A mixed interface-capturing/interface-tracking formulation for thermal multi-phase flows with emphasis on metal additive manufacturing processes

Qiming Zhu, Jinhui Yan

Research output: Contribution to journalArticlepeer-review


High fidelity thermal multi-phase flow simulations are in much demand to reveal the multi-scale and multi-physics phenomena in metal additive manufacturing (AM) processes, yet accurate and robust predictions remain challenging. In this paper, we present a novel computational framework by mixing interface-capturing/interface-tracking methods for simulating the thermal multi-phase flows in metal AM applications, focusing on better handling the gas-metal interface, where AM physics, such as phase transitions and laser-material interactions, mainly takes place. The framework, built on level set method and variational multi-scale formulation (VMS), features three major contributions: (1) a simple computational geometry-based re-initialization approach, which maintains excellent signed distance property on unstructured meshes, re-constructs an explicit representation of gas-metal interface from the level set, and facilitates the treatment of the multiple laser reflections during keyhole evolution in AM processes; (2) a fully coupled VMS formulation for thermal multi-phase governing equations, including Navier-Stokes, level set convection, and thermodynamics with melting, solidification, evaporation, and interfacial force models; and (3) a three-level recursive preconditioning technique to enhance the robustness of linear solvers. We first compare the geometry-based re-initialization with the Eikonal partial differential equation (PDE)-based approach on two benchmark problems on level set convection and bubble dynamics. The comparison shows the geometry-based approach attains equivalent and even better performance on key criteria than the PDE-based counterpart. We then apply the developed framework to simulate two AM experiments, which Argonne National Laboratory has recently conducted using in-situ high-speed, high-energy x-ray imaging. The proposed framework's accuracy is assessed by thoroughly comparing the simulated results against experimental measurements on various quantities. We also report important quantities that experiments cannot measure to show the modeling capability.

Original languageEnglish (US)
Article number113910
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Sep 1 2021


  • Additive manufacturing
  • Geometry based re-initialization
  • Level set method
  • VMS

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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