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Title: On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing

Abstract

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermalmore » and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.« less

Authors:
 [1]
  1. 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:
1361587
Report Number(s):
LLNL-TH-732004
DOE Contract Number:
AC52-07NA27344
Resource Type:
Thesis/Dissertation
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 42 ENGINEERING

Citation Formats

Weston, Brian T. On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing. United States: N. p., 2017. Web. doi:10.2172/1361587.
Weston, Brian T. On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing. United States. doi:10.2172/1361587.
Weston, Brian T. Wed . "On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing". United States. doi:10.2172/1361587. https://www.osti.gov/servlets/purl/1361587.
@article{osti_1361587,
title = {On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing},
author = {Weston, Brian T.},
abstractNote = {This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.},
doi = {10.2172/1361587},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed May 17 00:00:00 EDT 2017},
month = {Wed May 17 00:00:00 EDT 2017}
}

Thesis/Dissertation:
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  • We present high-order accurate spatiotemporal discretization of all-speed flow solvers using Jacobian-free Newton Krylov framework. One of the key developments in this work is the physics-based preconditioner for the all-speed flow, which makes use of traditional semi-implicit schemes. The physics-based preconditioner is developed in the primitive variable form, which allows a straightforward separation of physical phenomena. Numerical examples demonstrate that the developed preconditioner effectively reduces the number of the Krylov iterations, and the efficiency is independent of the Mach number and mesh sizes under a fixed CFL condition.
  • Multidimensional, higher-order (2nd and higher) numerical methods have come to the forefront in recent years due to significant advances of computer technology and numerical algorithms, and have shown great potential as viable design tools for realistic applications. To achieve this goal, implicit high-order accurate coupling of the multiphysics simulations is a critical component. One of the issues that arise from multiphysics simulation is the necessity to resolve multiple time scales. For example, the dynamical time scales of neutron kinetics, fluid dynamics and heat conduction significantly differ (typically >1010 magnitude), with the dominant (fastest) physical mode also changing during the coursemore » of transient [Pope and Mousseau, 2007]. This leads to the severe time step restriction for stability in traditional multiphysics (i.e. operator split, semi-implicit discretization) simulations. The lower order methods suffer from an undesirable numerical dissipation. Thus implicit, higher order accurate scheme is necessary to perform seamlessly-coupled multiphysics simulations that can be used to analyze the “what-if” regulatory accident scenarios, or to design and optimize engineering systems.« less
  • A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” familymore » of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.« less
  • There is an increasing interest to develop the next generation simulation tools for the advanced nuclear energy systems. These tools will utilize the state-of-art numerical algorithms and computer science technology in order to maximize the predictive capability, support advanced reactor designs, reduce uncertainty and increase safety margins. In analyzing nuclear energy systems, we are interested in compressible low-Mach number, high heat flux flows with a wide range of Re, Ra, and Pr numbers. Under these conditions, the focus is placed on turbulent heat transfer, in contrast to other industries whose main interest is in capturing turbulent mixing. Our objective ismore » to develop singlepoint turbulence closure models for large-scale engineering CFD code, using Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) tools, requireing very accurate and efficient numerical algorithms. The focus of this work is placed on fully-implicit, high-order spatiotemporal discretization based on the discontinuous Galerkin method solving the conservative form of the compressible Navier-Stokes equations. The method utilizes a local reconstruction procedure derived from weak formulation of the problem, which is inspired by the recovery diffusion flux algorithm of van Leer and Nomura [?] and by the piecewise parabolic reconstruction [?] in the finite volume method. The developed methodology is integrated into the Jacobianfree Newton-Krylov framework [?] to allow a fully-implicit solution of the problem.« less
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