Numerical instability may occur when simulating high Reynolds number flows by the lattice Boltzmann method(LBM).The multiple-relaxation-time(MRT)model of the LBM can improve the accuracy and stability,but is still subject to numerical instability when simulating flows with large single-grid Reynolds number(Reynolds number/grid number).The viscosity counteracting approach proposed recently is a method of enhancing the stability of the LBM.However,its effectiveness was only verified in the single-relaxation-time model of the LBM(SRT-LBM).This paper aims to propose the viscosity counteracting approach for the multiple-relaxationtime model(MRT-LBM)and analyze its numerical characteristics.The verification is conducted by simulating some benchmark cases:the two-dimensional(2D)lid-driven cavity flow,Poiseuille flow,Taylor-Green vortex flow and Couette flow,and threedimensional(3D)rectangular jet.Qualitative and Quantitative comparisons show that the viscosity counteracting approach for the MRT-LBMhas better accuracy and stability than that for the SRT-LBM.
The water temperature stratification in large reservoirs might have serious ecological and environmental consequences. The modeling of the temperature distribution and its history is of great importance both for studying the underlying mechanisms and for controlling the adverse effects. To develop an effective and efficient method for simulation of temporal and spatial temperature variations, a lattice Boltzmann method(LBM) model for 3-D thermal buoyancy flows is proposed and validated by the temperature data measured in a model reservoir. This paper discusses important aspects of the LBM and its turbulence model, analyzes the gravity sinking mechanism of cold currents, and demonstrates the complexity of the temperature redistribution process. Good agreement between the simulated and measured results shows that the newly developed method is feasible and powerful, and it will be used for the water temperature prediction in actual reservoirs in a near future.
The anadromous fish can pass through turbines of run-of-the-river hydropower stations to reach the downstream watershed, but their mortality is significant because of the complex turbine structure, the fast-rotating runner, and the special flow patterns. Numerical simulations of the dynamics of fish passing are a challenging task, because the fish motion in the turbines involves a strong fluid-structure interaction (FSI). In this paper, the 3-D immersed boundary-lattice Boltzmann (IB-LB) coupling scheme is proposed to treat the FSI between the water and the fish. The process of one fish and three fish passing through a tubular turbine is simulated on a graphics processing unit (GPU) platform. The fish motion postures (translation and rotation), the fish body pressure distributions and histories are analyzed, and the results are consistent with the previous studies. This paper presents the IB-LB models, the simulation procedures, the specific treatments, and related results, to demonstrate the effectiveness of the IB-LB coupling scheme in simulating FSI problems and its application prospects in developing fish-friendly turbines.
This paper aims to study the numerical features of a coupling scheme between the immersed boundary(IB)method and the lattice Boltzmann BGK(LBGK)model by four typical test problems:the relaxation of a circular membrane,the shearing flow induced by a moving fiber in the middle of a channel,the shearing flow near a non-slip rigid wall,and the circular Couette flow between two inversely rotating cylinders.The accuracy and robustness of the IB-LBGK coupling scheme,the performances of different discrete Dirac delta functions,the effect of iteration on the coupling scheme,the importance of the external forcing term treatment,the sensitivity of the coupling scheme to flow and boundary parameters,the velocity slip near non-slip rigid wall,and the origination of numerical instabilities are investigated in detail via the four test cases.It is found that the iteration in the coupling cycle can effectively improve stability,the introduction of a second-order forcing term in LBGK model is crucial,the discrete fiber segment length and the orientation of the fiber boundary obviously affect accuracy and stability,and the emergence of both temporal and spatial fluctuations of boundary parameters seems to be the indication of numerical instability.These elaborate results shed light on the nature of the coupling scheme and may benefit those who wish to use or improve the method.
