Abstract
The one-dimensional nonlinear saturation convection-diffusion equation in reservoir dynamics is solved numerically by an operator-splitting technique. This splitting, the implicit boundary conditions, and a saturation constraint give rise to an ill-conditioned system of nonlinear discretized equations allowing for multiple solutions which is analyzed. The consistency of the problem regarding grid spacing versus diffusion is discussed, and a simple criterion is given for when diffusion should be omitted in the numerical model.
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