We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann model.Technically,two effective approaches are presented to...We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann model.Technically,two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes.One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures;the other is to evaluate the growth rate of KHI from the slopes of morphological functionals.Physically,it is found that the time histories of width of mixing layer,TNE intensity,and boundary length show high correlation and attain their maxima simultaneously.The viscosity effects are twofold,stabilize the KHI,and enhance both the local and global TNE intensities.Contrary to the monotonically inhibiting effects of viscosity,the heat conduction effects firstly refrain then enhance the evolution afterwards.The physical reasons are analyzed and presented.展开更多
Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the fin...Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.展开更多
基金Y. G.,C.L., H. L. and Z. L. acknowledge the support from the National Natural Science Foundation of China (Grant Nos.11875001,51806116, and 11602162)Natural Science Foundation of Hebei Province (Grants Nos. A2017409014 and 2018J01654)+4 种基金Natural Science Foundations of Hebei Educational Commission (Grant No.ZD2017001)A. X. and G.Z.acknowledge the support from the National Natural Science Foundation of China (Grant No. 11772064)CAEP Foundation (Grant No. CX2019033)Science Challenge Project (Grant No.JCKY2016212A501)the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology, Grant No. KFJJ19-01M).
文摘We investigate the effects of viscosity and heat conduction on the onset and growth of Kelvin-Helmholtz instability (KHI) via an efficient discrete Boltzmann model.Technically,two effective approaches are presented to quantitatively analyze and understand the configurations and kinetic processes.One is to determine the thickness of mixing layers through tracking the distributions and evolutions of the thermodynamic nonequilibrium (TNE) measures;the other is to evaluate the growth rate of KHI from the slopes of morphological functionals.Physically,it is found that the time histories of width of mixing layer,TNE intensity,and boundary length show high correlation and attain their maxima simultaneously.The viscosity effects are twofold,stabilize the KHI,and enhance both the local and global TNE intensities.Contrary to the monotonically inhibiting effects of viscosity,the heat conduction effects firstly refrain then enhance the evolution afterwards.The physical reasons are analyzed and presented.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11301521, 11771467, 11071041）, the Natural Science Foundation of Fujian Province （Nos. 2016J01005, 2015J01578）, and the National Post- doctoral Program for Innovative Talents （No. BX201700234）.
文摘Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.
