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

Nourgaliev, R.; Luo, H.; Weston, B.; Anderson, A.; Schofield, S.; Dunn, T.; Delplanque, J. -P.

doi:10.1016/j.jcp.2015.11.004

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

Journal Article · Wed Nov 11 00:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2015.11.004· OSTI ID:1241930

Nourgaliev, R. ^[1]; Luo, H. ^[2]; Weston, B. ^[3]; Anderson, A. ^[1]; Schofield, S. ^[1]; Dunn, T. ^[1]; Delplanque, J. -P. ^[3]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
North Carolina State Univ., Raleigh, NC (United States)
Univ. of California, Davis, CA (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1241930

Alternate ID(s):: OSTI ID: 1359281

Report Number(s):: LLNL--JRNL-669889

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 305; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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

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