Controlling Numerical Dispersion by Variably Timed Flux Updating in Two Dimensions

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Abstract
The variably-timed flux updating (VTU) finite-difference technique is extended to two dimensions. VTU simulations of miscible floods on a repeated five-spot pattern are compared with exact solutions and with solutions obtained by front tracking. It is found that for neutral and favorable mobility ratios, VTU gives accurate results even on a coarse mesh and reduces numerical dispersion by a factor of 10 or more over the level generated by conventional single-point (SP) upstream weighting. For highly unfavorable mobility ratios, VTU reduces numerical dispersion, but on a coarse mesh the simulation is nevertheless inaccurate because of the inherent inadequacy of the finite-difference estimation of the flow field.

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