Pegase: A Navier-Stokes Solver for Direct Numerical Simulation of Incompressible Flows

Abstract

A hybrid conservative finite difference/finite element scheme is proposed for the solution of the unsteady incompressible Navier-Stokes equations. Using velocity-pressure variables on a non-staggered grid system, the solution is obtained with a projection method based on the resolution of a pressure Poisson equation.The new proposed scheme is derived from the finite element spatial discretization using the Galerkin method with piecewise bilinear polynomial basis functions defined on quadrilateral elements. It is applied to the pressure gradient term and to the non-linear convection term as in the so-called group finite element method. It ensures strong coupling between spatial directions, inhibiting the development of oscillations during long-term computations, as demonstrated by the validation studies.Two-and three-dimensional unsteady separated flows with open boundaries have been simulated with the proposed method using Cartesian uniform mesh grids. Several examples of calculations on the backward-facing step configuration are reported and the results obtained are compared with those given by other methods. # 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 833-861, 1997.

A computational error-assessment of central finite-volume discretizations in large-eddy simulation using a Smagorinsky model

“…This scheme is applied to the intermediate field r i,j,k that is obtained by interpolation of the flux-vector field f i,j,k in directions perpendicular to the direction with respect to which the derivative is evaluated. This additional averaging over j and k increases the robustness of the scheme and removes the occurrence of p-modes which may arise from the use of 1D schemes in each direction of space [7,34,38]. It is worth noting that such fully multidimensional schemes are similar to those deduced from multidimensional finite-element analysis.…”

Swirling flow structures in electrostatic precipitator

“…The maximum difference between the two expressions of Equation (11) was then ∼4 × 10 −4 m 2 /s 2 or about 1%. This small difference was well within the range of uncertainty and data reduction was based on the expression valid for N i = ∞.…”

“…Using the three-dimensional static body force, F , as input, the Navier Stokes equations were solved by use of the Large Eddy Simulation approach (LES), employing the finite difference code PEGASE developed at ONERA [11], closed by the Mixed Scale subgrid scale model in combination with a selective function [12,17]. The computational domain is 200 × 200 × 200 mm corresponding to two unit cell lengths of the full cross section of the experimental test section (see Figure 4), i.e.…”

“…Also, the Reynolds decomposition, x = X + x , has been applied to both gas, particle and drift velocities, with u e being a result of the particle size distribution. Basically, Equation (11) states that the Reynolds stresses may require a modification by the variance of the particle drift due to the particle size distribution, f (d p ). However, when N i is sufficiently large to be representative of the complete particle size distribution the influence of the particle size variance vanishes.…”

“…However, when N i is sufficiently large to be representative of the complete particle size distribution the influence of the particle size variance vanishes. In practice, u i u j will take values between those of Equation (11), whereas N i = 1 corresponds perfectly to e.g. LDA measurements, where each velocity realization is based on a single particle.…”