FullyImplicit 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 fullyimplicit NewtonKrylov 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 fluidsolid 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 Newtonbased methods. The performance of the developed method is investigated for highlystiff 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 Krylovbased linear solver.
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 North Carolina State Univ., Raleigh, NC (United States)
 Univ. of California, Davis, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1241930
 Alternate Identifier(s):
 OSTI ID: 1359281
 Report Number(s):
 LLNLJRNL669889
Journal ID: ISSN 00219991
 Grant/Contract Number:
 AC5207NA27344; 13SI002
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 305; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Discontinuous Galerkin Method; HighOrder SpaceTime Discretization; FullyImplicit Solvers; NewtonKrylov Algorithm; Fluid Dynamics; PhaseChange
Citation Formats
Nourgaliev, R., Luo, H., Weston, B., Anderson, A., Schofield, S., Dunn, T., and Delplanque, J. P. FullyImplicit 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. FullyImplicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change. United States. doi:10.1016/j.jcp.2015.11.004.
Nourgaliev, R., Luo, H., Weston, B., Anderson, A., Schofield, S., Dunn, T., and Delplanque, J. P. Wed .
"FullyImplicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change". United States. doi:10.1016/j.jcp.2015.11.004. https://www.osti.gov/servlets/purl/1241930.
@article{osti_1241930,
title = {FullyImplicit 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 fullyimplicit NewtonKrylov 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 fluidsolid 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 Newtonbased methods. The performance of the developed method is investigated for highlystiff 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 Krylovbased linear solver.},
doi = {10.1016/j.jcp.2015.11.004},
journal = {Journal of Computational Physics},
number = ,
volume = 305,
place = {United States},
year = {2015},
month = {11}
}
Web of Science