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Least-squares-based lattice Boltzmann method: a meshless approach for simulation of flows with complex geometry
1Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 3, 2001
Summary
A novel meshless Lattice Boltzmann Method (LBM) uses Taylor expansion and least squares for accurate, efficient simulation of viscous fluid flows on complex geometries.
Area of Science:
- Computational fluid dynamics
- Numerical methods
- Fluid mechanics
Background:
- Standard Lattice Boltzmann Method (LBM) can be computationally intensive and limited by grid structures.
- Simulating complex geometries and nonuniform grids poses challenges for traditional LBM.
- Accurate and efficient numerical methods are crucial for understanding incompressible viscous flows.
Purpose of the Study:
- To present a meshless Lattice Boltzmann Method (LBM) optimized for complex geometries and nonuniform grids.
- To demonstrate the method's applicability to various lattice models and its explicit update formulation.
- To validate the accuracy and computational efficiency of the proposed LBM for 2D incompressible viscous flows.
Main Methods:
- Derivation of a modified LBM using Taylor series expansion.
- Optimization of the LBM using the least squares method.
- Development of an algebraic formulation for explicit distribution function updates based on precomputed coefficients.
Main Results:
- The meshless LBM successfully simulates 2D incompressible viscous flows.
- Numerical results demonstrate high accuracy.
- The method significantly reduces computational time compared to existing approaches.
Conclusions:
- The proposed meshless LBM offers a powerful and efficient alternative for simulating complex fluid dynamics problems.
- The method's flexibility with geometries and grids makes it broadly applicable.
- Further applications to diverse fluid flow scenarios are warranted.
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