We show that stationary statistical properties for uniformly dissipative dynamical systems are upper semi-continuous under regular perturbation and a special type of singular perturbation in time of relaxation type. The results presented are applicable to many physical systems such as the singular limit of infinite Prandtl-Darcy number in the Darcy-Boussinesq system for convection in porous med...

Steady-state demand-driven water distribution system (WDS) solution is the bedrock for much research conducted in field related to WDSs. WDSs are modeled using Darcy–Weisbach equation with Swamee–Jain equation. However, approximates Colebrook–White equation, errors of which within 1% ϵ/D∈[10−6,10−2] and Re∈[5000,108]. A formulation presented The correctness efficacy head have been demonstrated ...

As a result of the limitations in the application of Darcy Law (V=ki) to linear-laminar flow regimes through porous media and due to the fact that in coarse alluviums, the Reynolds number may exceed its critical value, the so-called Laplas equation cannot be used for precise analyses of coarse granular foundations. A more general relationship is, therefore, required for such cases. However, a c...

Abstract This work is devoted to the analysis of linear temporal stability a laminar dynamic boundary layer on horizontal porous plane plate. The basic flow assumed be and two-dimensional. velocity profiles are obtained by numerically solving Blasius equation using Runge-Kutta method. perturbations these solutions expressed in form three-dimensional Tollmien-Schlichting waves. formulation probl...

Abstract. Consider an incompressible fluid in a region Ωf flowing both ways across an interface, I, into a porous media domain Ωp saturated with the same fluid. The physical processes in each domain have been well studied and are described by the Stokes equations in the fluid region and the Darcy equations in the porous media region. Taking the interfacial conditions into account produces a sys...

We investigate mortar multiscale numerical methods for coupled Stokes and Darcy flows with the Beavers–Joseph–Saffman interface condition. The domain is decomposed into a series of subdomains (coarse grid) of either Stokes or Darcy type. The subdomains are discretized by appropriate Stokes or Darcy finite elements. The solution is resolved locally (in each coarse element) on a fine scale, allow...

There are two types of mean flow velocity formulas for pipes, the Darcy-Weisbach equation and Hazen-Williams equation. In process deriving from equation, it was clarified that friction loss coefficient f is expressed by exponential function ＝ aRe-b. Next, C obtained eliminating effect Reynolds number Re. It confirmed only constant a remained in there almost no influence water temperature viscos...

A third-order in time numerical IMEX-type algorithm for the StokesDarcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams-Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy compon...

The goal of this short course is to review the analysis and the systematic discretization of saddlepoint systems that arise in the weak formulation of certain fluid flow problems by Galekrin methods. To demonstrate the applicability of the main arguments in various situations, we consider the slow flow of water through a channel surrounded by a porous aquiver. While the free flow of the fluid m...