Force evaluation in the lattice Boltzmann method involving curved geometry

Area of Science:

• Computational Fluid Dynamics
• Numerical Methods
• Fluid Mechanics

Background:

• The lattice Boltzmann equation (LBE) is a powerful numerical method for simulating fluid flow.
• Accurate force evaluation is crucial for analyzing fluid-structure interactions.
• Existing methods for force calculation in LBE have limitations, especially for complex geometries.

Purpose of the Study:

• To compare the momentum-exchange method and the stress-integration method for force evaluation in LBE.
• To implement second-order accurate boundary conditions for curved geometries.
• To assess the reliability, accuracy, and ease of implementation of both methods.

Main Methods:

• Investigated two force evaluation approaches: momentum-exchange and stress-integration.
• Employed second-order accurate boundary conditions for particle distribution functions on curved surfaces.
• Validated methods through simulations of various 2D and 3D flow cases.

Main Results:

• The stress-integration method is computationally intensive and difficult to implement for 3D flows.
• The momentum-exchange method is reliable, accurate, and easy to implement for both 2D and 3D flows.
• Simulations of channel flow, flow past cylinders, and flow past a sphere showed good agreement with existing results using the momentum-exchange method.

Conclusions:

• The momentum-exchange method is superior to the stress-integration method for force evaluation in LBE simulations.
• The implemented second-order accurate boundary conditions are effective for curved geometries.
• The momentum-exchange method provides accurate drag predictions for various flow configurations.