Abstract
The solutions of the compressible Euler equations are obtained as limit of the solutions of the Navier-Stokes equations when the viscosity and the heat conductivity tend to zero. First, the spatial derivatives in the NavierStokes equations are approximated by the least squares method and then the resulting system of ODEs is solved by an explicit second order Runge-Kutta method. The scheme is tested for the 1D shock tube problem. Also a fix grid Lagrangian method is proposed and the numerical results are compared with those from the moving grid approach.
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
T. Belytschko, Y. Krongauz, M. Flemming, D. Organ, W. K. S. LIu, Smoothing and accelerated computations in the element free Galerkin method; J. Comp. Appl. Maths. 74, 111–126, (1996)
G.A Dilts, Moving least squares particle hydrodynamics I, consistency and stability; Hydrodynamics methods group report, Los Alamos National Laboratory (1996)
S.M. Deshpande and P.S. Kulkarni, New developments in kinetics schemes; Comp. Math. Appl.35 1 75–93, (1998)
A.K Ghosh, Ph.D thesis; Dept of aerospace Eng., Indian Institute of Science Bangalore, India (1996)
R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars; Mon. Not. Roy. Astron. Soc. 181, 375–389, (1977)
C.Hirsch, Numerical computation of Internal and external flows; Springer eds., Vol 1,2, (1992)
J. Kuhnert, General smoothed particle hydrodynamics; Ph.D. thesis, University of Kaiserslautern, Germany (1999)
L. B. LUCY, A numerical approach to the testing of the fission hypothesis; Astron. J., 82 1013, (1977)
J.J. Monaghan, Smooth particle hydrodynamics; Annu. Rev. Astron. Astrop, 30 543–574, (1992)
J.J. Monaghan, Simulating free surface flows with SPH; J. Comput. Phys., 110 399, (1994)
J. J. Monaghan, A. Kocharyan, SPH simulation of multi-phase flow; Computer Phys. Commun., 87 225–235, (1995)
J. J. Monaghan and R. A. Gingold, Shock Simulation by particle method SPH; J. Comp. Phys., 52 374–389, (1983)
J.P. Morris, P.J. Fox and Y. ZhuModeling Low Reynolds Number Incompressible Flows Using SPH; J. Comput. Phys., 136 214–226, (1997)
G. A. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws; J. Comp. Phys. 27 1–31, (1978).
J. Stoer and R. Bulirsch, Introduction to numerical analysis; Spring-Verlag, New York (1980)
J. C. Tannehill, T. L. Holst, J. V. Rakich, Numerical computation of two-dimensional viscous blunt body flows with an impinging shock; AIAA Paper 75–0154, AIAA 13th Aerospace Sciences Meeting.
S. Tiwari and S. Manservisi, Modeling incompressible Navier-Stokes flows by LSQSPH, preprint, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Tiwari, S. (2001). A LSQ-SPH Approach for Solving Compressible Viscous Flows. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_44
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8372-6_44
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9538-5
Online ISBN: 978-3-0348-8372-6
eBook Packages: Springer Book Archive