A High-order Discontinuous Galerkin Method for Unsteady Flow Problems

Borker, Raunak; Farhat, Charbel; Tezaur, Radek

doi:10.2514/6.2016-1333

Cited by 1 publication

(1 citation statement)

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“…In recent years, discontinuous Galerkin method , which is originally introduced for solving hyperbolic equations, has received a huge amount of attention for simulating incompressible flows . It is efficient and precise to deal with the convection equation on the basis of suitable numerical flux, and there is no need of stabilization terms.…”

Section: Introductionmentioning

confidence: 99%

A coupled continuous and discontinuous finite element method for the incompressible flows

Gao

Ouyang

Peng-fei

et al. 2017

Numerical Methods in Fluids

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Summary In this paper, we develop a coupled continuous Galerkin and discontinuous Galerkin finite element method based on a split scheme to solve the incompressible Navier–Stokes equations. In order to use the equal order interpolation functions for velocity and pressure, we decouple the original Navier–Stokes equations and obtain three distinct equations through the split method, which are nonlinear hyperbolic, elliptic, and Helmholtz equations, respectively. The hybrid method combines the merits of discontinuous Galerkin (DG) and finite element method (FEM). Therefore, DG is concerned to accomplish the spatial discretization of the nonlinear hyperbolic equation to avoid using the stabilization approaches that appeared in FEM. Moreover, FEM is utilized to deal with the Poisson and Helmholtz equations to reduce the computational cost compared with DG. As for the temporal discretization, a second‐order stiffly stable approach is employed. Several typical benchmarks, namely, the Poiseuille flow, the backward‐facing step flow, and the flow around the cylinder with a wide range of Reynolds numbers, are considered to demonstrate and validate the feasibility, accuracy, and efficiency of this coupled method. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%