Entropy-based artificial dissipation as a corrective mechanism for numerical stability in convective heat transfer

Abstract

This article presents an entropy-based corrective mechanism to improve nonlinear stability of computational algorithms in numerical heat transfer. The approach uses the transport form of the entropy production equation to calculate a parameter called the entropy-based artificial viscosity. A diffusion coefficient in the momentum conservation equations was modified based on the entropy-based artificial viscosity formulation. The corrective mechanism with an entropy-based artificial viscosity aims to utilize the Second Law as a stabilizing influence on erroneous numerical computations and enhance numerical stability and accuracy. Negative values of numerical entropy production due to discretization errors normally lead to physically unrealistic results that violate the numerical form of the Second Law. The algorithm uses these negative values as a predictive indicator to reduce numerical error and ensure closer compliance with the Second Law. The results for natural convection within a cavity indicate that the entropy-based artificial dissipation can significantly reduce the erroneous values of numerical entropy production and predicted velocities and temperatures, thereby improving the numerical accuracy and stability of the formulation.

Keywords:

• Artificial viscosity
• corrective mechanism
• CVFEM
• entropy-based artificial viscosity
• entropy production
• numerical error indicator
• Second Law
• transport entropy

Additional information

Funding

Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and Memorial University School of Graduate Studies is gratefully acknowledged.