Adaptive Mesh Refinement for Two-Phase Viscoelastic Fluid Mixture Models

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.