Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations

A new multi-scale, stabilized method for Q1/P0 finite element computations of Lagrangian shock hydrodynamics is presented. Instabilities (of hourglass type) are controlled by a stabilizing operator derived using the variational multi-scale analysis paradigm. The resulting stabilizing term takes the...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 197; no. 9; pp. 1056 - 1079
Main Authors: Scovazzi, G., Love, E., Shashkov, M.J.
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.02.2008
Elsevier
Subjects:
Computational techniques
Exact sciences and technology
Fluid dynamics
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
General theory
Hourglass instability
Lagrangian shock hydrodynamics
Mathematical methods in physics
Physics
Physics of gases
Physics of gases, plasmas and electric discharges
Solid mechanics
Stabilization
Structural and continuum mechanics
Variational multi-scale method
Variational multi-scale method
Lagrangian shock hydrodynamics
Stabilization
Hourglass instability
Predictor-corrector methods
Lagrangian
Gas dynamics
Clausius Duhem inequality
Mechanical strength
Shear strength
Hydrodynamics
Momentum
Entropy
Finite element method
Equations of state
Lagrange interpolation
Multiscale method
Variational calculus
Modelling
Strength of materials
Numerical stability
ISSN:0045-7825, 1879-2138
Online Access:Get full text
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Summary:A new multi-scale, stabilized method for Q1/P0 finite element computations of Lagrangian shock hydrodynamics is presented. Instabilities (of hourglass type) are controlled by a stabilizing operator derived using the variational multi-scale analysis paradigm. The resulting stabilizing term takes the form of a pressure correction. With respect to broadly accepted hourglass control approaches, the novelty of the method resides in its residual-based character. The stabilizing residual has a definite physical significance, since it embeds a discrete form of the Clausius–Duhem inequality. Effectively, the proposed stabilization samples the production of entropy to counter numerical instabilities. The proposed technique is applied to materials with no shear strength (e.g., fluids), for which there exists a caloric equation of state, and extensions to the case of materials with shear strength (e.g., solids) are also envisioned. The stabilization operator is incorporated into a mid-point, predictor/multi-corrector time integration algorithm, which conserves mass, momentum and total energy. Encouraging numerical results in the context of compressible gas dynamics confirm the potential of the method.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2007.10.002