High-Order Methods for Diffusion Equation with Energy Stable Flux Reconstruction Scheme
نویسندگان
چکیده
This study investigates the viscous term formulation for the newly developed energy stable flux reconstruction (ESFR) scheme, as an extension to the linear advection flux formulation in the original ESFR scheme. The concept of energy stability for the flux reconstruction approach is put forward. This paper also discusses the formulation of inviscid first derivative flux based on flux reconstruction and diffusive second derivative flux based on solution reconstruction. Numerical experiments for the linear advection equation, diffusion equation, advection-diffusion equation and viscous Burger’s equations are performed. The stability and accuracy of three recovered schemes, i.e. Nodal Discontinuous Galerkin, Spectral Difference, and Huynh type methods, are studied. Lastly, the choice and implementation of the interface numerical flux are found to affect the stability and accuracy of the various schemes. In particular, central flux is compared with the unbiased upwind and downwind flux.
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