We present a second-order finite-difference scheme for viscoelastic flows based on a recent reformulation of the constitutive laws as equations for the matrix logarithm of the conformation tensor. We present a simple analysis that clarifies how the passage to logarithmic variables remedies the high-Weissenberg numerical instability. As a stringent test, we simulate an Oldroyd-B fluid in a lid-d...

This paper presents our numerical results for the application of the Isogeometric Analysis (IGA) to the velocity-pressure formulation of the steady state as well as the unsteady incompressible Navier-Stokes equations. For the approximation of the velocity and pressure fields, LBB compatible spline spaces are used which can be regarded as generalizations of Taylor-Hood pairs of finite element sp...

In this work, the PGD method will be considered for solving some problems of fluid mechanics by looking for the solution as a sum of tensor product functions. In the first stage, the equations of Stokes and Burgers will be solved. Then, we will solve the Navier–Stokes problem in the case of the lid-driven cavity for different Reynolds numbers (Re = 100, 1000 and 10,000). Finally, the PGD method...

A lattice Boltzmann method for a three dimensional lid driven cavity of cubic and parallelipedic geometries is developed on a desktop computer; No-slip boundary conditions are implemented by the so called Bounce back boundry conditions and the Dirichlet boundary condition for the upper moving wall is treated by the Zou/He boundary condition. The lattice Boltzmann simulation is carried out using...

We present a new wavelet numerical scheme for the discretization of Navier-Stokes equations with physical boundary conditions. The temporal discretization of the method is inspired from the projection method. Helmholtz-Hodge decomposition using divergence-free and curl-free wavelet bases satisfying physical boundary conditions allows to define the projection operator. This avoids the use of Poi...

Dissipative particle dynamics (DPD) is a potentially very effective approach in simulating mesoscale hydrodynamics. However, because of the soft potentials employed, the simple no-slip boundary conditions are difficult to impose. In this work, we first identify some of these difficulties and subsequently we propose a new method, based on an equivalent force between walland DPD-particles, to imp...

A simple isoparametric geometry mapping is applied to incorporate irregular four-node quadrilateral elements into Modified Nodal Integral Method for the two-dimensional, time-dependent, incompressible Navier-Stokes equations. The modified scheme has been applied to solve the twodimensional lid driven cavity problem with exact solution, solved over a sub-domain that necessitate non-rectangular e...

We investigate the performance of smoothers based on the Hermitian/skew-Hermitian (HSS) and augmented Lagrangian (AL) splittings applied to the Marker-and-Cell (MAC) discretization of the Oseen problem. Both steady and unsteady flows are considered. Local Fourier analysis and numerical experiments on a two-dimensional lid-driven cavity problem indicate that the proposed smoothers result in h-in...

A finite element study of two and three-dimensional incompressible viscoelastic flows in a planar lid-driven cavity and concentric rotating cylinders is presented. The hardware platforms consist of both homogeneous and heterogeneous clusters of workstations. A semi-implicit time-stepping TaylorGalerkin scheme is employed using the message passing mechanism provided by the Parallel Virtual Machi...

We present a new wavelet numerical scheme for the discretization of Navier-Stokes equations with physical boundary conditions. The temporal discretization of the method is inspired from the projection method. Helmholtz-Hodge decomposition using divergence-free and curl-free wavelet bases satisfying physical boundary conditions allows to define the projection operator. This avoids the use of Poi...