arXiv subjects

Xiaolei Yuan

Publications and source records attributed to Xiaolei Yuan.

5 recordsLinked to original sources

arXiv2025

A unified MRT-LB framework for Navier-Stokes and nonlinear convection-diffusion equations and beyond: moment equations, auxiliary moments, multispeed lattices, and Hermite matrices

We develop a unified multi-relaxation-time lattice Boltzmann (MRT-LB) framework based on discrete Hermite polynomials (Hermite matrices) for the Navier-Stokes equations (NSEs) and nonlinear convection-diffusion equations (NCDEs), using multispeed rectangular lattice (rD$d$Q$b$) models. For NSEs, the proposed MRT-LB model simulates incompressible and compressible isothermal flows in both single-phase and multiphase systems. Macroscopic moment equations are derived from the MRT-LB model via the direct Taylor expansion method. By selecting appropriate fundamental moments, the target NSEs and NCDE are recovered from these moment equations. Critically, the elimination of spurious terms and/or the recovery of the desired terms relies on specific auxiliary moments: the second-order auxiliary moment ($\mathbf{M}_{2G}$) of the source term distribution function (SDF) and the third-order auxiliary moment ($\mathbf{M}_{30}$) of the equilibrium distribution function (EDF) for NSEs, as well as the first-order auxiliary moment ($\mathbf{M}_{1G}$) of the SDF and the second-order auxiliary moment ($\mathbf{M}_{20}$) of the EDF for NCDE. Furthermore, using the weighted orthogonality of Hermite matrices, we establish essential relations for weight coefficients and construct several multispeed rectangular lattice models, including rD2Q25 and rD3Q53, with subgroup models rD2Q21, rD2Q17, rD2Q13, rD3Q45, and rD3Q33. A generalized third-order equilibrium distribution function is derived. We emphasize that for rectangular lattices, specific elements of the Hermite matrix corresponding to third-order discrete Hermite polynomials require correction to satisfy weighted orthogonality.

physics.flu-dyn↗

arXiv2024

Improving Building Temperature Forecasting: A Data-driven Approach with System Scenario Clustering

Heat, Ventilation and Air Conditioning (HVAC) systems play a critical role in maintaining a comfortable thermal environment and cost approximately 40% of primary energy usage in the building sector. For smart energy management in buildings, usage patterns and their resulting profiles allow the improvement of control systems with prediction capabilities. However, for large-scale HVAC system management, it is difficult to construct a detailed model for each subsystem. In this paper, a new data-driven room temperature prediction model is proposed based on the k-means clustering method. The proposed data-driven temperature prediction approach extracts the system operation feature through historical data analysis and further simplifies the system-level model to improve generalization and computational efficiency. We evaluate the proposed approach in the real world. The results demonstrated that our approach can significantly reduce modeling time without reducing prediction accuracy.

cs.LG↗

arXiv2022

Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues

In this paper, we develop a general rectangular multiple-relaxation-time lattice Boltzmann (RMRT-LB) method for the Navier-Stokes equations (NSEs) and nonlinear convection-diffusion equation (NCDE) by extending our recent unified framework of MRT-LB method [Z.H. Chai and B.C. Shi, Phys. Rev. E 102, 023306 (2020)], where a rectangular equilibrium distribution function (REDF) [J.H. Lu et al, Phil. Trans. R. Soc. A 369, 2311-2319 (2011)] on a rectangular lattice is utilized. Due to the anisotropy of discrete velocities on a rectangular lattice, the third-order moment of REDF is inconsistent with that of popular LB method, and thus the previous unified framework of MRT-LB method cannot be directly applied to the NSEs using the REDF on the rectangular rDdQq lattice. The macroscopic NSEs can be recovered from the RMRT-LB method through the direct Taylor expansion method by properly selecting the relaxation sub-matrix $\mathbf{S}_2$ which is related to kinetic viscosity and bulk viscosity. While the rectangular lattice does not lead to the change of the zero-th, first and second-order moments of REDF, thus the unified framework of MRT-LB method can be directly applied to the NCDE. It should be noted that the RMRT-LB model for NSEs can be derived on the rDdQq lattice, including rD2Q9, rD3Q19, and rD3Q27 lattices, and the RMRT-LB versions (if existed) of the previous MRT-LB models can be obtained, including those based on raw (natural)-moment, central-moment, Hermite-moment, and central Hermite-moment, respectively.

physics.comp-ph↗

arXiv2019

Phase-field-based lattice Boltzmann model for immiscible incompressible N-phase flows

In this paper, we develop an efficient lattice Boltzmann (LB) model for simulating immiscible incompressible $N$-phase flows $(N \geq 2)$ based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the $N$-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, $(N-1)$ LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible $N$-phase fluid flows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four fluid phases and dynamics of droplets and interfaces for five fluid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among $N$ ($N \geq 2$) immiscible incompressible flows.

physics.comp-ph↗

arXiv2019

A generalized lattice Boltzmann model for fluid flow system and its application in two-phase flows

In this paper, a generalized lattice Boltzmann (LB) model with a mass source is proposed to solve both incompressible and nearly incompressible Navier-Stokes (N-S) equations. This model can be used to deal with single-phase and two-phase flows problems with a mass source term. From this generalized model, we can not only get some existing models, but also derive new models. Moreover, for the incompressible model derived, a modified pressure scheme is introduced to calculate the pressure, and then to ensure the accuracy of the model. In this work, we will focus on a two-phase flow system, and in the frame work of our generalized LB model, a new phase-field-based LB model is developed for incompressible and quasi-incompressible two-phase flows. A series of numerical simulations of some classic physical problems, including a spinodal decomposition, a static droplet, a layered Poiseuille flow, and a bubble rising flow under buoyancy, are performed to validate the developed model. Besides, some comparisons with previous quasi-incompressible and incompressible LB models are also carried out, and the results show that the present model is accurate in the study of two-phase flows. Finally, we also conduct a comparison between quasi-incompressible and incompressible LB models for two-phase flow problems, and find that in some cases, the proposed quasi-incompressible LB model performs better than incompressible LB models.

physics.comp-ph↗