On Order Elevation for Unstructured Finite Volume Solvers Using Defect Correction

Abstract

Much of the effort in improving the accuracy of computational fluid dynamics (CFD) simulations is focused on mesh refinement and adaptation although studies have shown that the use of high-order methods are more efficient in improving accuracy. Stability issues, complexity of implementation, and demand of computational resources are some of the key factors hindering the use of high-order methods in commercial CFD solvers. This paper demonstrates an improvement in the order of accuracy of finite volume solutions on unstructured meshes without using a high-order solver. Defect correction and the error transport equation method are the techniques discussed, along with the method for obtaining an appropriate estimate of the truncation error, which is crucial in both these techniques. Methods to obtain high-order interpolation of the control volume averages and high-order integral functionals along curved boundaries are also discussed. Third-order accurate results are obtained for a variety of problems, including the 2D Euler equations, without using a third-order discretization scheme.