A 3D Lagrangian cellcentered hydrodynamic method with higherorder reconstructions for gas and solid dynamics
Abstract
The Lagrangian finite volume cellcentered hydrodynamic method introduces dissipation into the calculation by solving a multidirectional approximate Riemann problem. The amount of dissipation created is a function of the jump in the velocity and stress at the node. These jumps in velocity and stress can be reduced by using higherorder reconstructions that are constructed by fitting cellaverage values in neighboring cells. One challenge is that a large stencil is required to create highorder reconstructions. To address this challenge, a new twostep reconstruction process is proposed to build a quadratic polynomial by only communicating with faceneighboring cells. The twostep reconstruction method is applied to scalar, vector, and tensor fields. Another challenge is that limiters must be used to reduce the higher order reconstructions towards piecewise constant fields near discontinuities to prevent artificial new extrema. We address this second challenge and propose a new hierarchical limiter that uses a discrete Mach number as a smoothness indicator. The inclusion of the Mach number is essential for minimizing dissipation errors. The new limiter is used with the reconstructions of pressure, velocity, and deviatoric stress. The accuracy and robustness of the new twostep reconstruction method with the new limiter is demonstrated by simulating a suitemore »
 Authors:

 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 Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1479949
 Alternate Identifier(s):
 OSTI ID: 1702807
 Report Number(s):
 LAUR1730750
Journal ID: ISSN 08981221
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 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 08981221
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Lagrangian; Cellcentered hydrodynamics (CCH); Limiter; Higherorder solutions; Solid dynamics
Citation Formats
Chiravalle, Vincent P., and Morgan, Nathaniel R. A 3D Lagrangian cellcentered hydrodynamic method with higherorder reconstructions for gas and solid dynamics. United States: N. p., 2018.
Web. https://doi.org/10.1016/j.camwa.2018.06.011.
Chiravalle, Vincent P., & Morgan, Nathaniel R. A 3D Lagrangian cellcentered hydrodynamic method with higherorder reconstructions for gas and solid dynamics. United States. https://doi.org/10.1016/j.camwa.2018.06.011
Chiravalle, Vincent P., and Morgan, Nathaniel R. Fri .
"A 3D Lagrangian cellcentered hydrodynamic method with higherorder reconstructions for gas and solid dynamics". United States. https://doi.org/10.1016/j.camwa.2018.06.011. https://www.osti.gov/servlets/purl/1479949.
@article{osti_1479949,
title = {A 3D Lagrangian cellcentered hydrodynamic method with higherorder reconstructions for gas and solid dynamics},
author = {Chiravalle, Vincent P. and Morgan, Nathaniel R.},
abstractNote = {The Lagrangian finite volume cellcentered hydrodynamic method introduces dissipation into the calculation by solving a multidirectional approximate Riemann problem. The amount of dissipation created is a function of the jump in the velocity and stress at the node. These jumps in velocity and stress can be reduced by using higherorder reconstructions that are constructed by fitting cellaverage values in neighboring cells. One challenge is that a large stencil is required to create highorder reconstructions. To address this challenge, a new twostep reconstruction process is proposed to build a quadratic polynomial by only communicating with faceneighboring cells. The twostep reconstruction method is applied to scalar, vector, and tensor fields. Another challenge is that limiters must be used to reduce the higher order reconstructions towards piecewise constant fields near discontinuities to prevent artificial new extrema. We address this second challenge and propose a new hierarchical limiter that uses a discrete Mach number as a smoothness indicator. The inclusion of the Mach number is essential for minimizing dissipation errors. The new limiter is used with the reconstructions of pressure, velocity, and deviatoric stress. The accuracy and robustness of the new twostep reconstruction method with the new limiter is demonstrated by simulating a suite of 3D Cartesian test problems covering both gas and solid dynamics.},
doi = {10.1016/j.camwa.2018.06.011},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 2,
volume = 78,
place = {United States},
year = {2018},
month = {6}
}