A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier--Stokes equation
| Autor: | Yuwen Li, John M. Cimbala, Corina S. Drapaca, Xi Chen |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Discretization Applied Mathematics Mixed finite element method Numerical Analysis (math.NA) Computer Science Applications Physics::Fluid Dynamics Computational Mathematics Flow (mathematics) Discontinuous Galerkin method Modeling and Simulation Compressibility FOS: Mathematics Applied mathematics Potential flow Mathematics - Numerical Analysis Viscous stress tensor Galerkin method Mathematics |
| DOI: | 10.48550/arxiv.2008.09485 |
| Popis: | In this paper, we propose a unified numerical framework for the time-dependent incompressible Navier--Stokes equation which yields the $H^1$-, $H(\text{div})$-conforming, and discontinuous Galerkin methods with the use of different viscous stress tensors and penalty terms for pressure robustness. Under minimum assumption on Galerkin spaces, the semi- and fully-discrete stability is proved when a family of implicit Runge--Kutta methods are used for time discretization. Furthermore, we present a unified discussion on the penalty term. Numerical experiments are presented to compare our schemes with classical schemes in the literature in both unsteady and steady situations. It turns out that our scheme is competitive when applied to well-known benchmark problems such as Taylor--Green vortex, Kovasznay flow, potential flow, lid driven cavity flow, and the flow around a cylinder. Comment: 33 pages, 28 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|