Abstract
This chapter presents the construction of the approximation of the space derivatives by centered differences. The schemes must be able to treat discontinuities in the flowfield, i.e. shock waves or vortex sheets. Two ways to handle discontinuities are either to track the shock wave explicitly with an additional algorithm, or to capture it implicitly with the scheme.
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
Lax, P.D., Wendroff, B.: “Systems of Conservation Laws”. Comm. Pure. Math., Vol. 23, 1960, pp. 217–237.
Engqvist, B., Osher, S.: “One-Sided Difference Approximations for Nonlinear Conservation Laws”. Math. Comp., Vol. 36, 1981, pp. 321–351.
Gary, J.: “On Certain Finite Difference Schemes for Hyperbolic Systems”. Math. Comp., Vol. 18, 1964, pp. 1–18.
Jameson, A., Schmidt, W., Turkel, E.: “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes”. AIAA Paper 81–1259, 1981.
Jameson, A.: “The Evolution of Computational Methods in Aerodynamics”. J. A.pl. Mech., Vol. 50, 1983, pp. 1052–1070.
Rizzi, A., Eriksson, L.-E.: “Transfinite Mesh Generation and Damped Euler Equations”. AIAA Paper 81–0999, 1981.
MacCormack, R.W., Paullay, A.J.: “The Influence of the Compuational Mesh on Accuracy for Initial Value Problems with Discontinuous or Nonunique Solutions”. Computers & Fluids, Vol. 2, 1974, pp. 339–361.
Lomax, H.: “Some Prospects for the Future of Computational Fluid Dynamics”. AIAA J., Vol. 20, 1982, pp. 1033–1043.
Pulliam, T.H.: “Artificial Dissipation Models for the Euler Equations”. AIAA-Paper 85–0438, 1985.
Rizzi, A., Eriksson, L.-E.: “Computation of Flow Around Wings Based on the Euler Equations”. J. Fluid Mech., Vol. 148, 1984, pp. 45–71.
Eriksson, L.-E.: “Transfinite Mesh Generation and Computer-Aided Analysis of Mesh Effects”. Ph.D. Dissertation, Dept. Computer Science, Uppsala Univ., Sweden, 1984.
Olsson, P.: “Flow Calculations Using Explicit Methods on a Data Parallel Computer”. Report No. 117/1989, Uppsala Univ., 1989.
Eriksson. L.-E.: “Boundary Conditions for Artificial Dissipation Operators”. FFA TN 1984–53, Stockholm 1984.
Lomax, H., Pulliam, T.H., Jespersen, D.C.: “Eigensystem Analysis Techniques for Finite-Difference Equations”. AIAA-Paper No. 81–1027, 1981.
Eriksson, L.-E., Rizzi, A.: “Computer-Aided Analysis of the Convergence to Steady State of a Discrete Approximation to the Euler Equations”. J. Comp. Phys., Vol. 57, 1985, pp. 50–128.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer Fachmedien Wiesbaden
About this chapter
Cite this chapter
Eberle, A., Rizzi, A., Hirschel, E.H. (1992). Centered Differencing. In: Numerical Solutions of the Euler Equations for Steady Flow Problems. Notes on Numerical Fluid Mechanics (NNFM), vol 48. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-06831-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-663-06831-0_5
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07634-4
Online ISBN: 978-3-663-06831-0
eBook Packages: Springer Book Archive