On the Influence of Gradient Reconstruction Procedures Over the Accuracy of Finite Volume Based Schemes

In the context of the cell centered finite volume approach, care must be taken when performing the reconstruction of property gradients at cell interfaces. The present work analyzes three different gradient reconstruction procedures, using three different turbulent simulation test cases, namely the zero-gradient flat plate, the subsonic NACA 0012 airfoil and the transonic OAT15A airfoil. The analysis is concerned mainly with the usage of quadrilateral meshes. The gas dynamics equations are solved using an implicit implementation of Roe's second-order upwind scheme. The RANS closure problem is solved by using the negative Spalart-Allmaras turbulence model. The solution quality of each gradient discretization procedure is analyzed and compared to experimental data and other numerical solutions available in the literature. For the cases considered here, excellent agreement is obtained between the computed solutions and the expected results, regardless of which gradient reconstruction scheme is used.