravel) displacing the fluid that was initially in the reservoir. The nonstandard Galerkin method is presented for flow equations of hyperbolic structure in finite difference form. The Buckley-Leverett equation representing the above displacement problem is shown to be of this hyperbolic nature. Graphical results are presented that compare the analytical and numerical solutions to the problem. Specifically, it is shown that the method accurately tracks the saturation discontinuity (shock). A possible method for extending the numerical technique to the more general parabolic case is discussed.