Monotonicity in high‐order curvilinear finite element arbitrary Lagrangian–Eulerian remap
Abstract
Summary The remap phase in arbitrary Lagrangian–Eulerian (ALE) hydrodynamics involves the transfer of field quantities defined on a post‐Lagrangian mesh to some new mesh, usually generated by a mesh optimization algorithm. This problem is often posed in terms of transporting (or advecting) some state variable from the old mesh to the new mesh over a fictitious time interval. It is imperative that this remap process be monotonic, that is, not generate any new extrema in the field variables. It is well known that the only linear methods that are guaranteed to be monotonic for such problems are first‐order accurate; however, much work has been performed in developing non‐linear methods, which blend both high and low (first) order solutions to achieve monotonicity and preserve high‐order accuracy when the field is sufficiently smooth. In this paper, we present a set of methods for enforcing monotonicity targeting high‐order discontinuous Galerkin methods for advection equations in the context of high‐order curvilinear ALE hydrodynamics. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.
- Authors:
-
- Center for Applied Scientific Computing Lawrence Livermore National Laboratory Livermore CA USA
- Weapons and Complex Integration Lawrence Livermore National Laboratory Livermore CA USA
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1401591
- Resource Type:
- Publisher's Accepted Manuscript
- Journal Name:
- International Journal for Numerical Methods in Fluids
- Additional Journal Information:
- Journal Name: International Journal for Numerical Methods in Fluids Journal Volume: 77 Journal Issue: 5; Journal ID: ISSN 0271-2091
- Publisher:
- Wiley Blackwell (John Wiley & Sons)
- Country of Publication:
- United Kingdom
- Language:
- English
Citation Formats
Anderson, R. W., Dobrev, V. A., Kolev, Tz. V., and Rieben, R. N. Monotonicity in high‐order curvilinear finite element arbitrary Lagrangian–Eulerian remap. United Kingdom: N. p., 2014.
Web. doi:10.1002/fld.3965.
Anderson, R. W., Dobrev, V. A., Kolev, Tz. V., & Rieben, R. N. Monotonicity in high‐order curvilinear finite element arbitrary Lagrangian–Eulerian remap. United Kingdom. https://doi.org/10.1002/fld.3965
Anderson, R. W., Dobrev, V. A., Kolev, Tz. V., and Rieben, R. N. Tue .
"Monotonicity in high‐order curvilinear finite element arbitrary Lagrangian–Eulerian remap". United Kingdom. https://doi.org/10.1002/fld.3965.
@article{osti_1401591,
title = {Monotonicity in high‐order curvilinear finite element arbitrary Lagrangian–Eulerian remap},
author = {Anderson, R. W. and Dobrev, V. A. and Kolev, Tz. V. and Rieben, R. N.},
abstractNote = {Summary The remap phase in arbitrary Lagrangian–Eulerian (ALE) hydrodynamics involves the transfer of field quantities defined on a post‐Lagrangian mesh to some new mesh, usually generated by a mesh optimization algorithm. This problem is often posed in terms of transporting (or advecting) some state variable from the old mesh to the new mesh over a fictitious time interval. It is imperative that this remap process be monotonic, that is, not generate any new extrema in the field variables. It is well known that the only linear methods that are guaranteed to be monotonic for such problems are first‐order accurate; however, much work has been performed in developing non‐linear methods, which blend both high and low (first) order solutions to achieve monotonicity and preserve high‐order accuracy when the field is sufficiently smooth. In this paper, we present a set of methods for enforcing monotonicity targeting high‐order discontinuous Galerkin methods for advection equations in the context of high‐order curvilinear ALE hydrodynamics. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.},
doi = {10.1002/fld.3965},
journal = {International Journal for Numerical Methods in Fluids},
number = 5,
volume = 77,
place = {United Kingdom},
year = {Tue Oct 14 00:00:00 EDT 2014},
month = {Tue Oct 14 00:00:00 EDT 2014}
}
https://doi.org/10.1002/fld.3965
Web of Science
Works referenced in this record:
Flux Correction Tools for Finite Elements
journal, January 2002
- Kuzmin, D.; Turek, S.
- Journal of Computational Physics, Vol. 175, Issue 2
High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter
journal, July 2004
- Kuzmin, D.; Turek, S.
- Journal of Computational Physics, Vol. 198, Issue 1
The repair paradigm and application to conservation laws
journal, July 2004
- Shashkov, Mikhail; Wendroff, Burton
- Journal of Computational Physics, Vol. 198, Issue 1
Constrained-Optimization Based Data Transfer
book, January 2012
- Bochev, Pavel; Ridzal, Denis; Scovazzi, Guglielmo
- Flux-Corrected Transport
Strong Stability-Preserving High-Order Time Discretization Methods
journal, January 2001
- Gottlieb, Sigal; Shu, Chi-Wang; Tadmor, Eitan
- SIAM Review, Vol. 43, Issue 1
Fast optimization-based conservative remap of scalar fields through aggregate mass transfer
journal, August 2013
- Bochev, Pavel; Ridzal, Denis; Shashkov, Mikhail
- Journal of Computational Physics, Vol. 246
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics
journal, January 2012
- Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N.
- SIAM Journal on Scientific Computing, Vol. 34, Issue 5
A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction
journal, August 2010
- Galera, Stéphane; Maire, Pierre-Henri; Breil, Jérôme
- Journal of Computational Physics, Vol. 229, Issue 16
Optimization-based remap and transport: A divide and conquer strategy for feature-preserving discretizations
journal, January 2014
- Bochev, Pavel; Ridzal, Denis; Peterson, Kara
- Journal of Computational Physics, Vol. 257
A Synchronous and Iterative Flux-Correction Formalism for Coupled Transport Equations
journal, October 1996
- Schär, Christoph; Smolarkiewicz, Piotr K.
- Journal of Computational Physics, Vol. 128, Issue 1
Formulation, analysis and numerical study of an optimization-based conservative interpolation (remap) of scalar fields for arbitrary Lagrangian–Eulerian methods
journal, June 2011
- Bochev, Pavel; Ridzal, Denis; Scovazzi, Guglielmo
- Journal of Computational Physics, Vol. 230, Issue 13
Optimization-based synchronized flux-corrected conservative interpolation (remapping) of mass and momentum for arbitrary Lagrangian–Eulerian methods
journal, March 2010
- Liska, Richard; Shashkov, Mikhail; Váchal, Pavel
- Journal of Computational Physics, Vol. 229, Issue 5
An arbitrary Lagrangian–Eulerian discretization of MHD on 3D unstructured grids
journal, September 2007
- Rieben, R. N.; White, D. A.; Wallin, B. K.
- Journal of Computational Physics, Vol. 226, Issue 1
High-Resolution Conservative Algorithms for Advection in Incompressible Flow
journal, April 1996
- LeVeque, Randall J.
- SIAM Journal on Numerical Analysis, Vol. 33, Issue 2
Algebraic Flux Correction and Geometric Conservation in ALE Computations
book, January 2012
- Scovazzi, Guglielmo; López Ortega, Alejandro
- Flux-Corrected Transport
Slope limiting for discontinuous Galerkin approximations with a possibly non-orthogonal Taylor basis: SLOPE LIMITING FOR DG APPROXIMATIONS
journal, September 2012
- Kuzmin, Dmitri
- International Journal for Numerical Methods in Fluids, Vol. 71, Issue 9