A physical approach to the finite difference solution of the conduction equation in orthogonal curvilinear coordinates

A unified approach to the numerical solution of the transient heat conduction equation is presented. By formulating the numerical description of the heat conduction problem in a general orthogonal curvilinear coordinate system, advantages similar to those experienced in analytic solutions become available to the numerical analyst. Generalized finite difference coefficients are obtained by imposing a physical balance of the rates of heat flow, storage and generation on discrete curvilinear control volumes distributed spatially throughout the solution domain. This development is complemented by consideration of boundary condition application in general orthogonal coordinates which then permits the complete numerical description of conduction problems in any orthogonal coordinate system. Two references cited illustrate its successful usage on practical problems. The generalized derivation presented here has been shown to provide substantial flexibility, accuracy and economy of finite difference solutions when appropriate selection of the coordinate system is made.