Abstract
We develop, implement and test a new third order accurate MUSCL type finite volume scheme for the two-dimensional Euler equations of compressible fluid flow and compare the scheme with an analogous second order scheme. It turns out that for many applications the third order scheme is less efficient than the second order one.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. Cockburn and C.-W. Shu, The Runge-Kutta local discontinuous Galerkin finite element method for conservation laws V: Multidimensional systems. ICASE-Report 97–433 (1997). To appear in J. Comput. Phys.
A. Harten, B. Engquist, S. Osher and S. Chakravarthy, Uniformly high-order accurate essentially non-oscillatory schemes III. J. Comput. Phys., 71 (1987), 231–303.
G.-S. Jiang and C.-W. Shu, Efficient implementation of weighted ENO schemes. J. Comput. Phys., 126 (1996), 202–228.
B.P. Leonard, The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection. Comp. Meth. Appl. Mech. Eng., 88 (1991), 17–74.
B.P. Leonard and H.S. Niknafs, Sharp monotonic resolution of discontinuities without clipping of narrow extrema. Computers & Fluids, 19 (1991), 141–154.
R.J. LeVeque and R. Walder, Grid alignment effects and rotated methods for computing complex flows in astrophysics. eds. J.B. Vos, A. Rizzi and I.L. Rhyming, Proceedings of the Ninth GAMM Conference on numerical methods in fluid mechanics. Notes Num. Fluid. Mech., 35 (1992), 376–385.
X.-D. Liu and S. Osher, Nonoscillatory high order accurate self-similar maximum principle satisfying shock capturing schemes I. SIAM J. Numer. Anal., 33 (1996), 760–779.
X.-D. Liu, S. Osher and T. ChanWeighted essentially non-oscillatory schemes. J. Comput. Phys., 115 (1994), 200–212.
X.-D. Liu and E.TadmorThird order nonoscillatory central scheme for hyperbolic conservation laws. Preprint 1996.
S. Noelle, High order finite volume schemes for the two-dimensional compressible Euler equations. Habilitationsschrift, Universität Bonn, Germany, 1997.
R. Sanders, A third-order accurate variation nonexpansive difference scheme for single nonlinear conservation laws. Math. Comp., 51 (1988), 535–558.
C.-W. ShuTVB uniformly high order schemes for conservation laws. Math. Comp., 49 (1987), 105–121.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Basel AG
About this paper
Cite this paper
Noelle, S. (1999). A Comparison of Third and Second Order Accurate Finite Volume Schemes for the Two-dimensional Compressible Euler Equations. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_26
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8724-3_26
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9744-0
Online ISBN: 978-3-0348-8724-3
eBook Packages: Springer Book Archive