The 'recovered space' advection scheme for lowest-order compatible finite element methods

JOURNAL OF COMPUTATIONAL PHYSICS

卷:390

Article

关键词: Advection scheme;    Discontinuous Galerkin;    Compatible finite element methods;    Numerical weather prediction;   

DOI  :  10.1016/j.jcp.2019.04.013

来源: Elsevier

【 摘 要 】

We present a new compatible finite element advection scheme for the compressible Euler equations. Unlike the discretisations described in Cotter and Kuzmin (2016) and Shipton et al.(2018), the discretisation uses the lowest-order family of compatible finite element spaces, but still retains second-order numerical accuracy. This scheme obtains this second-order accuracy by first 'recovering' the function in higher-order spaces, before using the discontinuous Galerkin advection schemes of Cotter and Kuzmin (2016). As well as describing the scheme, we also present its stability properties and a strategy for ensuring boundedness. We then demonstrate its properties through some numerical tests, before presenting its use within a model solving the compressible Euler equations. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free