Higher-Order Spatial Discretization for Turbulent Aerodynamic Computations

A high-order accurate unstructured finite volume Newton–Krylov algorithm for inviscid compressible flows

“…More recently, De Rango and Zingg [8] dramatically reduced numerical error in drag using relatively coarse structured grids for steady turbulent flow over a 2D airfoil by applying a globally third-order accurate algorithm. Their results provide a convincing demonstration of the accuracy benefits of high-order methods compared with a secondorder method for practical flows.…”

Effect of discretization order on preconditioning and convergence of a high-order unstructured Newton-GMRES solver for the Euler equations

“…The question, historically, has always been whether a high-order scheme can be made to converge rapidly enough to be competitive with second-order schemes on a computational cost basis. While there are some results that suggest this is the case for structured meshes [41,21,46,14], the situation for unstructured meshes is less clear, because little work has been done on optimizing convergence rates for high-order unstructured mesh solvers. The main contribution of much of our recent research [30,31,29,33] has been to fill this gap by developing an efficient implicit time advance scheme for our high-order accurate solver.…”

Globalized matrix-explicit Newton-GMRES for the high-order accurate solution of the Euler equations

“…High-order discretizations on structured grids have been shown [1,2] to reduce computational effort for a given level of solution accuracy. High-order methods for unstructured grids are also relatively well established.…”