Multiple Relaxation Time Lattice Boltzmann Models for Multigrid Phase-Field Segmentation of Tumors in 3D Ultrasound Images

2019 ◽  
Vol 12 (3) ◽  
pp. 1324-1346 ◽  
Author(s):  
Khac L. Nguyen ◽  
Mohamed M. Tekitek ◽  
Philippe Delachartre ◽  
Michel Berthier
Keyword(s):  
Relaxation Time ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
3D Ultrasound ◽  
Ultrasound Images ◽  
Multiple Relaxation Time ◽  
Lattice Boltzmann Models

A GENERAL MULTIPLE-RELAXATION-TIME BOLTZMANN COLLISION MODEL

2007 ◽  
Vol 18 (04) ◽  
pp. 635-643 ◽  
Author(s):  
XIAOWEN SHAN ◽  
HUDONG CHEN
Keyword(s):  
Relaxation Time ◽  
Lattice Boltzmann ◽  
Lattice Structure ◽  
Transport Coefficients ◽  
Hermite Polynomials ◽  
Simple Extension ◽  
Relaxation Rates ◽  
Collision Model ◽  
Multiple Relaxation Time ◽  
Lattice Boltzmann Models

We formulate a simple extension to the Bhatnagar-Gross-Krook collision model by expanding the distribution function in Hermite polynomials and assigning a relaxation time to each hydrodynamic moment. By discretizing the velocity space, multiple-relaxation-time lattice Boltzmann models can be constructed. The transport coefficients are analytically calculated and numerically verified. At the lowest order, allowing different relaxation rates for the second and third Hermite components results in a variable Prandtl number. Comparing with the previously proposed multiple-relaxation-time lattice Boltzmann models, the present formulation is general in the sense that it is independent of the underlying lattice structure and does not require a procedure for transformation of base vectors.

A Three-Dimensional Phase Field Based Nonorthogonal Multiple-Relaxation-Time Lattice Boltzmann Method for Interface Tracking

2021 ◽  
Author(s):  
Shengyuan Zhang ◽  
Jun Tang ◽  
Huiying Wu
Keyword(s):  
Relaxation Time ◽  
Phase Field ◽  
Computational Efficiency ◽  
Lattice Boltzmann ◽  
Present Model ◽  
Three Dimensional ◽  
Transformation Matrix ◽  
Phase Field Method ◽  
Interface Tracking ◽  
Multiple Relaxation Time

Abstract Based on a conservative Allen-Cahn phase field method, a three-dimensional nonorthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for interface tracking in multiphase flow is proposed in this paper. Different from the traditional MRT LB model, the transformation matrix in the present model is constructed based on a set of nonorthogonal basis vectors to simplify the transformation process between the discrete velocity space and the moment space. Therefore, a higher computational efficiency is achieved by the present model. The present model is developed on two different three-dimensional lattice sets (D3Q19 and D3Q27) to obtain a thorough perspective about the performance of the nonorthogonal matrix. Coupled with the nonorthogonal transformation matrix, simplified discrete source terms are also developed for both two lattice sets to further improve the efficiency of the present model. Numerical tests demonstrate that compared with the traditional MRT LB model, the present model shows a significantly higher computational efficiency and better stability while maintaining a comparable accuracy. It is also found that the D3Q19 nonorthogonal model does not obviously weaken the accuracy of D3Q27 nonorthogonal model while D3Q27 nonorthogonal model dose not decrease the stability of the D3Q19 nonorthogonal model, which is different from the orthogonal model.

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