We consider a special class of similarity solutions of the stationary Navier-Stokes equations and prove the existence of the solution for all the Reynolds numbers. We further prove that the solution exhibits interior and boundary layers as the Reynolds number tends to +1 and ?1, respectively.

In this paper a singularly perturbed convection–diffusion equation with a discontinuous source term is examined. Boundary and weak interior layers appear in the solution. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter.

Thin layers of magnetic substance are often used in magnetic shieldings. Since the scale of the spatial change in electromagnetic fields in the direction of the thickness of such a thin layer is considerably different from that in the transverse directions, the numerical treatment of the interior electromagnetic fields is formidable. In this paper, it is shown that the impedance boundary condit...

Earth dams have been used widely recently in flood and sedimentation control projects and feeding ground waters in country's watersheds and correct locating for such structures is necessary for increasing their efficiency. In this work, it is attempted to determine the correct locations for constricting earth dams in Yoosef-abad watershed in Tabas using v and incorporating information layers. T...

Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

We study a singularly perturbed boundary value problrm in R”““: i =.f(s. J, E). cj= glx, .r, s), B,(s(w,), .tj(uo), E)=O, B,(.~(m,+to), ~(w,+oJ), E) =O. Given a candidate for the 0th order approximation which exhibits both boundary layers and interior layers, we present a complete procedure to compute higher order expansions and a procedure to compute the real solution near a truncated asymptot...

In this article, we simplify and improve the asymptotic analysis of the solutions of the NavierStokes problem given in [8]. This problem is characterized by the presence of a small term which corresponds to the inverse of Reynolds number Re very large for the Navier-Stokes equations (Re >> 1). This small parameter is called the viscosity and denoted hereafter ε (ε = 1/Re). Thus, when the viscos...

high weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. the flow is considered to be steady and two dimensional. flows of viscoelastic liquids at high weissenberg number exhibit stress boundary layers near walls. these boundary layers are caused by the memory of the fluid. upon proper scaling and by means of an exact similarity transformation, the n...

We explore the reflection off a sonic curve and the domain of determinacy, via the method of characteristics, of self-similar solutions to the two dimensional isentropic Euler system through several examples with axially symmetric initial data. We find that characteristics in some cases can be completely absorbed by the sonic curve so that the characteristics vanish tangentially into the sonic ...