Multi-material closure model for high-order finite element Lagrangian hydrodynamics

• Published in: International journal for numerical methods in fluids Vol. 82; no. 10; pp. 689 - 706
• Main Authors: Dobrev, V. A., Kolev, T. V., Rieben, R. N., Tomov, V. Z.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 10.12.2016; Wiley Subscription Services, Inc; Wiley
• Subjects: Balancing; closure models; Closures; Computational fluid dynamics; Entropy; finite element methods; Fluid flow; Fluid mechanics; high-order methods; Hydrodynamics; Mathematical analysis; Mathematical models; MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; multi-material hydrody- namics; pressure equilibration; shock hydrodynamics
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4236

Summary We present a new closure model for single fluid, multi‐material Lagrangian hydrodynamics and its application to high‐order finite element discretizations of these equations . The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high‐order variational generalization of the method of Tipton . This computation is defined by the notion of partial non‐instantaneous pressure equilibration, while the full pressure equilibration is achieved by both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one‐dimensional two‐material problems, followed by two‐dimensional and three‐dimensional multi‐material high‐velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA. We present a closure model that evolves material properties at quadrature point level. The method is general with respect to the number of materials, dimension and space and time discretizations.Material volumes are evolved by imposing partial pressure equilibration, and internal energy exchange between materials is determined by considerations of the expected behavior of the entropy production. Results are presented for standard one‐dimensional two‐material problems, followed by two‐dimensional and three‐dimensional multi‐material arbitrary Lagrangian‐Eulerian high‐velocity impacts.