A New Class of High-Order Energy Stable Flux Reconstruction Schemes

Abstract The flux reconstruction approach to high-order methods is robust, efficient, simple to implement, and allows various high-order schemes, such as the nodal discontinuous Galerkin method and the spectral difference method, to be cast within a single unifying framework. Utilizing a flux reconstruction formulation, it has been proved (for onedimensional linear advection) that the spectral difference method is stable for all orders of accuracy in a norm of Sobolev type, provided that the interior flux collocation points are located at zeros of the corresponding Legendre polynomials. In this article the aforementioned result is extended in order to develop a new class of one-dimensional energy stable flux reconstruction schemes. The energy stable schemes are parameterized by a single scalar quantity, which if chosen judiciously leads to the recovery of various well known high-order methods (including a particular nodal discontinuous Galerkin method and a particular spectral dif...

• Type: Journal
• Year: 2011
• Where: JSCIC
• Authors: Peter E. Vincent, Patrice Castonguay, Antony Jameson
• Keywords: JSCIC 2011, Nodal Discontinuous Galerkin, Spectral Difference Method, flux Reconstruction