We present a discontinuous Galerkin method on a fully unstructured grid for the modeling of unsteady incompressible fluid flows with free surfaces. The surface is modeled by embedding and represented by a level set. We discuss the discretization of the flow equations and the level set equation as well a various ways of advancing the equations in time using velocity projection techniques. The ef...

The fluid dynamics of expanding and contracting tube is investigated mathematically using both the Navier-Stokes and continuity equations for an incompressible viscous fluid. The problem admits similarity solution, thereby reducing the unsteady Navier-Stokes equations to a parameter dependent fourth order nonlinear ordinary differential equation. Analytical solutions are constructed for the pro...

The problem of the unsteady peristaltic mechanism with heat and mass transfer of an incompressible micropolar non-Newtonian fluid in a two-dimensional channel. The flow includes the viscoelastic wall properties and micropolar fluid parameters using the equations of the fluid as well as of the deformable boundaries. A perturbation solution is obtained, which satisfies the momentum, angular momen...

Analytical solutions are developed for the unsteady Navier-Stokes equations for incompressible fluids in unbounded flow systems with external, time-dependent driving pressure gradients using the degeneracy of the (1 1 1) axis to reduce the inherent non-linearity of the coupled partial differential equations, which is normally performed with boundary conditions. These solutions are then extended...

The direction splitting approach proposed earlier in [7], aiming at the efficient solution of Navier-Stokes equations, is extended and adopted here to solve the Navier-Stokes-Brinkman equations describing incompressible flows in pure fluid and in porous media. The resulting pressure equation is a perturbation of the incompressibility constraint using a direction-wise factorized operator as prop...

We present a discontinuous Galerkin method on a fully unstructured grid for the modeling of unsteady incompressible fluid flows with free surfaces. The surface is modeled by embedding and represented by a levelset. We discuss the discretization of the flow equations and the level set equation as well a various ways of advancing the equations in time using velocity projection techniques. The eff...

We study the solutions of the nonstationary incompressible Navier–Stokes equations in R , d ≥ 2, of self-similar form u(x, t) = 1 √

We study the solutions of the nonstationary incompressible Navier–Stokes equations in R , d ≥ 2, of self-similar form u(x, t) = 1 √

In this article, we studied the effects of variable viscosity and thermal conductivity on an unsteady twodimensional laminar flow of a viscous incompressible electrically conducting fluid past a semi-infinite vertical plate taking into account the mass transfer. The fluid viscosity is assumed to vary as a linear function of temperature. The governing equations for the flow are transformed into ...

The unsteady two-dimensional, laminar flow of a viscous, incompressible, electrically conducting fluid towards a shrinking surface in the presence of a uniform transverse magnetic field is studied. Taking suitable similarity variables, the governing boundary layer equations are transformed to ordinary differential equations and solved numerically by a perturbation technique for a small magnetic...