The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, ...The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.展开更多
We consider the inhomogeneous incompressible Navier-Stokes equation on thin domains T^(2)×∈T,∈→0.It is shown that the weak solutions on T^(2)×∈T converge to the strong/weak solutions of the 2D inhomogene...We consider the inhomogeneous incompressible Navier-Stokes equation on thin domains T^(2)×∈T,∈→0.It is shown that the weak solutions on T^(2)×∈T converge to the strong/weak solutions of the 2D inhomogeneous incompressible Navier-Stokes equations on T^(2)as∈→0 on arbitrary time interval.展开更多
基金Project supported by the National Natural Science Foundation of China (No.40975031)
文摘The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.
基金The research is supported by NSFC underGrant Nos.11571167,11771395,11771206 and PAPD of Jiangsu Higher Education Institutions.
文摘We consider the inhomogeneous incompressible Navier-Stokes equation on thin domains T^(2)×∈T,∈→0.It is shown that the weak solutions on T^(2)×∈T converge to the strong/weak solutions of the 2D inhomogeneous incompressible Navier-Stokes equations on T^(2)as∈→0 on arbitrary time interval.
