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Adaptive Mesh Refinement for Two-Phase Viscoelastic Fluid Mixture Models.

Bindi M Nagda1, Aaron Barrett2, Boyce E Griffith3,4

  • 1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL, USA.

Computers & Fluids
|May 20, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces an adaptive mesh refinement (AMR) technique for simulating multiphase flows. The new method accurately captures fluid dynamics while significantly reducing computational costs.

Keywords:
Adaptive Mesh RefinementCo-incompressibilityGeometric MultigridMixture ModelsMultiphase

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Area of Science:

  • Computational fluid dynamics
  • Multiphase flow modeling
  • Numerical analysis

Background:

  • Multiphase flows are crucial in industrial, natural, and biomedical systems.
  • Simulating these flows presents numerical challenges due to non-linear terms and co-incompressibility.
  • Accurate simulation requires methods that handle high stresses and material gradients efficiently.

Purpose of the Study:

  • To develop an adaptive mesh refinement (AMR) technique for simulating multiphase flow mixtures.
  • To create an accurate, robust, and efficient computational method for adaptive grids.
  • To address the numerical challenges in multiphase flow simulations.

Main Methods:

  • Utilized a continuum model with separate momentum equations for each phase.
  • Implemented an adaptive mesh refinement (AMR) technique.
  • Employed a multigrid solver to precondition the saddle-point system.

Main Results:

  • The AMR discretization achieves second-order accuracy in L1, L2, and L-infinity norms.
  • The solver accurately resolves sharp gradients in the solution.
  • Linear solver iterations are independent of grid spacing due to multigrid preconditioning.

Conclusions:

  • The developed AMR solver provides significant cost savings, offering up to a ten-fold speedup over uniform grids.
  • This method enhances the efficiency and accuracy of multiphase flow simulations.
  • The technique is applicable to diverse industrial, natural, and biomedical systems.