Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible m...Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.展开更多
We investigate the nonlinear instability of a smooth steady density profile solution to the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field,inclu...We investigate the nonlinear instability of a smooth steady density profile solution to the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field,including a Rayleigh-Taylor steady-state solution with heavier density with increasing height(referred to the Rayleigh-Taylor instability).We first analyze the equations obtained from linearization around the steady density profile solution.Then we construct solutions to the linearized problem that grow in time in the Sobolev space H k,thus leading to a global instability result for the linearized problem.With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations,we can then demonstrate the instability of the nonlinear problem in some sense.Our analysis shows that the third component of the velocity already induces the instability,which is different from the previous known results.展开更多
This article reports the homotopy solution for stagnation point flow of a non-Newtonian fluid. An incompressible second grade fluid impinges on the wall either orthogonally or obliquely. The resulting nonlinear proble...This article reports the homotopy solution for stagnation point flow of a non-Newtonian fluid. An incompressible second grade fluid impinges on the wall either orthogonally or obliquely. The resulting nonlinear problems have been solved by a homotopy analysis method （HAM）. Convergence of the series solutions is checked. Such solutions are compared with the numerical solutions presented in a study lint. J. Non-Linear Mech. 43 （2008） 941]. Excellent agreement is noted between the numerical and series solutions.展开更多
文摘Lattice Boltzmann Method is recently developed within numerical schemes for simulating a variety of physical systems. In this paper a new lattice Bhatnagar-Gross-Krook (LBGK) model for two-dimensional incompressible magnetohydrodynamics (IMHD) is presented. The model is an extension of a hydrodynamics lattice BGK model with 9 velocities on a square lattice, resulting in a model with 17 velocities. Most of the existing LBGK models for MHD can be viewed as compressible schemes to simulate incompressible flows. The compressible effect might lead to some undesirable errors in numerical simulations. In our model the compressible effect has been overcome successfully. The model is then applied to the Hartmann flow, giving reasonable results.
基金supported by National Natural Science Foundation of China (Grant Nos. 11101044,11271051,11229101 and 91130020)National Basic Research Program of China (Grant No.2011CB309705)
文摘We investigate the nonlinear instability of a smooth steady density profile solution to the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field,including a Rayleigh-Taylor steady-state solution with heavier density with increasing height(referred to the Rayleigh-Taylor instability).We first analyze the equations obtained from linearization around the steady density profile solution.Then we construct solutions to the linearized problem that grow in time in the Sobolev space H k,thus leading to a global instability result for the linearized problem.With the help of the constructed unstable solutions and an existence theorem of classical solutions to the original nonlinear equations,we can then demonstrate the instability of the nonlinear problem in some sense.Our analysis shows that the third component of the velocity already induces the instability,which is different from the previous known results.
文摘This article reports the homotopy solution for stagnation point flow of a non-Newtonian fluid. An incompressible second grade fluid impinges on the wall either orthogonally or obliquely. The resulting nonlinear problems have been solved by a homotopy analysis method （HAM）. Convergence of the series solutions is checked. Such solutions are compared with the numerical solutions presented in a study lint. J. Non-Linear Mech. 43 （2008） 941]. Excellent agreement is noted between the numerical and series solutions.
