SOLUTION OF RADIATION-CONDUCTION PROBLEMS WITH COLLOCATION METHOD USING B-SPLINES AS APPROXIMATING FUNCTIONS

A collocation method employing B-splines as approximating functions and the Gaussian quadrature points as the collocation points is introduced for the first time to the solution of heat transfer problems governed by simultaneous conduction and radiation. It is demonstrated that this method provides an alternative noniterative technique which, with only a small number of equations, can produce solutions as accurate as the finite-difference method, and at a very reasonable computational cost By comparison with exact analytical solution for the case of pure radiation, it is shown that, for up to moderate values of optical thickness, one needs to solve no more than 6 equations to obtain an accuracy better than 2%. The method with these characteristics appears to be an attractive candidate for the solution of radiation-conduction problems pertaining to LMFBR core disruptive meltdown accident analyses. © 1979.