We have implemented total variation diminishing (TVD) higher-order differencing schemes for two-dimensional non-uniform grids in the multiphase and multicomponent reservoir simulator TOUGH2. Higher-order differencing may be more efficient in reducing numerical dispersion than grid refinement.
Much existing work in the literature on higher-order differencing schemes has focused on one- and two-dimensional tracer transport using explicit
formulations for the convection-dispersion equation. We find that higher-order differencing schemes can also increase the accuracy of component transport,
phase transport, and thermal energy transport in strongly advective situations in an implicit and multicomponent framework such as that used in TOUGH2. We have verified our implementation of higher-order schemes in TOUGH2/EOS7R by comparison with an analytical solution. We further
applied the method to a problem of reinjection into a geothermal reservoir and compared results calculated using the Leonard TVD scheme against full upstream weighting. Higher-order differencing schemes show promise for decreasing numerical dispersion and improving geothermal reservoir simulation.

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