A stabilization approach for mesh-free simulations of systems developing shocks or extreme strain localizations

Pimprikar, N and Sarkar, S and Devaraj, G and Roy, D and Reid, SR (2015) A stabilization approach for mesh-free simulations of systems developing shocks or extreme strain localizations. In: INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 91 . pp. 18-32.

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Abstract

A new stabilization scheme, based on a stochastic representation of the discretized field variables, is proposed with a view to reduce or even eliminate unphysical oscillations in the mesh-free numerical simulations of systems developing shocks or exhibiting localized bands of extreme deformation in the response. The origin of the stabilization scheme may be traced to nonlinear stochastic filtering and, consistent with a class of such filters, gain-based additive correction terms are applied to the simulated solution of the system, herein achieved through the element-free Galerkin method, in order to impose a set of constraints that help arresting the spurious oscillations. The method is numerically illustrated through its Applications to inviscid Burgers' equations, wherein shocks may develop as a result of intersections of the characteristics, and to a gradient plasticity model whose response is often characterized by a developing shear band as the external load is gradually increased. The potential of the method in stabilized yet accurate numerical simulations of such systems involving extreme gradient variations in the response is thus brought forth. (C) 2014 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Additional Information:	Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Keywords:	COMPUTATIONAL FLUID-DYNAMICS; FINITE-ELEMENT FORMULATION; GRADIENT-DEPENDENT PLASTICITY; ADVECTIVE-DIFFUSIVE SYSTEMS; CONVECTION-DOMINATED FLOWS; NAVIER-STOKES EQUATIONS; FREE GALERKIN METHOD; KERNEL-METHOD; BOUNDARY; IMPLEMENTATIONS
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	24 Apr 2015 06:03
Last Modified:	24 Apr 2015 06:03
URI:	http://eprints.iisc.ac.in/id/eprint/51391

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