Upstream-weighted differencing schemes and their application to elliptic problems involving fluid flow

Abstract A flexible finite-difference formulation is developed for the system of elliptic equations normally encountered in problems involving heat, mass, and momentum transfer. The flexible formulation allows selection of one of four different solution procedures for the steady-state equations (one of which is the solution of the time-dependent equations). A special diffrencing of the connective and diffusive terms is introduced (containing free parameters) which allows any several differencing schemes to be represented by the same formulae. Two example problems are solved which permit a comparison of central, upstream, and several upstream-weighted, differencing schemes. Emphasis is placed on obtaining efficient and accurate steady- state solutions of the example problems

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