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Comparisons of some difference forms for compressible flow in cylindrical geometry on arbitrary Lagrangian and Eulerian framework

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Abstract

The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view. In this paper, the typical spherical symmetry properties of the numerical schemes are discussed, and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian (ALE) method. Numerical results are presented to compare three discrete configurations, i.e., the control volume scheme, the area weighted scheme, and the plane scheme with the addition of a geometrical source. The fact that the singularity arises from the geometrical source term in the plane scheme is illustrated. A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Zhijun Shen & Jian Ren

  2. Center for Applied Physics and Technology, Peking University, Beijing, 100071, China

    Zhijun Shen

  3. Graduate School, Chinese Academy of Engineering Physics, Beijing, 100088, China

    Xiao Li & Jian Ren

Authors
  1. Zhijun Shen
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  2. Xiao Li
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  3. Jian Ren
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Corresponding author

Correspondence to Zhijun Shen.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11471048 and U1630249), the Foundation of Chinese Academy of Engineering Physics (No. 2014A0202010), and the Foundation of Laboratory of Computational Physics (No. 9140C690202140C69293)

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Shen, Z., Li, X. & Ren, J. Comparisons of some difference forms for compressible flow in cylindrical geometry on arbitrary Lagrangian and Eulerian framework. Appl. Math. Mech.-Engl. Ed. 37, 1571–1586 (2016). https://doi.org/10.1007/s10483-016-2105-8

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  • DOI: https://doi.org/10.1007/s10483-016-2105-8

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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