High-Order Unstructured Essentially Nonoscillatory and Weighted Essentially Nonoscillatory Schemes for Aerodynamic Flows

Abstract

In the present work, essentially nonoscillatory schemes and weighted essentially nonoscillatory schemes are implemented in a cell centered finite volume context on unstructured meshes. The two-dimensional Euler equations are considered to represent the flows of interest. The essentially nonoscillatory and weighted essentially nonoscillatory schemes have been developed with the purpose of accurately capturing discontinuities appearing in problems governed by hyperbolic conservation laws. In the aerodynamic studies of interest in the paper, these discontinuities are mainly represented by shock waves. The entire reconstruction process of essentially nonoscillatory and weighted essentially nonoscillatory schemes is described in detail for any order of accuracy with an emphasis on the implementation of second-order and third-order schemes. A flux-difference splitting method and a flux-vector splitting method are tested and compared. The code developed also features an agglomeration multigrid procedure for convergence acceleration, and an adaptive mesh refinement tool. Applications for aerodynamic flows are performed to assess the capability implemented against data available in the literature.