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Title: Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

Abstract

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.

Authors:
 [1];  [2];  [3];  [1];  [1];  [1];  [3]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. North Carolina State Univ., Raleigh, NC (United States)
  3. Univ. of California, Davis, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1241930
Alternate Identifier(s):
OSTI ID: 1359281
Report Number(s):
LLNL-JRNL-669889
Journal ID: ISSN 0021-9991
Grant/Contract Number:  
AC52-07NA27344; 13-SI-002
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 305; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Discontinuous Galerkin Method; High-Order Space-Time Discretization; Fully-Implicit Solvers; Newton-Krylov Algorithm; Fluid Dynamics; Phase-Change

Citation Formats

Nourgaliev, R., Luo, H., Weston, B., Anderson, A., Schofield, S., Dunn, T., and Delplanque, J. -P. Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change. United States: N. p., 2015. Web. doi:10.1016/j.jcp.2015.11.004.
Nourgaliev, R., Luo, H., Weston, B., Anderson, A., Schofield, S., Dunn, T., & Delplanque, J. -P. Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change. United States. https://doi.org/10.1016/j.jcp.2015.11.004
Nourgaliev, R., Luo, H., Weston, B., Anderson, A., Schofield, S., Dunn, T., and Delplanque, J. -P. Wed . "Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change". United States. https://doi.org/10.1016/j.jcp.2015.11.004. https://www.osti.gov/servlets/purl/1241930.
@article{osti_1241930,
title = {Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change},
author = {Nourgaliev, R. and Luo, H. and Weston, B. and Anderson, A. and Schofield, S. and Dunn, T. and Delplanque, J. -P.},
abstractNote = {A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.},
doi = {10.1016/j.jcp.2015.11.004},
journal = {Journal of Computational Physics},
number = ,
volume = 305,
place = {United States},
year = {Wed Nov 11 00:00:00 EST 2015},
month = {Wed Nov 11 00:00:00 EST 2015}
}

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Cited by: 15 works
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Works referencing / citing this record:

A reconstructed discontinuous Galerkin method for multi‐material hydrodynamics with sharp interfaces
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