Abstract
A finite element method for the compressible Navier-Stokes equations is introduced. The discretization is based on entropy variables. The methodology is developed within the framework of a Galerkin/least-squares formulation to which a discontinuity-capturing operator is added. Results for three test cases selected among those of the Workshop on Hypersonic Flows for Reentry Problems are presented.
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
A. Harten, On the Symmetric Form of Systems of Conservation Laws with Entropy, Journal of Computational Physics, 49 (1983) 151–164.
T.J.R. Hughes, L.P. Franca and M. Mallet, A New Finite Element Method for Computational Fluid Dynamics: I. Symmetric Forms of the Compressible Euler and Navier-Stokes Equations and the Second Law of Thermodynamics, Computer Methods in Applied Mechanics and Engineering, 54 (1986) 223–234.
T.J.R. Hughes and M. Mallet, A New Finite Element Method for Computational Fluid Dynamics: III. The Generalized Streamline Operator for Multidimensional Advective-Diffusive Systems, Computer Methods in Applied Mechanics and Engineering, 58 (1986) 305–328.
T.J.R. Hughes and M. Mallet, A New Finite Element Method for Computational Fluid Dynamics: IV. A Discontinuity-Capturing Operator for Multidimensional Advective-Diffusive Systems, Computer Methods in Applied Mechanics and Engineering, 58 (1986) 329–336.
M. Mallet, A Finite Element Method for Computational Fluid Dynamics, Ph.D. Thesis, Stanford University, 1985.
F. Shakib, Finite Element Analysis of the Compressible Euler and Navier-Stokes Equations, Ph.D. Thesis, Stanford University, 1989.
F. Shakib, T.J.R. Hughes and Z. Johan, A Multi-Element Group Preconditioned GMRES Algorithm for Nonsymmetric Systems arising in Finite Element Analysis, Computer Methods in Applied Mechanics and Engineering, 75 (1989) 415–456.
E. Tadmor, Skew-Selfadjoint Forms for Systems of Conservation Laws, Journal of Mathematical Analysis and Applications, 103 (1984) 428–442.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chalot, F., Hughes, T.J.R., Johan, Z., Shakib, F. (1991). Application of the Galerkin/Least-Squares Formulation to the Analysis of Hypersonic Flows: I. Flow Over a Two-Dimensional Ramp. In: Désidéri, JA., Glowinski, R., Périaux, J. (eds) Hypersonic Flows for Reentry Problems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76527-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-76527-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-76529-2
Online ISBN: 978-3-642-76527-8
eBook Packages: Springer Book Archive