Fully-Implicit Orthogonal Reconstructed Discontinuous Petrov-Galerkin Method for Multiphysics Problems

Technical Report · Wed Feb 18 04:00:00 EST 2015

DOI:https://doi.org/10.2172/1178386· OSTI ID:1178386

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

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

This document is focussed on the development of reconstructed discontinuous Galerkin (RDG_PnPm ) method, based on orthogonal basis functions. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time discretization. The method is designed for generic partial differential equations, including transient hyperbolic, parabolic and/or elliptic operators, which are attributed to many multiphysics problems. Our driving application of interest is additive manufacturing, which requires simulations of fluid-solid-gas systems, with compressibility effects and phase change (melting/ solidification). Thus, we demonstrate the method capabilities for solving nonlinear heat conduction equation coupled with multi-material Navier-Stokes based compressible fluid (in low Mach number limit) systems. We focus our attention to the method accuracy (in both time and space), as well as solvability of linear algebra involved in linear steps of the Newton-based solver. We demonstrate the accuracy and efficacy of the method, emphasizing the advantages from the orthogonality of basis functions, which makes better conditioning of underlying (approximate) Jacobian matrices, and rapid convergence of Krylov methods. iii

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC52-07NA27344
• OSTI ID: 1178386
• Report Number(s): LLNL-TR--664250
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING