Second order symmetry-preserving conservative Lagrangian scheme for compressible Euler equations in two-dimensional cylindrical coordinates

Journal Article · Mon Sep 01 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.04.031· OSTI ID:22314896

Cheng, Juan ^[1]; Shu, Chi-Wang ^[2]

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1. Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China)
2. Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)

In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, a critical issue for the schemes is to keep spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In the past decades, several Lagrangian schemes with such symmetry property have been developed, but all of them are only first order accurate. In this paper, we develop a second order cell-centered Lagrangian scheme for solving compressible Euler equations in cylindrical coordinates, based on the control volume discretizations, which is designed to have uniformly second order accuracy and capability to preserve one-dimensional spherical symmetry in a two-dimensional cylindrical geometry when computed on an equal-angle-zoned initial grid. The scheme maintains several good properties such as conservation for mass, momentum and total energy, and the geometric conservation law. Several two-dimensional numerical examples in cylindrical coordinates are presented to demonstrate the good performance of the scheme in terms of accuracy, symmetry, non-oscillation and robustness. The advantage of higher order accuracy is demonstrated in these examples.

• OSTI ID: 22314896
• Journal Information: Journal of Computational Physics, Vol. 272; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ASTROPHYSICS
COMPRESSIBLE FLOW
COMPUTERIZED SIMULATION
COORDINATES
CYLINDRICAL CONFIGURATION
INERTIAL CONFINEMENT
LAGRANGIAN FUNCTION
ONE-DIMENSIONAL CALCULATIONS
OSCILLATIONS
SPHERICAL CONFIGURATION
SYMMETRY
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS