On the Preconditioning of a NewtonKrylov Solver for a HighOrder reconstructed Discontinuous Galerkin Discretization of AllSpeed Compressible Flow with Phase Change for Application in LaserBased Additive Manufacturing
Abstract
This dissertation focuses on the development of a fullyimplicit, highorder compressible ow solver with phase change. The work is motivated by laserinduced phase change applications, particularly by the need to develop largescale multiphysics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multimaterial solidliquidgas interfaces, due to laserinduced 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 nonisothermal 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 4thorder accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5thorder accuracy with Lstable fully implicit time discretization schemes (BDF2 and ESDIRK35). The resulting set of nonlinear equations is solved using a robust NewtonKrylov method, with the Jacobianfree version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermalmore »
 Authors:
 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):
 LLNLTH732004
 DOE Contract Number:
 AC5207NA27344
 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 NewtonKrylov Solver for a HighOrder reconstructed Discontinuous Galerkin Discretization of AllSpeed Compressible Flow with Phase Change for Application in LaserBased Additive Manufacturing. United States: N. p., 2017.
Web. doi:10.2172/1361587.
Weston, Brian T. On the Preconditioning of a NewtonKrylov Solver for a HighOrder reconstructed Discontinuous Galerkin Discretization of AllSpeed Compressible Flow with Phase Change for Application in LaserBased Additive Manufacturing. United States. doi:10.2172/1361587.
Weston, Brian T. Wed .
"On the Preconditioning of a NewtonKrylov Solver for a HighOrder reconstructed Discontinuous Galerkin Discretization of AllSpeed Compressible Flow with Phase Change for Application in LaserBased Additive Manufacturing". United States.
doi:10.2172/1361587. https://www.osti.gov/servlets/purl/1361587.
@article{osti_1361587,
title = {On the Preconditioning of a NewtonKrylov Solver for a HighOrder reconstructed Discontinuous Galerkin Discretization of AllSpeed Compressible Flow with Phase Change for Application in LaserBased Additive Manufacturing},
author = {Weston, Brian T.},
abstractNote = {This dissertation focuses on the development of a fullyimplicit, highorder compressible ow solver with phase change. The work is motivated by laserinduced phase change applications, particularly by the need to develop largescale multiphysics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multimaterial solidliquidgas interfaces, due to laserinduced 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 nonisothermal 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 4thorder accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5thorder accuracy with Lstable fully implicit time discretization schemes (BDF2 and ESDIRK35). The resulting set of nonlinear equations is solved using a robust NewtonKrylov method, with the Jacobianfree 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 velocitypressure (vP) and velocitytemperature (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 (liddriven cavity ow and natural convection heat transfer) as well as for laserinduced 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}
}

We present highorder accurate spatiotemporal discretization of allspeed flow solvers using Jacobianfree Newton Krylov framework. One of the key developments in this work is the physicsbased preconditioner for the allspeed flow, which makes use of traditional semiimplicit schemes. The physicsbased 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.

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