HIGHER-ORDER DIFFERENCING FOR PHASE-FRONT PROPAGATION IN GEOTHERMAL SYSTEMS

摘要

We are testing higher-order differencing total variationdiminishing schemes implemented in the reservoirsimulator TOUGH2 to reduce numerical dispersion ofphase fronts in geothermal flow problems. Theschemes are called total variation diminishing becausethey employ flux limiters to prevent spuriousoscillations that sometimes occur with other higher-order differencing schemes near sharp fronts. Thus itappears that total variation diminishing schemes relyon an implicit assumption that the overall variabilityof advected quantities stays constant or diminisheswith time. We use the Leonard total variationdiminishing scheme in two special problems designedto test the applicability of the scheme for cases wherethis implicit assumption is violated. In the firstproblem, we investigate the isothermal propagationof a phase front in a composite porous medium wherephase saturation increases as the front enters thesecond medium. In the second problem, weinvestigate the propagation of a phase front whereboiling increases the saturation difference across thefront as it propagates. In the composite porousmedium problem, we find that spurious phasesaturations can arise if the weighting scheme is basedon relative permeability; for weighting based onphase saturation, no such oscillation arises. In theboiling front propagation problem, the front positionis highly sensitive to weighting scheme, and theLeonard total variation diminishing scheme is moreaccurate than upstream weighting because it decreasesnumerical dispersion in the thermal energy equation.