Popular high-order schemes with compact stencils for Computational Fluid Dynamics (CFD)
include Discontinuous Galerkin (DG), Spectral Difference (SD), and Spectral Volume (SV) …

High-order numerical methods for unstructured grids combine the superior accuracy of high-
order spectral or finite difference methods with the geometric flexibility of low-order finite …

Emerging as the mathematical expression of principles of conservation, conservation laws
have proven themselves to provide effective and accurate predictive models of our physical …

Abstract Computational Fluid Dynamics (CFD) methods that are third-order accurate or
higher are generally considered high-order methods in the aerospace community. These …

The correction procedure via reconstruction (CPR, formerly known as flux reconstruction) is
a framework of high order methods for conservation laws, unifying some discontinuous …

When controlling the trailing-edge (TE) interference noise of airfoil, the design of the TE
serration shape is still an open issue. To this end, the flow and noise generation for different …

All numerical calculations will fail to provide a reliable answer unless the continuous
problem under consideration is well posed. Well-posedness depends in most cases only on …

In this paper, the ability of high-order flux reconstruction numerical schemes to perform
accurate and stable computations of compressible turbulent flows on coarse meshes is …

We report the development of a discontinuous spectral element flow solver that includes the
implementation of both spectral difference and flux reconstruction formulations. With this …

We derive new boundary conditions and implementation procedures for nonlinear initial
boundary value problems (IBVPs) with non-zero boundary data that lead to bounded …