High-order compact finite volume schemes for solving the Reynolds averaged Navier-Stokes equations on the unstructured mixed grids with a large aspect ratio

In this paper, high-order compact finite volume schemes on the unstructured grids based on the variational reconstruction are developed to solve the Reynolds averaged Navier-Stokes equations closed by the Spalart-Allmaras one-equation turbulence model. Encouraging progress is made in addressing the following two challenging problems: reducing the numerical errors on the large aspect ratio grids and avoiding the negative turbulent viscosity associated with the high-order methods. On grids with large aspect ratios, a three-step procedure is designed to optimize the functional parameters of variational reconstruction. In addition, an exponential decay procedure is proposed to cure the negative turbulent viscosity problem of the Spalart-Allmaras model. The exponential decay procedure has the advantage of being able to be used with any spatial discretization method and with the implicit temporal discretization. Numerical tests show significant benefits of the high-order schemes in predicting the skin frictions, capturing some important flow structures, and achieving grid-independent solutions. The numerical tests also show that the proposed schemes are sufficiently robust for practical applications. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

This paper presents high-order compact finite volume schemes based on variational reconstruction to solve the Reynolds averaged Navier-Stokes equations. Through optimizing functional parameters and introducing an exponential decay process, the challenging issues of numerical errors on large aspect ratio grids and negative turbulent viscosity associated with high-order methods have been successfully addressed.