Preconditioning of a Fully-Implicit, High-Order, AllSpeed Compressible Flow Solver with Phase Change for Applications in Laser-Based Additive Manufacturing
By: Brian Weston Advisors: Professor Jean-Pierre Delplanque
This work focuses on the development of a fully-implicit, high-order compressible flow 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 solidliquid-gas interfaces, due to laser-induced melting/solidification 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.
The governing equations are discretized up to 4th-order accuracy with our rDG spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK35). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobianfree version of the GMRES solver for linear iterations. Due to the stiffness associated with the acoustic waves and thermal and viscous/material strength effects, preconditioning the GMRES solver is essential.
A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure and velocity-temperature Schur complement systems. This multigrid block reduction preconditioning technique converges on problems with high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in fluid dynamics as well as for laser-induced phase change problems in 2D and 3D.
1147 Mathematical Sciences Bldg
Date(s) - 05/26/2017
10:00 am - 11:00 am