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Numerical Techniques

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Part of the Scientific Computation book series (SCIENTCOMP)

Abstract

The finite difference equations presented here follow the format and notation used by von Neumann [2.1] for the solutions of the differential equations that describe fluid dynamics in one space dimension. The material is divided into a Lagrange grid that moves with the flow. The space between consecutive grid lines is referred to as a zone. For multidimensional problems a zone is defined as the interior space of intersecting grid lines. The intersections are called zone node points. Subscripts define the Lagrange coordinates and superscripts the corresponding times. See Refs. [2.2, 3] for complete descriptions of mesh generators. For a one-dimensional network, X j n represents the X position of Lagrange coordinate j at time t n . Intermediate points are given by X j n+1/2 = 1/2(X j n+1 + X j n ) and X j+1/2 n = 1/2(X j+1 n + X j n ). A dot over a parameter represents a time derivative. Thus, X j n+1/2 represents the velocity of node point j at time t n+1/2 The complete set of equations for one-dimensional calculations in gas dynamics as well as elastic—plastic flow are given in Appendix B.

Keywords

Shock Wave Finite Difference Scheme Artificial Viscosity Finite Difference Equation Grid Distortion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [2.1]
    J. von Neumann, R.D. Richtmyer: A Method for the Numerical Calculation of Hydrodynamic Shocks, J. Appl. Phys. 21, 232–237 (1950)MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. [2.2]
    D. Giroux: HEMP User’s Manual, Lawrence Livermore National Laboratory, UCRL-51079 Rev. 1 (1973)Google Scholar
  3. [2.3]
    K.H. Warren: HEMP DS User’s Manual, UCID-18075 Rev. 1 (1983)Google Scholar
  4. [2.4]
    M.L. Wilkins: Use of Artificial Viscosity in Multi-dimensional Fluid Dynamic Calculations, J. Comp. Phys. 36 281–303 (1980)MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA

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