FOURTH-ORDER, CONSERVATIVE, CONTROL-VOLUME FINITE DIFFERENCES FOR BOUNDARY CELLS

Abstract

A general strategy is developed to construct accurate, and conservative, finite-differences of control-volume variables, for boundary cells. Conservation losses of standard finite differences can be attributed to nonunique fluxes at cell faces. Developing unique finite differences at cell faces of an integral variable guarantees conservation. Fourth-order accuracy for this construction is minimally obtained by constraining the coefficient of the leading truncation term of adjacent cell faces to be equal. Finite differences developed through this approach are compared for accuracy and conservation properties with other standard approaches applied to analytical functions and transient thermal conduction. Analyses demonstrate that the new stencils are internally conservative and fourth-order-accurate.