Theoretical studies and numerical experiments suggest that unstructured high-order
methods can provide solutions to otherwise intractable fluid flow problems within complex …

The flux reconstruction (FR) approach allows various well-known high-order schemes, such
as collocation based nodal discontinuous Galerkin (DG) methods and spectral difference …

The purpose of this article is to summarize our recent progress in high-order and high
accurate CFD methods for flow problems with complex grids as well as to discuss the …

This paper presents the development of a 2D solver for inviscid and viscous compressible
flows using the spectral difference (SD) method for unstructured grids with mixed elements …

This paper presents simulations of unsteady flow past plunging and pitching airfoils using a
high-order spectral difference (SD) method. Both third-order and fourth-order SD methods …

This paper presents a simple, efficient, and high-order accurate sliding-mesh interface
approach to the spectral difference (SD) method. We demonstrate the approach by solving …

This work studies three multigrid variants for matrix-free finite-element computations on
locally refined meshes: geometric local smoothing, geometric global coarsening (both h …

In this paper, we improve the Navier–Stokes flow solver developed by Sun et al. based on
the spectral volume method (SV) in the following two aspects: the development of a more …

We report development of a high-order compact flux reconstruction method for solving
unsteady incompressible flow on unstructured grids with implicit dual time stepping. The …

This paper reports development of a two-dimensional solver for compressible viscous flow
using spectral difference (SD) method and its applications on simulating laminar flow past …