Abstract
A method of lines approach is proposed for solving the fluid dynamic equations. The method is based on a combination of the central finite difference approximation to the space variables with a rational Runge-Kutta or a classical Runge-Kutta time integration scheme. Numerical results for both compressible and incompressible flow problems are presented to demonstrate the utility of the present approach.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Machura, M. and Sweet, R.A., A survey of software for partial differential equations, ACM Trans. Math. Software 6, 1980, pp. 461–488.
Jones, D.J., The Numerical Solution of Elliptic Equations by the Method of Lines, Computer Physics Communication 4, 1972, pp. 165–172.
Jones, D.J., South, J.C., and Klunker, E.B., On the Numerical Solution of Elliptic Partial Differential Equations by the Method of Lines, J. Comp. Phys. 9, 1972, pp. 496–527.
Jameson, A. and Baker, T.J., Solution of the Euler Equations for Complex Configuration, AIAA paper 83-1929, 1983.
Beam, R. and Warming, R.F., An Implicit Factored Scheme for the Compressible Navier-Stokes Equations, AIAA paper 77-645, 1977.
Wambecq, A., Rational Runge-Kutta Methods for Solving Systems of Ordinary Differential Equations, Computing 20, 1978, pp. 333–342.
Hicks, J.S. and Wei, J., Numerical Solution of Parabolic Partial Differential Equations With Two-Point Boundary Conditions by Use of the Method of Lines, J. Association for Computing Machinery 14, 3, 1967, pp. 549–562.
Hyman, J.M., A Method of Lines Approach to the Numerical Solution of Conservation Laws, 3rd IMACS Int. Symp. Computer Methods for Partial Differential Equation, 1979.
Heydweiller, J.C. and Sincovec, R.F., A Stable Scheme for the Solution of Hyperbolic Equations Using the Method of Lines, J. Comp. Phys. 22, 1976, pp. 377–388.
Satofuka, N., Modified Differential Quadrature Method for Numerical Solution of Multi-Dimensional Flow Problems, Int. Symp. Appl. Math. Inf. Sci., 1982.
Pulliam, T.H., Jespersen, D.C. and Childs, R.E., An Enhanced Version of an Implicit Code for the Euler Equations, AIAA Paper 83-0314, 1983.
Baldwin, B.S. and Lomax, H., Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows, AIAA Paper 78-257, 1978.
Briggs, W.B., Effect of Mach Number on the Flow and Application of Compressibility Corrections in a Two-Dimensional Subsonic-Transonic Compression Cascade Having Varied Porous-Wall Suction at the Blade Tips, NASA TN-2649, 1952.
Ta Phuoc, L., Daube, O., Monnet, P. and Coutanceau, M., A Comparison of Numerical Simulation and Experimental Visualization of the Early Stage of the Flow Generated by an Impulsively Started Elliptic Cylinder, Numerical Methods in Laminar and Turbulent Flow, 1983, pp. 269-279.
Satofuka, N. and Nishida, H., A New Method for the Numerical Simulation of Turbulence, BAIL III Conf., 1984.
Satofuka, N., Nakamura, H. and Nishida, H., Higher Order Method of Lines for the Numerical Simulation of Turbulence, IC9NMFD, 1984.
Tokunaga, H., Satofuka, N. and Tanimura, Y., Higher Order Accurate Difference Method with New Direct Poisson Solver and its Application to Direct Simulation of Boundary Layer Instability, Int. Symp. Comp. Fluid Dynamics-Tokyo, 1985.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Satofuka, N. (1986). Method of lines approach to the numerical solution of fluid dynamic equations. In: Zhuang, F.G., Zhu, Y.L. (eds) Tenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0041767
Download citation
DOI: https://doi.org/10.1007/BFb0041767
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17172-0
Online ISBN: 978-3-540-47233-9
eBook Packages: Springer Book Archive