This paper presents the development of a 2D high-order solver with spectral difference method for unsteady incompressible Navier–Stokes equations accelerated by a p-multigrid method. This solver is designed for unstructured quadrilateral elements. Time-marching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. An artificial compressib...

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second-order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also invest...

HMM-like multiscale integrators and projective integration methods are two different types of multiscale integrators which have been introduced to simulate efficiently systems with widely disparate time scales. The original philosophies of these methods, reviewed here, were quite different. Recently, however, projective integration methods seem to have evolved in a way that make them increasing...

In this paper we study the Leray weak solutions of the incompressible Navier Stokes equation in an exterior domain.We describe, in particular, an hyperbolic version of the so called artificial compressibility method investigated by J.L.Lions and Temam. The convergence of these type of approximation show in general a lack of strong convergence due to the presence of acoustic waves. In this paper...

This paper presents the development of a 2D high-order solver with unstructured spectral difference method for unsteady incompressible Navier-Stokes equations. Timemarching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. An artificial compressibility method (ACM) is employed in order to treat the inviscid fluxes using the traditiona...

The sparsity and compressibility of finite-dimensional signals are of great interest in fields such as compressed sensing. The notion of compressibility is also extended to infinite sequences of i.i.d. or ergodic random variables based on the observed error in their nonlinear k-term approximation. In this work, we use the entropy measure to study the compressibility of continuous-domain innovat...

We introduce a structural quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass-forming liquid consisting of a two-component mixture of soft spheres in three dimensions. As the temperature is lowered (or as the density is increased), the ge...

Fluid flow and heat transfer of viscoelastic materials in noncircular duct are complicated subject because of nonlinear behavior of rheological properties. In this paper flow and heat transfer of CEF fluids are studied with numerical modeling. Numerical solution is based on the artificial compressibility method and by using staggered mesh. The effect of secondary flows on the forced and natural...

T he history of IOLs began in 1949 with Sir Harold Ridley’s insertion of an artificial lens into the posterior chamber. Although placing an IOL within the space from which the cataract had been removed seemed (and seems still) a natural, almost obvious choice, ophthalmologists abandoned posterior chamber lens implantation within a few years. I reawakened surgeons’ interest in posterior chamber ...

We show that meshfree variational methods may be utilized for solution of incompressible fluid dynamics problems using the R-function method (RFM). The proposed approach constructs an approximate solution that satisfies all prescribed boundary conditions exactly using approximate distance fields for portions of the boundary, transfinite interpolation, and computations on a non-conforming spatia...