Two-relaxation-time regularized lattice Boltzmann model for Navier-Stokes equations
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909151818416128 |
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| author | Yu, Yuan Qin, Zuojian Chen, Siwei Shu, Shi Yuan, Hai-Zhuan |
| author_facet | Yu, Yuan Qin, Zuojian Chen, Siwei Shu, Shi Yuan, Hai-Zhuan |
| contents | In this paper, we propose a novel two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows. A free relaxation parameter, $τ_{s,2}$, is employed to relax the regularized non-equilibrium third-order terms. Chapman-Enskog analysis reveals that our model can accurately recover the Navier-Stokes equations (NSEs). Theoretical analysis of the Poiseuille flow problem demonstrates that the slip velocity magnitude in the proposed model is controlled by a magic parameter, which can be entirely eliminated under specific values, consistent with the classical TRT model. Our simulations of the double shear layer problem, Taylor-Green vortex flow, and force-driven Poiseuille flow confirm that the stability and accuracy of our model significantly surpass those of both the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models, even under super-high Reynolds numbers as $Re=10^7$. Concurrently, the TRT-RLB model exhibits superior performance in very high viscosity scenarios. The simulations of creeping flow around a square cylinder demonstrates the model's capability to accurately compute ultra-low Reynolds numbers as $Re=10^{-7}$. This study establishes the TRT-RLB model as a flexible and robust tool in computational fluid dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_10318 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Two-relaxation-time regularized lattice Boltzmann model for Navier-Stokes equations Yu, Yuan Qin, Zuojian Chen, Siwei Shu, Shi Yuan, Hai-Zhuan Fluid Dynamics In this paper, we propose a novel two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows. A free relaxation parameter, $τ_{s,2}$, is employed to relax the regularized non-equilibrium third-order terms. Chapman-Enskog analysis reveals that our model can accurately recover the Navier-Stokes equations (NSEs). Theoretical analysis of the Poiseuille flow problem demonstrates that the slip velocity magnitude in the proposed model is controlled by a magic parameter, which can be entirely eliminated under specific values, consistent with the classical TRT model. Our simulations of the double shear layer problem, Taylor-Green vortex flow, and force-driven Poiseuille flow confirm that the stability and accuracy of our model significantly surpass those of both the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models, even under super-high Reynolds numbers as $Re=10^7$. Concurrently, the TRT-RLB model exhibits superior performance in very high viscosity scenarios. The simulations of creeping flow around a square cylinder demonstrates the model's capability to accurately compute ultra-low Reynolds numbers as $Re=10^{-7}$. This study establishes the TRT-RLB model as a flexible and robust tool in computational fluid dynamics. |
| title | Two-relaxation-time regularized lattice Boltzmann model for Navier-Stokes equations |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2312.10318 |