Lattice Boltzmann method for incompressible flows with large pressure gradients

Area of Science:

• Computational fluid dynamics
• Nonideal fluid dynamics
• Numerical methods

Background:

• Conventional lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models are limited to simulating incompressible flows with negligible Mach number and density variations.
• The standard equation of state in LBGK models restricts their application to flows with small pressure gradients.
• Simulating nonideal fluids requires models that account for realistic equations of state and transport properties.

Purpose of the Study:

• To propose a finite difference lattice BGK model based on the Enskog equation for isothermal incompressible flows.
• To develop a model suitable for nonideal fluids, incorporating a realistic equation of state and transport properties.
• To enhance the accuracy of incompressible flow simulations, particularly under increased pressure gradients.

Main Methods:

• Development of a finite difference lattice BGK model derived from the Enskog equation.
• Implementation of an equation of state and transport properties suitable for nonideal fluids.
• Validation through numerical simulations of standard fluid dynamics problems: plane Poiseuille flow, 2D Womersley flow, and backward-facing step flow.

Main Results:

• The proposed model accurately simulates isothermal incompressible flows.
• Numerical results demonstrate superior accuracy compared to conventional LBGK models when simulating flows with significant pressure gradients.
• The model effectively handles nonideal fluid properties and transport phenomena.

Conclusions:

• The novel finite difference lattice BGK model extends the applicability of lattice Boltzmann methods to nonideal fluids and higher pressure gradients.
• This approach offers a more accurate simulation tool for complex fluid dynamics problems involving nonideal behaviors.
• The study validates the model's effectiveness across various benchmark flow scenarios.