For Newtonian fluid flow in a right circular tube, with a linear Navier slip boundary, we show that a second flow field arises which is different to conventional Poiseuille flow in the sense that the corresponding pressure is quadratic in its dependence on the length along the tube, rather than a linear dependence which applies for conventional Poiseuille flow. However, assuming that the quadra...

For the purpose of engineering, it is important to study convergent rates in process low Mach number limit. However, there are only a few results on this issue, which focus cases isentropic regime or ones without solid boundaries. In paper, we obtain convergence for local strong solutions non-isentropic compressible Navier-Stokes equations with well-prepared initial data and Navier-slip boundar...

We present an immersed interface method for the incompressible Navier-Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid. The forces are related to the jumps in pressure and the jumps in t...

We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pr...

We develop divergence-conforming B-spline discretizations for the numerical solution of the steady Navier-Stokes equations. These discretizations are motivated by the recent theory of isogeometric discrete differential forms and may be interpreted as smooth generalizations of Raviart-Thomas elements. They are (at least) patchwise C and can be directly utilized in the Galerkin solution of steady...

An efficient and accurate algorithm for solving the two-dimensional (2D) incompressible Navier–Stokes equations on a disk with no-slip boundary conditions is described. The vorticitystream function formulation of these equations is used, and spatially the vorticity and stream functions are expressed as Fourier–Chebyshev expansions. The Poisson and Helmholtz equations which arise from the implic...

Pressure driven microscale gas flow-separation has been investigated by solving the compressible Navier-Stokes (NS) system of equations. A two dimensional explicit finite volume (FV) compressible flow solver has been developed using modified advection upwind splitting methods (AUSM+) with no-slip/first order Maxwell’s velocity slip conditions to predict the flowseparation behavior in microdimen...

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...