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Title: Continuum-atomistic modeling of shock dynamics using a bridging scale decomposition scheme: proof of principle in one dimension.

Abstract

No abstract prepared.

Authors:
 [1];  [1];  [1];  [2];
  1. (North Carolina State University, Raleigh, NC)
  2. (North Carolina State University, Raleigh, NC)
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
908864
Report Number(s):
SAND2007-0094J
TRN: US200722%%795
DOE Contract Number:
AC04-94AL85000
Resource Type:
Journal Article
Resource Relation:
Journal Name: Proposed for publication in Molecular Simulation.
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; COMPUTERIZED SIMULATION; DYNAMICS; IMPACT SHOCK; ATOMIC MODELS; ONE-DIMENSIONAL CALCULATIONS

Citation Formats

Brenner, D.W., Broom, B., Shi, Yuhui., Hu, Y., and Wagner, Gregory John. Continuum-atomistic modeling of shock dynamics using a bridging scale decomposition scheme: proof of principle in one dimension.. United States: N. p., 2007. Web.
Brenner, D.W., Broom, B., Shi, Yuhui., Hu, Y., & Wagner, Gregory John. Continuum-atomistic modeling of shock dynamics using a bridging scale decomposition scheme: proof of principle in one dimension.. United States.
Brenner, D.W., Broom, B., Shi, Yuhui., Hu, Y., and Wagner, Gregory John. Mon . "Continuum-atomistic modeling of shock dynamics using a bridging scale decomposition scheme: proof of principle in one dimension.". United States. doi:.
@article{osti_908864,
title = {Continuum-atomistic modeling of shock dynamics using a bridging scale decomposition scheme: proof of principle in one dimension.},
author = {Brenner, D.W. and Broom, B. and Shi, Yuhui. and Hu, Y. and Wagner, Gregory John},
abstractNote = {No abstract prepared.},
doi = {},
journal = {Proposed for publication in Molecular Simulation.},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • Abstract not provided.
  • We combine the Spacetime Discontinuous Galerkin (SDG) method for elastodynamics with the mathematically consistent Atomistic Discontinuous Galerkin (ADG) method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids. The formulation couples non-overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions, for both momentum balance and kinematic compatibility, using Riemann values to preserve the characteristic structure of the underlying hyperbolic system. Momentum balances to within machine-precision accuracy over every element, on each atom, and over the coupled system, with small, controllable energy dissipation in the continuum region that ensures numericalmore » stability. When implemented on suitable unstructured spacetime grids, the continuum SDG model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time. A special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface. The trace operator depends on parameters that specify, at the scale of the atomic spacing, the position of the coupling interface relative to the atoms. In a key finding, we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non-physical damping or special boundary conditions. We formulate the implicit SDG-ADG coupling scheme in up to three spatial dimensions, and describe an efficient iterative solution scheme that outperforms common explicit schemes, such as the Velocity Verlet integrator. Numerical examples, in 1dxtime and employing both linear and nonlinear potentials, demonstrate the performance of the SDG-ADG method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic-scale signals in the continuum.« less