A numerical investigation of a spectral‐type nodal collocation discontinuous Galerkin approximation of the Euler and Navier–Stokes equations

F. Bassi; N. Franchina; A. Ghidoni; S. Rebay

doi:10.1002/fld.3713

journal article Jul 24, 2012

A numerical investigation of a spectral‐type nodal collocation discontinuous Galerkin approximation of the Euler and Navier–Stokes equations

F. Bassi N. Franchina A. Ghidoni

S. Rebay

International Journal for Numerical Methods in Fluids Vol. 71 No. 10 pp. 1322-1339 · Wiley

View at Publisher Save 10.1002/fld.3713

Abstract

SUMMARYIn this paper, we focus on the applicability of spectral‐type collocation discontinuous Galerkin methods to the steady state numerical solution of the inviscid and viscous Navier–Stokes equations on meshes consisting of curved quadrilateral elements. The solution is approximated with piecewise Lagrange polynomials based on both Legendre–Gauss and Legendre–Gauss–Lobatto interpolation nodes. For the sake of computational efficiency, the interpolation nodes can be used also as quadrature points. In this case, however, the effect of the nonlinearities in the equations and/or curved elements leads to aliasing and/or commutation errors that may result in inaccurate or unstable computations. By a thorough numerical testing on a set of well known test cases available in the literature, it is here shown that the two sets of nodes behave very differently, with a clear advantage of the Legendre–Gauss nodes, which always displayed an accurate and robust behaviour in all the test cases considered.Copyright © 2012 John Wiley & Sons, Ltd.

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References

Details

Published: Jul 24, 2012
Vol/Issue: 71(10)
Pages: 1322-1339
License: View

Authors

F

F. Bassi

Dipartimento di Ingegneria Industriale Università degli Studi di Bergamo Dalmine Italy

N

N. Franchina

Dipartimento di Ingegneria Industriale Università degli Studi di Bergamo Dalmine Italy

A

A. Ghidoni

Dipartimento di Ingegneria Meccanica e Industriale Università degli Studi di Brescia Brescia Italy

S

S. Rebay

Dipartimento di Ingegneria Meccanica e Industriale Università degli Studi di Brescia Brescia Italy

Cite This Article

F. Bassi, N. Franchina, A. Ghidoni, et al. (2012). A numerical investigation of a spectral‐type nodal collocation discontinuous Galerkin approximation of the Euler and Navier–Stokes equations. International Journal for Numerical Methods in Fluids, 71(10), 1322-1339. https://doi.org/10.1002/fld.3713

A numerical investigation of a spectral‐type nodal collocation discontinuous Galerkin approximation of the Euler and Navier–Stokes equations

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