the methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. in the geoid computations witho...

A simple isoparametric geometry mapping is applied to incorporate irregular four-node quadrilateral elements into Modified Nodal Integral Method for the two-dimensional, time-dependent, incompressible Navier-Stokes equations. The modified scheme has been applied to solve the twodimensional lid driven cavity problem with exact solution, solved over a sub-domain that necessitate non-rectangular e...

We consider the steady-state Navier-Stokes equation in the whole space R driven by a forcing function f . The class of source functions f under consideration yield the existence of at least one solution with finite Dirichlet integral (‖∇U‖2 < ∞). Under the additional assumptions that f is absent of low modes and the ratio of f to viscosity is sufficiently small in a natural norm we construct so...

We present a new method for the solution of the Stokes equations. Our goal is to develop a robust and scalable methodology for two and three dimensional, moving-boundary, flow simulations. Our method is based on Anita Mayo’s method for the Poisson’s equation: “The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions”, SIAM J. Num. Anal., 21 (1984), pp. 285– 299. We embed...

A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability are given. Moreover, it is shown that we can obtain ...

It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity, if the gauge field under consideration is a non-trivial one. This point is illustrated by the specific examples of the computation of a non-local operator. The non-Abelian Stokes theorem is widely applied to compute Wilson loop (closed nonAb...

We present an integral equation formulation for the unsteady Stokes equations in two dimensions. This problem is of interest in its own right, as a model for slow viscous flow, but perhaps more importantly, as an ingredient in the solution of the full, incompressible Navier-Stokes equations. Using the unsteady Green’s function, the velocity evolves analytically as a divergence-free vector field...

We describe the method for finding the non-Gaussian tails of the probability distribution function ~PDF! for solutions of a stochastic differential equation, such as the convection equation for a passive scalar, the random driven Navier-Stokes equation, etc. The existence of such tails is generally regarded as a manifestation of the intermittency phenomenon. Our formalism is based on the WKB ap...

We consider a boundary value problem for the time-dependent Oseen system in a 3D exterior domain. This problem is reduced to an integral equation for the single-layer potential related to the that system. This integral equation, in turn, is solved by applying a result by Shen [11] pertaining to the evolutionary Stokes system. Since it automatically leads to an integral representation of the sol...