A Hierarchical Grid Solver for Simulation of Flows of Complex Fluids

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Meshing techniques

Background:

• Tree-based grids offer efficient Cartesian discretizations with local mesh refinement.
• Adapting discretization stencils at interfaces between different grid sizes is a key challenge.
• Existing methods often limit mesh complexity to simplify interface treatments.

Purpose of the Study:

• To develop a robust method for handling complex mesh configurations in tree-based grids.
• To implement a moving least squares meshless interpolation technique for improved accuracy.
• To simulate various fluid flows, including viscoelastic fluids, using the enhanced meshing approach.

Main Methods:

• Employed a moving least squares (MLS) meshless interpolation technique.
• Implemented the MLS method within the HiG-Flow computational fluid dynamics code.
• Applied the technique to simulate Newtonian, generalized Newtonian, and viscoelastic fluid flows.

Main Results:

• The MLS method successfully handles complex mesh configurations without sacrificing accuracy.
• Demonstrated the flexibility and robustness of the approach through numerical tests.
• Successfully simulated viscoelastic fluid flows, showcasing the method's applicability.

Conclusions:

• The moving least squares meshless interpolation technique provides a flexible and accurate solution for tree-based grids.
• This approach overcomes limitations of traditional methods, allowing for more complex and efficient simulations.
• The implemented method is robust for a range of fluid flow problems, including advanced viscoelastic simulations.