A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for elastic–plastic flows
Abstract
Here, we present a new high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas and solid dynamics. The evolution equations for specific volume, momentum, and total energy are discretized using the modal DG approach. The specific volume, velocity, and specific total energy fields are approximated with up to quadratic Taylor series polynomials. The specific internal energy, pressure, and stress deviators are nodal quantities. The stress deviators are evolved forward in time using a hypoelastic–plastic approach, which requires a velocity gradient. A new method is presented for calculating a high-order polynomial for the velocity gradient in an element. Plasticity is handled by applying a radial return model to the stress deviators. Limiting approaches are presented for modal and nodal fields. The TVD RK time integration method is used to temporally advance all governing evolution equations. Generalized Lagrangian DG equations are derived but test problems are calculated for 1D Cartesian coordinates. A suite of gas and solid dynamics test problem results are calculated to demonstrate the stability and formal accuracy of the new Lagrangian DG method.
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1989710
- Alternate Identifier(s):
- OSTI ID: 1469545; OSTI ID: 1702814
- Report Number(s):
- LA-UR-17-30257
Journal ID: ISSN 0898-1221; S0898122118304383; PII: S0898122118304383
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Published Article
- Journal Name:
- Computers and Mathematics with Applications (Oxford)
- Additional Journal Information:
- Journal Name: Computers and Mathematics with Applications (Oxford) Journal Volume: 78 Journal Issue: 2; Journal ID: ISSN 0898-1221
- Publisher:
- Elsevier
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Lagrangian; Hydrodynamics; Discontinuous Galerkin; solid dynamics; compressible flows; shocks
Citation Formats
Lieberman, Evan J., Morgan, Nathaniel R., Luscher, Darby J., and Burton, Donald E. A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for elastic–plastic flows. United Kingdom: N. p., 2019.
Web. doi:10.1016/j.camwa.2018.08.020.
Lieberman, Evan J., Morgan, Nathaniel R., Luscher, Darby J., & Burton, Donald E. A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for elastic–plastic flows. United Kingdom. https://doi.org/10.1016/j.camwa.2018.08.020
Lieberman, Evan J., Morgan, Nathaniel R., Luscher, Darby J., and Burton, Donald E. Mon .
"A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for elastic–plastic flows". United Kingdom. https://doi.org/10.1016/j.camwa.2018.08.020.
@article{osti_1989710,
title = {A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for elastic–plastic flows},
author = {Lieberman, Evan J. and Morgan, Nathaniel R. and Luscher, Darby J. and Burton, Donald E.},
abstractNote = {Here, we present a new high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method for gas and solid dynamics. The evolution equations for specific volume, momentum, and total energy are discretized using the modal DG approach. The specific volume, velocity, and specific total energy fields are approximated with up to quadratic Taylor series polynomials. The specific internal energy, pressure, and stress deviators are nodal quantities. The stress deviators are evolved forward in time using a hypoelastic–plastic approach, which requires a velocity gradient. A new method is presented for calculating a high-order polynomial for the velocity gradient in an element. Plasticity is handled by applying a radial return model to the stress deviators. Limiting approaches are presented for modal and nodal fields. The TVD RK time integration method is used to temporally advance all governing evolution equations. Generalized Lagrangian DG equations are derived but test problems are calculated for 1D Cartesian coordinates. A suite of gas and solid dynamics test problem results are calculated to demonstrate the stability and formal accuracy of the new Lagrangian DG method.},
doi = {10.1016/j.camwa.2018.08.020},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 2,
volume = 78,
place = {United Kingdom},
year = {Mon Jul 01 00:00:00 EDT 2019},
month = {Mon Jul 01 00:00:00 EDT 2019}
}
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https://doi.org/10.1016/j.camwa.2018.08.020
https://doi.org/10.1016/j.camwa.2018.08.020
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Cited by: 9 works
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Works referenced in this record:
A Lagrangian Discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems
journal, February 2004
- Loubère, R.; Ovadia, J.; Abgrall, R.
- International Journal for Numerical Methods in Fluids, Vol. 44, Issue 6
A Lagrangian staggered grid Godunov-like approach for hydrodynamics
journal, February 2014
- Morgan, Nathaniel R.; Lipnikov, Konstantin N.; Burton, Donald E.
- Journal of Computational Physics, Vol. 259
A cell-centered Lagrangian Godunov-like method for solid dynamics
journal, August 2013
- Burton, D. E.; Carney, T. C.; Morgan, N. R.
- Computers & Fluids, Vol. 83
A Lagrangian discontinuous Galerkin hydrodynamic method
journal, February 2018
- Liu, Xiaodong; Morgan, Nathaniel R.; Burton, Donald E.
- Computers & Fluids, Vol. 163
The cell-centered discontinuous Galerkin method for Lagrangian compressible Euler equations in two-dimensions
journal, June 2014
- Li, Zhenzhen; Yu, Xijun; Jia, Zupeng
- Computers & Fluids, Vol. 96
A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids
journal, November 2014
- Vilar, François; Maire, Pierre-Henri; Abgrall, Rémi
- Journal of Computational Physics, Vol. 276
An approach for treating contact surfaces in Lagrangian cell-centered hydrodynamics
journal, October 2013
- Morgan, Nathaniel R.; Kenamond, Mark A.; Burton, Donald E.
- Journal of Computational Physics, Vol. 250
An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces
journal, March 2003
- Udaykumar, H. S.; Tran, L.; Belk, D. M.
- Journal of Computational Physics, Vol. 186, Issue 1
Analytic solutions of hydrodynamics equations
journal, May 1991
- Coggeshall, S. V.
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978
- Sod, Gary A.
- Journal of Computational Physics, Vol. 27, Issue 1
Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics
journal, July 2012
- Vilar, François
- Computers & Fluids, Vol. 64
A new high-order discontinuous Galerkin spectral finite element method for Lagrangian gas dynamics in two-dimensions
journal, April 2011
- Jia, Zupeng; Zhang, Shudao
- Journal of Computational Physics, Vol. 230, Issue 7
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