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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 99

An Integrated Gradient Scheme for the Preservation of Symmetry in Lagrangian Hydrodynamics

H. Yong

Institute of Applied Physics and Computational Mathematics, Beijing, China

Full Bibliographic Reference for this paper
H. Yong, "An Integrated Gradient Scheme for the Preservation of Symmetry in Lagrangian Hydrodynamics", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 99, 2008. doi:10.4203/ccp.89.99
Keywords: IGTSP scheme, conservation of total momentum, preservation of symmetry, staggered mesh, cells with large mass ratio.

For many physical problems, for example in the numerical simulation of the inertial confinement fusion (ICF) [1], the preservation of the spherical symmetry is crucial.

A new scheme IGTSP (integrated gradient total symmetry -preserving), which combines the advantages of the IGA (integrated gradient average) [2] and IGT (integrated gradient total) [2] scheme, is presented.

The IGT scheme evaluates a mass weighted average acceleration of the four subcells around a node, which is reasonable from the physical point of view. Unfortunately, the IGT scheme can not preserve spherical symmetry. The IGA scheme overcomes the nonsymmetry result of the IGT scheme, then the IGA scheme is appealing mathematically, and this scheme has worked well in many real problems. However, the IGA scheme evaluates an arithmetic average acceleration of the four subcells around a node, then the scheme will get an abnormally large acceleration when there is a large mass ratio, which results from a much smaller mass of one subcell than that of three others around a node.

The IGTSP scheme can not only give the spherical motion in a spherical problem with equal angular spacing, but also describes the reasonable fluid motion even if the initial cell masses are widely disparate.

First we describe the construction of the IGTSP scheme, which also takes a mass weighted average acceleration as IGT. Then we prove that the new scheme preserves the spherical symmetry with equal angle zoning. Further we prove the accuracy of the conservation of total momentum is of order one for the IGTSP scheme. Finally we present numerical examples on model examples as well as for the Lagrangian numerical simulations of implosions.

R.P.J. Town and A.R. Bell, "Three-dimensional simulations of the implosions of inertial confinement fusion targets", Phy. Rev. Lett., 67(14), 1863-1866, 1991. doi:10.1103/PhysRevLett.67.1863
P.L. Browne, "Integrated Gradients: A derivation of some difference forms for the equation of motion for compressible flow in two-dimensional Lagrangian hydrodynamics", Los Alamos National Laboratory Report LA-10587-MS, 1986.

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