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

There have been growing research interests in high-order discontinuous schemes over
recent years. With established theoretical basis and framework, more efforts have recently …

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 …

The design of flow control systems remains a challenge due to the nonlinear nature of the
equations that govern fluid flow. However, recent advances in computational fluid dynamics …

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

UCNS3D is an open-source computational solver for compressible flows on unstructured
meshes. State-of-the-art high-order methods and their associated benefits can now be …

In this work, we present a positivity-preserving entropy-based adaptive filtering method for
shock capturing in discontinuous spectral element methods. By adapting the filter strength to …

In this paper we develop a family of very high-order central (up to 6th-order) non-oscillatory
schemes for mixed-element unstructured meshes. The schemes are inherently compact in …

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

High-order methods are becoming increasingly attractive in both academia and industry,
especially in the context of computational fluid dynamics. However, before they can be more …