A numerical scheme for treating fluid–land boundaries in inviscid shallow water flows is derived that conserves the domain-summed mass, energy, vorticity, and potential enstrophy in domains with arbitrarily shaped boundaries. The boundary scheme is derived from a previous scheme that conserves all four domain-summed quantities only in periodic domains without boundaries. It consists of a method...

The various industrial and engineering applications of flow of fluid between parallel plates have continued to generate renewed interests. In this work, a comparative study of approximate analytical methods is carried out using differential transformation,homotopy perturbation, Adomian decomposition, variation of parameter and variational iteration methods for the analysis of a steady two-dimen...

We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the us...

The inviscid limit for the two-dimensional compressible viscoelastic equations in half plane is considered under no-slip boundary condition. When initial deformation tensor a perturbation of identity matrix and density near positive constant, we establish uniform estimates solutions to flows conormal Sobolev spaces. It well-known that corresponding Navier-Stokes with condition, one does not exp...

An efficient and accurate algorithm for solving the two-dimensional (2D) incompressible Navier–Stokes equations on a disk with no-slip boundary conditions is described. The vorticitystream function formulation of these equations is used, and spatially the vorticity and stream functions are expressed as Fourier–Chebyshev expansions. The Poisson and Helmholtz equations which arise from the implic...

We consider incompressible Navier-Stokes equations in a bounded 3D regular domain, coupled with the so-called dynamic boundary condition. rigorously establish principle of linearized stability. Namely, given smooth stationary state, we prove that equation has complete basis generalized eigenfunctions, and non-linear stability depends on supremum real part spectrum usual way. work class weak sol...