The Navier–Stokes (NS) equations involving MHD effects with time-fractional derivatives are discussed in this paper. This paper investigates the local and global existence uniqueness of mild solution to NS for time fractional differential operator. In addition, we work on regularity such types which caused by flow.

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

In this paper we describe recent advances in the development of particle methods for the direct numerical simulations of three-dimensional wakes. Both body-fitted and immersed boundary techniques are considered. The accuracy and numerical cost of the proposed numerical methods are discussed on the benchmark cases of a flow past a cylinder and of a vortex ring impinging on a cylinder. PACS numbe...

we are concerned with the development of a k−step method for the numerical solution of fuzzy initial value problems. convergence and stability of the method are also proved in detail. moreover, a specific method of order 4 is found. the numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

The choice of an intravenous solution for the attenuation of ischaemia/reperfusion (I/R) lung injury is still a difficult one. Although 10% (w/v) pentastarch has been used in ICU settings, its use in I/R lung injury has not been well explored. We hypothesized that this synthetic colloid substance, which maintains colloid osmotic pressure and potentially 'seals' capillary leaks, in combination w...

Inviscid regularization modeling of turbulent flow is investigated. Homogeneous, isotropic, decaying turbulence is simulated at a range of filter widths. A coarse-graining of turbulent flow arises from the direct regularization of the convective nonlinearity in the Navier–Stokes equations. The regularization is translated into its corresponding sub-filter model to close the equations for large-...