Meshless lattice Boltzmann method for the simulation of fluid flows.

Area of Science:

• Computational fluid dynamics
• Numerical methods
• Fluid mechanics

Background:

• Traditional lattice Boltzmann methods rely on mesh-based discretizations.
• Mesh-based methods can introduce significant numerical errors and require complex mesh quality improvements.
• Developing meshless alternatives is crucial for enhancing simulation accuracy and efficiency.

Purpose of the Study:

• To propose and validate a novel meshless lattice Boltzmann numerical method.
• To address limitations associated with mesh-based discretizations in fluid flow simulations.
• To demonstrate the method's effectiveness for benchmark fluid flow problems.

Main Methods:

• Separation of collision and streaming operators in the lattice Boltzmann equation.
• Discretization of the streaming equation using the Lax-Wendroff scheme (time) and a meshless local Petrov-Galerkin scheme with augmented radial basis functions (space).
• Application to plane Couette flow, circular Couette flow, and impulsively started cylinder flow.

Main Results:

• The meshless lattice Boltzmann method demonstrated excellent agreement with analytical solutions and literature data.
• The method effectively reduces numerical errors inherent in mesh-based approaches.
• Despite higher per-node computational cost, the meshless method shows superior performance when the total number of nodes is reduced.

Conclusions:

• The proposed meshless lattice Boltzmann method is a viable and powerful alternative for fluid flow simulations.
• This approach offers advantages in accuracy and efficiency, particularly for complex flow scenarios.
• The meshless nature provides flexibility and reduces the burden of mesh generation and quality control.