Application of schemes on moving grids for numerical simulation of hypervelocity impact problems

Vorobiev, O.; Lomov, I.; Shutov, A.; Kondaurov, V. I.; Ni, Angxiu; Fortov, V. E.

doi:10.1016/0734-743x(95)99908-a

Cited by 4 publications

(6 citation statements)

References 9 publications

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“…(28) will not be satisfied by the initial guess, and instead it is expected that jR c j > 0. Therefore (28) can be solved for improved estimates of the wavespeeds using Newton's method…”

Section: ½Ud ¼ ½F ; ð26þmentioning

confidence: 99%

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Exact and approximate solutions of Riemann problems in non-linear elasticity

Barton

Drikakis

Romenski

et al. 2009

Journal of Computational Physics

105

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a b s t r a c tEulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to non-linear elastic theory. In this paper one such class of solver is examined based upon characteristic tracing in conjunction with high-order monotonicity preserving weighted essentially non-oscillatory (MPWENO) reconstruction. Furthermore, a new iterative method for finding exact solutions of the Riemann problem in non-linear elasticity is presented. Access to exact solutions enables an assessment of the performance of the numerical techniques with focus on the resolution of the seven wave structure. The governing model represents a special case of a more general theory describing additional physics such as material plasticity. The numerical scheme therefore provides a firm basis for extension to simulate more complex physical phenomena. Comparison of exact and numerical solutions of one-dimensional initial values problems involving three-dimensional deformations is presented.

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“…(28) will not be satisfied by the initial guess, and instead it is expected that jR c j > 0. Therefore (28) can be solved for improved estimates of the wavespeeds using Newton's method…”

Section: ½Ud ¼ ½F ; ð26þmentioning

confidence: 99%

“…In [11,24] approximate one-dimensional Riemann solvers are presented for two-dimensional deformations. 0021 Godunov methods for elastic-plastic media are demonstrated in [27,29] for one-dimension, in [28] for two-dimensions, and in [13] for three-dimensions.…”

Section: Introductionmentioning

confidence: 99%

Exact and approximate solutions of Riemann problems in non-linear elasticity

Barton

Drikakis

Romenski

et al. 2009

Journal of Computational Physics

105

View full text Add to dashboard Cite

show abstract

“…It is mentioned that a level set method is by no means a definitive approach for extending the proposed single component scheme for modelling multi-components. Similar models to those employed in the current paper have been combined with volume-of-fluid (VOF) methods [28], marker particle methods [10] and moving grid methods [8]. A level set method has been chosen since, unlike conventional VOF methods, this has the potential to allow the sliding between components, and does not posses the complexity of marker particle methods when extending to multi-dimensions.…”

Section: One-dimensional Test Casesmentioning

confidence: 99%

“…The multiplicative decomposition of the total deformation tensor into elastic and plastic parts can be used to yield additional conservation laws for the plastic deformation tensor [3,4]. Developments using these models include the work of Vorobiev et al [8], Wang et al [9], Walter et al [10], and Miller and Colella [11]. A disadvantage of this approach is the additional expense of solving a much larger system of equations.…”

Section: Introductionmentioning

confidence: 99%

An Eulerian finite‐volume scheme for large elastoplastic deformations in solids

Barton

Drikakis

Romenski

2009

Numerical Meth Engineering

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SUMMARYConservative formulations of the governing laws of elastoplastic solid media have distinct advantages when solved using high-order shock capturing methods for simulating processes involving large deformations and shock waves. In this paper one such model is considered where inelastic deformations are accounted for via conservation laws for elastic strain with relaxation source terms. Plastic deformations are governed by the relaxation time of tangential stresses. Compared with alternative Eulerian conservative models, the governing system consists of fewer equations overall. A numerical scheme for the inhomogeneous system is proposed based upon the temporal splitting. In this way the reduced system of non-linear elasticity is solved explicitly, with convective fluxes evaluated using high-order approximations of Riemann problems locally throughout the computational mesh. Numerical stiffness of the relaxation terms at high strain rates is avoided by utilizing certain properties of the governing model and performing an implicit update. The methods are demonstrated using test cases involving large deformations and high strain rates in one-, two-, and three-dimensions.

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“…Computing the normal velocity from (2.69) gives a consistent 1D representation of the mesh motion for the flux calculation. This is the same normal velocity used in Vorobiev et al [55]. As a side note, issues with the GCLs are generally handled implicitly in Lagrange-Remap ALE schemes.…”

Section: Geometric Conservation Lawsmentioning

confidence: 99%

A Cell-Centered Multiphase ALE Scheme With Structural Coupling

Dunn

2012

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Application of schemes on moving grids for numerical simulation of hypervelocity impact problems

Cited by 4 publications

References 9 publications

Exact and approximate solutions of Riemann problems in non-linear elasticity

Exact and approximate solutions of Riemann problems in non-linear elasticity

An Eulerian finite‐volume scheme for large elastoplastic deformations in solids

A Cell-Centered Multiphase ALE Scheme With Structural Coupling

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