Similarity and Comparison of Three Finite-Volume Methods for Diffusive Fluxes Computation on Nonorthogonal Meshes

Abstract

Three widely used finite-volume methods for diffusive fluxes computation on nonorthogonal meshes, namely, the coordinate transformation (CT), surface decomposition (SD), and direct gradient evaluation (DGE) methods, are investigated and compared with respect to their accuracy and computational cost. The deep relationship among the three methods is revealed. If some specific choices are made, the three methods may lead to the same implicit principal fluxes when combing with the deferred correction technique. Two Poisson problems are used to examine their performances. The importance of accurate gradient evaluation method for the SD and DGE methods and accurate interpolation method for the CT method on distorted meshes is highlighted.

Acknowledgments

This work was partially funded by the French Government program “Investissements d'Avenir” (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01). The authors wish to thank Dr. Fang-bao Tian of Vanderbit University for his fruitful discussion with the interpolation methods.

Notes

Note: —means the DFC loop is not required.

Note: L ₂ (× 10⁻⁴) and L _∞ (× 10⁻⁴); IT_def, iteration times for the deferred correction loop; IT_ls, total iteration times for the linear system solver.

Note: L ₂ (× 10⁻³) and L _∞ (× 10⁻³); IT_def, iteration times for the deferred correction loop; IT_ls, total iteration times for the linear system solver.

Note: L ₂ (× 10⁻²) and L _∞ (× 10⁻²); IT_def, iteration times for the deferred correction loop; IT_ls, total iterations times for the linear system solver; — means no convergent solution.