In the current work, the mesh free Smoothed Particle Hydrodynamics (SPH) method, was employed to numerically investigate the transient flow of a viscoplastic material. Using this method, large deformation of the sample and its free surface boundary were captured without the cumbersome process of the grid generation. This three-step SPH scheme employs an explicit predictor-corrector technique an...

This report performs a complete analysis of convergence and rates of convergence of finite element approximations of the Navier-Stokes-α (NS-α) regularization of the NSE, under a zero-divergence constraint on the velocity, to the true solution of the NSE. Convergence of the discrete NS-α approximate velocity to the true Navier-Stokes velocity is proved and rates of convergence derived, under no...

A recently developed high-order velocity-slip boundary condition is validated for gas micro ows, by comparing predictions of the new model against the Ž rst-order slip condition and the direct-simulation Monte Carlo (DSMC) results. Numerical solutions of gas  ow through microchannels and backward-facing step geometry are presented. The backwardfacing step geometry is a suitable testbed for st...

The local asymptotic behaviour at the stick-slip singularity is determined for the Giesekus fluid in the presence of a solvent viscosity. In planar steady flow, the method of matched asymptotic expansions is used to show that it comprises a three region structure. Specifically, an outer or core region that links boundary layers at the rigid stick and free slip surfaces. In the outer region, the...

A combined analytical, numerical, and experimental study of the traveling-wave wall mode in rotating Rayleigh-Bénard convection is presented. No-slip top and bottom boundary conditions are used for the numerical computation of the linear stability, and the coefficients of the linear complex Ginzburg-Landau equation are then computed for various rotation rates. Numerical results for the no-slip ...

An earthquake source mechanism is described from the standpoint that the dynamic characteristics of friction play a more important role in the dislocation motion than the boundary condition does. By considering an earthquake dislocation as a slip motion in a mechanical system involving friction, which depends upon velocity during slip, a displacement time function G(t)=1-exp(-t/τ)(1+t/τ) which ...

This technical brief presents a numerical study regarding the required development length ðL 1⁄4 Lfd=HÞ to reach fully developed flow conditions at the entrance of a planar channel for Newtonian fluids under the influence of slip boundary conditions. The linear Navier slip law is used with the dimensionless slip coefficient kl 1⁄4 kl l=H ð Þ, varying in the range 0 < kl 1. The simulations were ...

This paper evaluates the suitability of a newly developed hybrid “Langmuir-Maxwell” and “LangmuirSmoluchowski” slip/jump boundary conditions in the Navier-Stokes-Fourier equations for nano/micro backward-facing step geometry flow which experiences separation and reattachment. Additionally, this paper investigates the effect of different parameters such as step pressure ratio, inflow temperature...

Incompressible two dimensional lattice Boltzmann method (LBM) is adopted to simulate flow inside a pipe commonly called Poiseuille flow. Instead of D2Q9 lattice Boltzmann model, we used an incompressible two-dimensional model, D2Q9i to simulate the flow conditions. At the inlet, velocity boundary condition, while at outlet, pressure boundary condition and at the surfaces, no slip boundary condi...