Skip to main content
Journal cover image

Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations

Publication ,  Journal Article
Scovazzi, G; Love, E; Shashkov, MJ
Published in: Computer Methods in Applied Mechanics and Engineering
February 1, 2008

A new multi-scale, stabilized method for Q1/P0 finite element computations of Lagrangian shock hydrodynamics is presented. Instabilities (of hourglass type) are controlled by a stabilizing operator derived using the variational multi-scale analysis paradigm. The resulting stabilizing term takes the form of a pressure correction. With respect to broadly accepted hourglass control approaches, the novelty of the method resides in its residual-based character. The stabilizing residual has a definite physical significance, since it embeds a discrete form of the Clausius-Duhem inequality. Effectively, the proposed stabilization samples the production of entropy to counter numerical instabilities. The proposed technique is applied to materials with no shear strength (e.g., fluids), for which there exists a caloric equation of state, and extensions to the case of materials with shear strength (e.g., solids) are also envisioned. The stabilization operator is incorporated into a mid-point, predictor/multi-corrector time integration algorithm, which conserves mass, momentum and total energy. Encouraging numerical results in the context of compressible gas dynamics confirm the potential of the method. © 2007 Elsevier B.V. All rights reserved.

Duke Scholars

Published In

Computer Methods in Applied Mechanics and Engineering

DOI

ISSN

0045-7825

Publication Date

February 1, 2008

Volume

197

Issue

9-12

Start / End Page

1056 / 1079

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Scovazzi, G., Love, E., & Shashkov, M. J. (2008). Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations. Computer Methods in Applied Mechanics and Engineering, 197(9–12), 1056–1079. https://doi.org/10.1016/j.cma.2007.10.002
Scovazzi, G., E. Love, and M. J. Shashkov. “Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations.” Computer Methods in Applied Mechanics and Engineering 197, no. 9–12 (February 1, 2008): 1056–79. https://doi.org/10.1016/j.cma.2007.10.002.
Scovazzi G, Love E, Shashkov MJ. Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations. Computer Methods in Applied Mechanics and Engineering. 2008 Feb 1;197(9–12):1056–79.
Scovazzi, G., et al. “Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations.” Computer Methods in Applied Mechanics and Engineering, vol. 197, no. 9–12, Feb. 2008, pp. 1056–79. Scopus, doi:10.1016/j.cma.2007.10.002.
Scovazzi G, Love E, Shashkov MJ. Multi-scale Lagrangian shock hydrodynamics on Q1/P0 finite elements: Theoretical framework and two-dimensional computations. Computer Methods in Applied Mechanics and Engineering. 2008 Feb 1;197(9–12):1056–1079.
Journal cover image

Published In

Computer Methods in Applied Mechanics and Engineering

DOI

ISSN

0045-7825

Publication Date

February 1, 2008

Volume

197

Issue

9-12

Start / End Page

1056 / 1079

Related Subject Headings

  • Applied Mathematics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences