The total velocity sequential semi-implicit method has received significant use since it was originally develped in about 1970 by Spillette, Hillestad, and Stone. Its advantage is a reduction in the per-timestep computational requirement. it comprises two major steps: a solution of the IMPES pressure equation, then a solution of coupled saturation equations. Since the pressure solution is for a single unknown at each gridblock, it requires less work than solving fully implicit equations. Since the set of saturation equations does not have the elliptic nature of the pressure equation or of the fully implicit coupled set of equations, the saturation solution coverges rapidly. Overall, the per-timestep computational work requried is typically a half to a fifth that required for fully implicit computations.
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