Recent developments in linear/nonlinear computational algorithms for transient heat transfer

Recent developments dealing with computational single step algorithms for linear and nonlinear transient heat conduction problems are described in this paper. With the advancements in computing technology and the advent of high performance computing platforms, there is a need to develop high order of accuracy algorithms which circumvent the deficiencies associated with low order of accuracy transient algorithms. From a broad perspective, the framework and general theoretical basis should systematically permit the design of computational algorithm to lead to the exact solution response with increase in the order of accuracy. In particular, we describe: (i) recent developments in single step high order of accuracy unconditionally stable algorithms for linear problems, and (ii) for nonlinear problems, we develop a second-order time accurate explicit single step methodology and some simple illustrative cases are described to support the present developments.