Apparent entropy production difference for numerical error characterization

An entropy-based error indicator is presented to evaluate the solution accuracy in fluid flow problems with heat transfer using the Second Law of Thermodynamics. This article presents a new approach for the characterization of numerical error using a newly developed parameter called an "apparent entropy production difference". A control-volume-based finite-element method (CVFEM) is used to discretize the governing conservation equations and the Second Law. The procedure involves the computation and comparison of local entropy production rates obtained from two forms of the discretized entropy production equations – transport and positive-definite forms of the entropy generation equation. The computed local entropy generation for two problems involving heat transfer in fluid flow agrees well with benchmark solutions. The results of the numerical studies indicated that there is a correlation between the solution error in the computed scalar variable value in each control volume and the apparent entropy production difference.