Many uid ow problems of practical interest|particularly at high Reynolds num-ber|are characterized by small regions of complex and rapidly-varying uid motion surrounded by larger regions of relatively smooth ow. EEcient solution of such problems requires an adaptive mesh reenement capability to concentrate computational eeort where it is most needed. We present in this paper a fractional-step v...

In the polar regions, atmospheric boundary layer (ABL) characteristics are strongly influenced by convection over leads, which elongated channels in sea ice covered ocean. The effects on ABL depend meteorological forcing and lead geometry. non-convection-resolving models, several leads of potentially different might be present a single grid cell, such surface corresponding patterns not resolved...

This study examines viscoelastic fractional nanofluid flow through Darcy medium. Memory characteristics due to elasticity are explored with noninteger time derivatives. The unsteady motion of MHD is modeled by nonlinear differential equations. Buoyancy forces incorporated via convection parameters in the domain. Fractional relaxation considered control propagation speed temperature. A finite di...

We address the numerical simulation of fluid-structure interaction problems dealing with an incompressible fluid whose density is close to the structure density. We propose a semi-implicit coupling scheme based on an algebraic fractional-step method. The basic idea of a semi-implicit scheme consists in coupling implicitly the added-mass effect, while the other terms (dissipation, convection and...

In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order α ∈ (3/2, 2) in the leading term and both convection and potential terms. They arise in the mathematical modeling of asymmetric super-diffusion processes in heterogeneous media. The well-posedness of t...

A new formulation is presented for the modeling of immiscible compressible two-phase flow in porous media taking into account gravity, capillary effects and heterogeneity. The formulation is intended for the numerical simulation of multi-dimensional flows and is fully equivalent to the original equations, unlike the one introduced in Chavent and Jaffré (1986). The main feature of this formulati...

Integrodifferential equations arise in many fields of science and engineering such as fluid dynamics, biological models, and chemical kinetics. A detailed investigation of integrodifferential equations and their solution via the Laplace transform method can be found in the work of Burton (1983). Recently, fractional integrodifferential equations have been used to model various physical phenomen...