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Modeling the flow in diffuse interface methods of solidification.

A Subhedar1, I Steinbach1, F Varnik1

  • 1Interdisciplinary Centre for Advanced Materials Simulation, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany.

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Summary
This summary is machine-generated.

This study simplifies fluid dynamics simulations for solidification by adapting the Navier-Stokes equation. The diffuse interface model accurately captures flow profiles, comparable to exact simulations.

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Area of Science:

  • Fluid Dynamics
  • Materials Science
  • Computational Physics

Background:

  • Simulating fluid dynamics with solid-liquid interfaces is computationally challenging.
  • Existing models often struggle with diffuse interfaces, impacting accuracy in solidification processes.

Purpose of the Study:

  • To develop a simplified fluid dynamical model for diffuse solid-liquid interfaces.
  • To assess the accuracy of this model using the lattice Boltzmann method.
  • To investigate the impact of the solid phase fraction on fluid flow.

Main Methods:

  • Volume averaging approach to derive fluid dynamical equations.
  • Lattice Boltzmann method for fluid dynamics simulations.
  • Quasiexact numerical integration for comparison.

Main Results:

  • The derived equations maintain the Navier-Stokes structure, incorporating solid phase fraction into drag force.
  • The diffuse interface model satisfies Galilean invariance.
  • Simulated flow profiles using the lattice Boltzmann method achieve accuracy comparable to quasiexact simulations when the solid-liquid coupling parameter is optimized.

Conclusions:

  • The volume averaging approach provides a computationally efficient and accurate method for simulating fluid dynamics at diffuse solid-liquid interfaces.
  • The lattice Boltzmann method, when applied with this model, is a viable tool for solidification simulations.
  • Optimizing the diffuse interface parameter enhances simulation accuracy significantly.