Benchmark results in computational heat and fluid flow : the integral transform method

Abstract The integral transform method is reviewed as a benchmark tool in computational heat and fluid flow, with special emphasis on nonlinear problems. The hybrid numerical-analytical nature of this approach collapses the numerical task into one single independent variable, and thus allows for a simple computational procedure with automatic global error control and mild increase in computational effort for multidimensional situations. Various applications on nonlinear diffusion and convection-diffusion are more closely considered, followed by sample results from recent contributions.