A fast numerical technique for the solution of partial differential equations describing timedependent two- or three-dimensional transport phenomena is developed. It is based on transforming the original time-domain equations into the Laplace domain where numerical integration is performed and by subsequent numerical inverse transformation the final solution can be obtained. The computation time is thus reduced by more than one order of magnitude in comparison with the conventional finite-difference techniques. The effectiveness of the proposed technique is demonstrated by illustrative examples.
Kolev, S. D., & van der Linden, W. E. (1993). Application of Laplace transforms for the solution of transient mass- and heat-transfer problems in flow systems. International journal of heat and mass transfer, 36(1), 135-139. https://doi.org/10.1016/0017-9310(93)80072-3