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Title: Constrained optimization framework for interface-aware sub-scale dynamics discrete closure model for multimaterial cells in Lagrangian cell-centered hydrodynamics

Journal Article · · Computers and Mathematics with Applications (Oxford)
 [1]; ORCiD logo [2];  [2]
  1. AWE Aldermaston, Reading (United Kingdom). Computational Physics Group
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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In this paper, we present the new discrete optimization-based interface-aware sub-scale dynamics (IA-SSD) closure model for multimaterial cells for Lagrangian cell-centered hydrodynamics. For the multimaterial cell, the kinematic and thermodynamic properties (e.g., velocity, density, pressure and internal energy) will typically vary between the materials. The discrete closure model is responsible for an accurate update of the thermodynamic states of the individual material components in the multimaterial cell, and for determining the nodal forces that move the vertices of the cell. The IA-SSD closure model consists of two stages — a bulk stage followed by a sub-scale stage. During the bulk stage, the total change in the volume of the cell, total force applied to the cell, and total work done on the cell are distributed between the materials to update their volume, velocity and total energy. This distribution is performed using volume fractions of the materials. During the second stage, sub-scale interactions of the materials inside the multimaterial cell are taken into account. At this stage, information about the topology of the materials inside the multimaterial cell is used, allowing the orientations of internal interfaces to be included in the model. Each material interacts in a pair-wise fashion with the materials with which it has a common boundary. The interactions are based on the solution of the acoustic Riemann problem between each pair of materials and are limited using physically justified constraints: positivity of volume, positivity of internal energy, and controlled rate of pressure relaxation. To determine the values of the limiter coefficients, a constrained-optimization framework is employed using a quadratic objective function with linear constraints. It is a first-of-its kind application of constrained optimization to develop discrete closure models in a more rigorous fashion. The pair-wise interaction between materials is essentially one dimensional in the direction that is normal to interface. Finally, for this reason, we demonstrate in this paper the performance of our new model on one dimensional numerical examples.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
Grant/Contract Number:
AC52-06NA25396
OSTI ID:
1458958
Report Number(s):
LA-UR-17-30494
Journal Information:
Computers and Mathematics with Applications (Oxford), Vol. 78, Issue 2; ISSN 0898-1221
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

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97 MATHEMATICS AND COMPUTING
Lagrangian
hydrodynamics
closure model
multimaterial cell