Efficient high-order radial basis-function-based differential quadrature-finite volume method for incompressible...

Area of Science:

• Computational Fluid Dynamics
• Numerical Methods

Background:

• Incompressible flows on unstructured grids present significant computational challenges.
• Existing methods may lack the desired accuracy or efficiency for complex simulations.

Purpose of the Study:

• To develop and validate an efficient high-order method for incompressible flows on unstructured grids.
• To enhance the accuracy and computational efficiency of fluid flow simulations.

Main Methods:

• A high-order polynomial approximation using Taylor series expansion within control cells.
• Mesh-free radial basis-function-based differential quadrature for derivative approximation.
• Lattice Boltzmann flux solver for evaluating inviscid and viscous fluxes.
• Implicit time-marching techniques (LUSGS, DIRK) for solving ordinary differential equations.

Main Results:

• The proposed method demonstrates higher accuracy compared to the k-exact method.
• The method exhibits superior computational efficiency.
• Validation through several numerical examples on unstructured grids confirms accuracy, efficiency, and robustness.

Conclusions:

• The presented high-order radial basis-function-based differential quadrature-finite volume method is accurate, efficient, and robust for incompressible flows.
• This method offers a significant improvement over existing techniques for complex fluid dynamics problems on unstructured grids.