Forthethree-dimensionalconvection-dominatedproblemofdynamicsoffluidsinporousmedia,thesecondorderupwindfinitedifferencefractionalstepsschemesapplicabletoparallelarithmeticareputforward.Fractionalstepstechniquesareneededtoconvertamulti-dimensionalproblemintoaseriesofsuccessiveone-dimensionalproblems.Sometechniques,suchascalculusofvariations,energymethod,multiplicativecommutationruleofdifferenceoperators,decompositionofhighorderdifferenceoperators,andthetheoryofpriorestimatesareadopted.Optimalorderestimatesarederivedtodeterminetheerrorinthesecondorderapproximatesolution.Thesemethodshavealreadybeenappliedtothenumericalsimulationofmigration-accumulationofoilresourcesandpredictingtheconsequencesofseawaterintrusionandprotectionprojects.
