skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics

Abstract

We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J 2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J 2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.

Authors:
 [1];  [1];  [2];  [2]
  1. Czech Technical Univ. in Prague, Praha (Czech Republic)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1338785
Report Number(s):
LA-UR-17-20068
DOE Contract Number:
AC52-06NA25396
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Klima, Matej, Kucharik, MIlan, Shashkov, Mikhail Jurievich, and Velechovsky, Jan. Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics. United States: N. p., 2017. Web. doi:10.2172/1338785.
Klima, Matej, Kucharik, MIlan, Shashkov, Mikhail Jurievich, & Velechovsky, Jan. Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics. United States. doi:10.2172/1338785.
Klima, Matej, Kucharik, MIlan, Shashkov, Mikhail Jurievich, and Velechovsky, Jan. Fri . "Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics". United States. doi:10.2172/1338785. https://www.osti.gov/servlets/purl/1338785.
@article{osti_1338785,
title = {Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics},
author = {Klima, Matej and Kucharik, MIlan and Shashkov, Mikhail Jurievich and Velechovsky, Jan},
abstractNote = {We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.},
doi = {10.2172/1338785},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 06 00:00:00 EST 2017},
month = {Fri Jan 06 00:00:00 EST 2017}
}

Technical Report:

Save / Share:
  • From the very origins of numerical hydrodynamics in the Lagrangian work of von Neumann and Richtmyer [83], the issue of total energy conservation as well as entropy production has been problematic. Because of well known problems with mesh deformation, Lagrangian schemes have evolved into Arbitrary Lagrangian–Eulerian (ALE) methods [39] that combine the best properties of Lagrangian and Eulerian methods. Energy issues have persisted for this class of methods. We believe that fundamental issues of energy conservation and entropy production in ALE require further examination. The context of the paper is an ALE scheme that is extended in the sense thatmore » it permits cyclic or periodic remap of data between grids of the same or differing connectivity. The principal design goals for a remap method then consist of total energy conservation, bounded internal energy, and compatibility of kinetic energy and momentum. We also have secondary objectives of limiting velocity and stress in a non-directional manner, keeping primitive variables monotone, and providing a higher than second order reconstruction of remapped variables. Particularly, the new contributions fall into three categories associated with: energy conservation and entropy production, reconstruction and bounds preservation of scalar and tensor fields, and conservative remap of nonlinear fields. Our paper presents a derivation of the methods, details of implementation, and numerical results for a number of test problems. The methods requires volume integration of polynomial functions in polytopal cells with planar facets, and the requisite expressions are derived for arbitrary order.« less
  • We are proposing a fundamentally new approach to ALE methods for solids undergoing large deformation due to extreme loading conditions. Our approach is based on a physically-motivated and mathematically rigorous construction of the underlying Lagrangian method, vector/tensor reconstruction, remapping, and interface reconstruction. It is transformational because it deviates dramatically from traditionally accepted ALE methods and provides the following set of unique attributes: (1) a three-dimensional, finite volume, cell-centered ALE framework with advanced hypo-/hyper-elasto-plastic constitutive theories for solids; (2) a new physically and mathematically consistent reconstruction method for vector/tensor fields; (3) advanced invariant-preserving remapping algorithm for vector/tensor quantities; (4) moment-of-fluid (MoF)more » interface reconstruction technique for multi-material problems with solids undergoing large deformations. This work brings together many new concepts, that in combination with emergent cell-centered Lagrangian hydrodynamics methods will produce a cutting-edge ALE capability and define a new state-of-the-art. Many ideas in this work are new, completely unexplored, and hence high risk. The proposed research and the resulting algorithms will be of immediate use in Eulerian, Lagrangian and ALE codes under the ASC program at the lab. In addition, the research on invariant preserving reconstruction/remap of tensor quantities is of direct interest to ongoing CASL and climate modeling efforts at LANL. The application space impacted by this work includes Inertial Confinement Fusion (ICF), Z-pinch, munition-target interactions, geological impact dynamics, shock processing of powders and shaped charges. The ALE framework will also provide a suitable test-bed for rapid development and assessment of hypo-/hyper-elasto-plastic constitutive theories. Today, there are no invariant-preserving ALE algorithms for treating solids with large deformations. Therefore, this is a high-impact effort that will significantly advance the state of ALE methods and position LANL as world leaders in advanced ALE methods.« less
  • This report presents a simplified numerical fluid-dynamics computing technique for calculating time-dependent flows in three dimensions. An implicit treatment of the pressure equation permits calculation of flows far subsonic without stringent constraints on the time step. In addition, the grid vertices may be moved with the fluid in Lagrangian fashion or held fixed in an Eulerian manner, or moved in some prescribed manner to give a continuous rezoning capability. This report describes the combination of Implicit Continuous-fluid Eulerian (ICE) and Arbitrary Lagrangian-Eulerian (ALE) to form the ICEd-ALE technique in the framework of the Simplified-ALE (SALE-3D) computer program, for which amore » general flow diagram and complete FORTRAN listing are included. Sample problems show how to modify the code for a variety of applications. SALE-3D is patterned as closely as possible on the previously reported two-dimensional SALE program.« less
  • SALE3D calculates three-dimensional fluid flow at all speeds, from the incompressible limit to highly supersonic. An implicit treatment of the pressure calculation similar to that in the Implicit Continuous-fluid Eulerian (ICE) technique provides this flow speed flexibility. In addition, the computing mesh may move with the fluid in a typical Lagrangian fashion, be held in an Eulerian manner, or move in some arbitrarily specified way to provide a continuous rezoning capability. This latitude results from use of an Arbitrary Lagrangian-Eulerian (ALE) treatment of the mesh. The partial differential equations solved are the Navier-Stokes equations and the mass and internal energymore » equations. The fluid pressure is determined from an equation of state and supplemented with an artificial viscous pressure for the computation of shock waves. The computing mesh consists of a three-dimensional network of arbitrarily shaped, six-sided deformable cells, and a variety of user-selectable boundary conditions are provided in the program.« less