Apparent entropy production difference for error characterization in numerical heat transfer

An entropy-based error indicator is presented to assess the solution accuracy of fluid flow simulations with heat transfer using the second law of thermodynamics. This paper presents a new approach for the characterization of numerical error using a parameter called an "apparent entropy production difference." A control-volume-based finite-element method is used to discretize and solve the governing equations and the second law. The procedure involves the computation and comparison of local entropy production rates obtained from two forms of the discretized second law: transport and positive-definite forms of the entropy generation. The computed local entropy generation rates from both methods are compared and related to expected numerical errors from benchmark solutions. The results of the numerical studies indicate that there is a relationship between the solution error in the computed scalar variables and the apparent entropy production difference.