Flow force calculation in the lattice Boltzmann method

Area of Science:

• Computational Fluid Dynamics
• Fluid-Structure Interaction
• Numerical Methods

Background:

• Accurate force evaluation is crucial for simulating rigid particles in viscous fluids using the lattice Boltzmann method (LBM).
• Existing methods face challenges due to the noncommutativity of streaming and collision operators near solid boundaries.

Purpose of the Study:

• To propose a discrete force calculation scheme with enhanced accuracy for LBM simulations.
• To provide a theoretical explanation for operator noncommutativity in force evaluation.
• To develop a method applicable to complex geometries and reduce computational cost.

Main Methods:

• Theoretical analysis of streaming and collision operators in LBM with solid boundaries.
• Development of a discrete force calculation scheme based on a lattice Boltzmann formulation of the Reynolds transport theorem (RTT).
• Benchmark simulations including flow past a cylinder and NACA0012 airfoil.

Main Results:

• The proposed scheme demonstrates enhanced accuracy and reliability.
• The method effectively handles force evaluation on complex geometries.
• Significantly reduced grid size requirements for accurate force evaluation were observed across a range of Reynolds numbers (10^2 to 0.5x10^6).

Conclusions:

• The novel discrete force calculation scheme offers a more accurate and efficient approach for LBM simulations.
• This method simplifies the analysis of fluid-particle interactions, particularly for complex shapes.
• The reduced grid dependency makes LBM simulations more computationally feasible for engineering applications.