Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: While the lattice Boltzmann method (LBM) has become a porful numerical approach for solving complex flows, the standard lattice Boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions. For inhomogeneous and anisotropic flows, it is desirable to have a LBM model that utilizes a rectangular grid. There re two previous attempts to extend the multiple-relaxation-time (MRT) LBM to a rectangular lattice grid in 2D, hover, the resulting hydrodynamic momentum equation was not fully consistent with the Navier-Stokes equation, due to anisotropy of the transport coefficients. In the present work, a new MRT model with an additional degree of freedom is developed in order to match precisely the Navier-Stokes equation when a rectangular lattice grid is used.  first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the Chapman-Enskog procedure. Then an additional adjustable parameter that governs the relative orientation in the energy-normal stress subspace is introduced. It is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients, thus the exact Navier-Stokes equation can be derived on a rectangular grid. Our theoretical findings are confirmed by numerical solutions using three two-dimension benchmark problems, i.e. the channel flow, the cavity flow, and the decaying Taylor-Green vortex flow. The numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters.
['Yuan Zong', 'Cheng Peng', 'Zhaoli Guo', 'Lian-Ping Wang']
I am writing a research paper on a idea Designing correct fluid hydrodynamics on a rectangular grid using MRT lattice Boltzmann approach
[{"from": "human", "value": "I am writing a research paper on a idea Designing correct fluid hydrodynamics on a rectangular grid using MRT lattice Boltzmann approach"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: While the lattice Boltzmann method (LBM) has become a porful numerical approach for solving complex flows, the standard lattice Boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions. For inhomogeneous and anisotropic flows, it is desirable to have a LBM model that utilizes a rectangular grid. There re two previous attempts to extend the multiple-relaxation-time (MRT) LBM to a rectangular lattice grid in 2D, hover, the resulting hydrodynamic momentum equation was not fully consistent with the Navier-Stokes equation, due to anisotropy of the transport coefficients. In the present work, a new MRT model with an additional degree of freedom is developed in order to match precisely the Navier-Stokes equation when a rectangular lattice grid is used.  first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the Chapman-Enskog procedure. Then an additional adjustable parameter that governs the relative orientation in the energy-normal stress subspace is introduced. It is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients, thus the exact Navier-Stokes equation can be derived on a rectangular grid. Our theoretical findings are confirmed by numerical solutions using three two-dimension benchmark problems, i.e. the channel flow, the cavity flow, and the decaying Taylor-Green vortex flow. The numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters."}]