Abstract. We propose a mathematical derivation of Brinkman’s force for a cloud of particles immersed in an incompressible viscous fluid. Specifically, we consider the Stokes or steady Navier-Stokes equations in a bounded domain Ω ⊂ R for the velocity field u of an incompressible fluid with kinematic viscosity ν and density 1. Brinkman’s force consists of a source term 6πνj where j is the curren...

The growth rate of the compressible Rayleigh-Taylor instability is studied in the presence of a background temperature gradient, Θ, using a normal mode analysis. The effect of Θ variation is examined for three interface types corresponding to combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous and viscous-inviscid) at different Atwood numbers, At, and, when ...

The Eulerian description of an incompressible viscous fluid of constant density and temperature is concerned with the fluid velocity u(x, t) and pressure p(x, t) recorded at fixed positions x ∈ R, n = 3 as functions of time t. The solutions of the incompressible, inviscid Euler equations can be thought of as geodesic paths on an infinite dimensional group of transformations ([1]). This is done ...

We study the flow of an incompressible viscous fluid through a long tube with compliant walls. The flow is governed by a given time-dependent pressure drop between the inlet and the outlet boundary. The pressure drop is assumed to be small, thereby introducing creeping flow in the tube. Stokes equations for incompressible viscous fluid are used to model the flow, and the equations of a curved, ...

In this report, we propose a semi-implicit coupling scheme for the numerical simulation of fluid-structure interaction systems involving a viscous incompressible fluid. The scheme is stable irrespectively of the so-called addedmass effect and allows for conservative time-stepping within the structure. The efficiency of the scheme is based on the explicit splitting of the viscous effects and geo...

We present a class of numerical algorithms for simulating viscous fluid problems of incompressible flow interacting with moving rigid structures. The proposed Cartesian grid embedded boundary algorithms employ a slightly different idea from the traditional direct-forcing Immersed Boundary Methods; i.e. the proposed algorithms calculate and apply the force-density in the extended solid domain to...

The paper studies a splitting method for the numerical time-integration of the system of partial differential equations describing the motion of viscous incompressible fluid with free boundary subject to surface tension forces. The method splits one time step into a semi-Lagrangian treatment of the surface advection and fluid inertia, an implicit update of viscous terms and the projection of ve...

In the present paper an analysis of mixed convection of an unsteady magneto hydrodynamic (MHD) flow of an incompressible viscous fluid through porous media due to a vertical porous stretching sheet in the presence of viscous dissipation, thermal radiation and heat source /sink has been carried out. The fluid considered is viscous and incompressible. The governing partial differential equations ...