Comparison of Boundary-Fitted Coordinates with Finite-Element Approach for Solution of Conduction Problems

This paper compares the boundary-filled coordinates/finite-difference scheme with a finite-element method for solving transient conduction problems in complex geometries. Various boundary conditions are considered on two-dimensional bodies with square and completely circular cross sections and a circular airfoil cross section. Wherever possible, the temperature distribution obtained numerically using both methods is compared with the analytic solution. For an identical mesh system, the boundary-fitted coordinates approach is found to be more accurate and economical in terms of both computational time and storage requirement than the finite-element method. A parametric study of the conduction problem for various heat generation rates and Biot numbers has been performed.