A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D poten...

This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gaskinetic Navier-Stokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent the gas distribution function at the beginning of each time step. As a result, the requir...

The spectral transformation Lanczos method and the shift-invert Arnoldi method are probably the most popular methods for the solution of linear generalized eigenvalue problems originating from engineering applications, including structural and acoustic analyses and fluid dynamics. The orthogonalization of the Krylov vectors requires inner products. Often, one employs the standard inner product,...

It is noted that the Jones-matrix formalism for polarization optics is a sixparameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This fourby-four formalis...

It is noted that the Jones-matrix formalism for polarization optics is a sixparameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This fourby-four formalis...

We prove existence and uniqueness of global in time weak solutions for the Stokes system compressible fluids with a general, non-monotone pressure. construct solution at level Lagrangian formulation then define transformation to original Eulerian coordinates. For nonnegative bounded initial density, is all t>0 as well belongs L∞([0,∞)×Td). A key point our considerations such transformation. Sin...

A computational procedure based on a divergence-free H(div) method is presented for the Stokes and Navier-Stokes equations in this article. This method is designed to find velocity approximation in an exact divergence-free subspace of the corresponding H(div) finite element space. That is, the continuity equation is strongly enforced a priori and the pressure is eliminated from the calculation....

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed ‘Non-linear grid system’ is presented. The linear terms in Navier-Stokes equation are solved by CrankNicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Split...