Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow

Area of Science:

• Computational fluid dynamics
• Multiphase flow modeling
• Numerical methods

Background:

• Standard lattice Boltzmann (LB) models exhibit spurious cubic velocity terms.
• These terms can introduce numerical errors in multiphase flow simulations.
• The pseudopotential LB model is widely used but susceptible to these errors.

Purpose of the Study:

• To investigate the elimination of additional cubic velocity terms in the pseudopotential LB model.
• To analyze the impact of these terms on multiphase flow simulations.
• To maintain the computational simplicity of the LB model.

Main Methods:

• Retaining high-order (≥3) Hermite terms in equilibrium distribution and discrete force.
• Introducing correction terms into the LB equation.
• Investigating force terms and density gradients.

Main Results:

• Successfully eliminated additional cubic velocity terms.
• Elimination of cubic terms reduced numerical errors, especially at high velocities.
• Cubic terms primarily affect the interfacial region, with density-gradient terms being most significant.

Conclusions:

• The developed technique effectively removes spurious cubic velocity terms.
• This method enhances the accuracy of multiphase flow simulations using the pseudopotential LB model.
• The findings are crucial for precise computational fluid dynamics analysis.