Cell-centered Lagrangian Lax-Wendroff HLL hybrid scheme in cylindrical geometry

•A new numerical method for Lagrangian hydrodynamics in cylindrical geometry is proposed.•Conservation laws are approximated by a cell-centered Lax-Wendroff HLL hybrid scheme.•Proposed scheme keeps exact spherical symmetry on equiangular meshes while symmetry for Cartesian grids remains very good.•T...

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Bibliographic Details
Published in:Journal of computational physics Vol. 417; p. 109605
Main Authors: Fridrich, David, Liska, Richard, Wendroff, Burton
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 15.09.2020
Elsevier Science Ltd
Subjects:
Artificial viscosity
Cartesian coordinates
Computational fluid dynamics
Computational physics
Computer simulation
Cylindrical geometry
Energy dissipation
Euler-Lagrange equation
Finite element method
Fluid flow
Fluxes
Geometry
Hydrodynamics
Lagrangian hydrodynamics
Lax-Wendroff
Lax-Wendroff method
Predictor-corrector methods
Symmetry
Symmetry preservation
Viscosity
Artificial viscosity
Symmetry preservation
Lax-Wendroff
Lagrangian hydrodynamics
Cylindrical geometry
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:•A new numerical method for Lagrangian hydrodynamics in cylindrical geometry is proposed.•Conservation laws are approximated by a cell-centered Lax-Wendroff HLL hybrid scheme.•Proposed scheme keeps exact spherical symmetry on equiangular meshes while symmetry for Cartesian grids remains very good.•The geometric conservation law is satisfied by the method. Lagrangian hydrodynamics as described by the Euler equations is treated by an improved version of the basic predictor-corrector Lax-Wendroff method that also has added HLL-type dissipative fluxes, including both artificial viscosity and energy dissipation. The method in Cartesian geometry is enhanced by a different weighting of the conservative variables in the predictor and a new treatment of material interfaces. The basic method is extended to cylindrical r,z geometry, where it satisfies the geometric conservation law and keeps exact spherical symmetry on equiangular polar meshes. The added viscosity does not preserve symmetry, so in order to achieve that we have added a symmetry correction. Numerical hydrodynamic tests, including the Noh, Sedov, spherical Sod, free expansion and Kidder problems show a reasonable performance of the method. In addition, the spherical Noh problem was simulated on an initially rectangular mesh with a very good result regarding its symmetry.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2020.109605