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Lattice Centering and Coordination Number02:33

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The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
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Evolution of Staircase Structures in Diffusive Convection
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Consistent second-order boundary implementations for convection-diffusion lattice Boltzmann method.

Liangqi Zhang1, Shiliang Yang1, Zhong Zeng2,3

  • 1School of Chemical and Biomedical Engineering, Nanyang Technological University, Singapore 637459, Singapore.

Physical Review. E
|March 18, 2018
PubMed
Summary
This summary is machine-generated.

A new second-order boundary scheme for the convection-diffusion lattice Boltzmann (LB) method is presented. This method accurately implements Dirichlet, Neumann, and Robin conditions for both straight and curved boundaries with improved locality and consistency.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Methods
  • Statistical Mechanics

Background:

  • The lattice Boltzmann (LB) method is a powerful numerical technique for simulating fluid flows.
  • Accurate implementation of boundary conditions is crucial for the fidelity of LB simulations.
  • Existing methods often struggle with complex geometries and diverse boundary types.

Purpose of the Study:

  • To develop an alternative second-order boundary scheme for the convection-diffusion LB method.
  • To enable consistent implementation of Dirichlet, Neumann, and linear Robin boundary conditions.
  • To address challenges in both straight and curved geometries.

Main Methods:

  • Utilized Chapman-Enskog analysis and Hermite polynomial expansion for second-order accuracy.
  • Derived an explicit expression for the general distribution function.
  • Developed boundary implementations for straight and curved geometries using local curvilinear coordinates and Taylor expansion.

Main Results:

  • Proposed a novel second-order boundary scheme for convection-diffusion LB method.
  • Successfully implemented Dirichlet, Neumann, and linear Robin conditions consistently.
  • Demonstrated applicability to both straight and curved geometries with high accuracy.

Conclusions:

  • The proposed scheme offers improved locality and consistency for LB boundary implementations.
  • It provides a robust and accurate approach for simulating fluid dynamics with complex boundaries.
  • This advancement enhances the capability of the LB method in various scientific and engineering applications.