This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...

Abstract. Superconvergence of the velocity is established for mimetic finite difference approximations of second-order elliptic problems over h2-uniform quadrilateral meshes. The superconvergence result holds for a full tensor coefficient. The analysis exploits the relation between mimetic finite differences and mixed finite element methods via a special quadrature rule for computing the scalar...

We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Γ-convergence, and a compactness result which implies, in particular, the convergence of minima and minimizers. AMS (MOS) subject classifications: 49J45, 65K10.

A technique derived from two related methods suggested earlier by some of the authors for optimization of finite-difference grids and absorbing boundary conditions is applied to discretization of perfectly matched layer (PML) absorbing boundary conditions for wave equations in Cartesian coordinates. We formulate simple sufficient conditions for optimality and implement them. It is found that th...

jet impingement heat transfer is an effective and practical approach that is employed in many industrial processes where heating, cooling, or drying is required. details of the heat or mass transfer rate have been investigated both experimentally and numerically and can be found in the published literature. in most of the numerical studies, control-volume approach has been employed to solve the...

In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

unsteady flow through non - homogeneous and anisotropic porous media can be modeled by a partial differential equation.&apos; this-equation cannot be solved analytically. hence, numerical methods. such as the finite element and the finite difference methods might be employed. in this study a mathematical model has been developed using the fully implicit finite difference method with control vol...

We consider the third–order, wide–angle, parabolic approximation of underwater acoustics in a medium with depth– and range–dependent speed of sound in the presence of dissipation and horizontal interfaces. We first discuss the theory of existence and uniqueness of solutions to the problem and derive an energy estimate. We then discretize the problem in the depth variable using two types of Gale...