DSC solution for flow in a staggered double lid driven cavity

Abstract

SUMMARYA benchmark quality solution is presented for ow in a staggered double lid driven cavity obtained by using the wavelet-based discrete singular convolution (DSC). The proposed wavelet based algorithm combines local methods' exibility and global methods' accuracy, and hence, is a promising approach for achieving the high accuracy solution of the Navier-Stokes equations. Block structured grids with pseudo-overlapping subdomains are employed in the present simulation. A third order RungeKutta scheme is used for the temporal discretization. Quantitative results are presented, apart from the qualitative uid ow patterns. The prevalence of rich features of ow morphology, such as two primary vortex patterns, merged single primary vortex patterns, and secondary eddies, makes this problem very attractive and interesting. The problem is quite challenging for the possible existence of numerically induced asymmetric ow patterns and elliptic instability. Important computational issues like consistence, convergence and reliability of the numerical scheme are examined. The DSC algorithm is tested on the single lid driven cavity ow and the Taylor problem with a closed form solution. The double lid driven cavity simulations are cross-validated with the standard second order ÿnite volume method.

Fundamentals of the Finite Element Method for Heat and Fluid Flow

“…Theoretically, the steady state solution, if one exists, should be symmetric with respect to either of the diagonals. However, at higher Reynolds numbers, a steady state solution may not exist as reported by Zhou et al (Zhou et al 2003).…”

“…Geometry and mesh was chosen. This problem was suggested as a benchmark by Zhou et al (Zhou et al 2003), and it is a diagonally symmetrical enclosure with a longer side of size L and a smaller side of size 0.4L. The top lid is assumed to move at a prescribed positive horizontal velocity and the bottom lid moves with a negative velocity, with a magnitude equal to the velocity of the top lid.…”

“…This was expected because of the singularity introduced by the sudden change in the velocity at the top and the bottom corners. A comparison of the unstructured mesh solution with the published structured fine mesh solution (Zhou et al 2003) is shown in Figure 9.15. It is clear that both the finite element solution on unstructured meshes and the fine structured mesh solution are almost identical.…”

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

“…The two most representative cases discussed in the literature as demonstrators of algorithms for the numerical solution of the equations of motion in complex geometries are the L-shaped cavity, introduced by Perng & Street (1991) and further studied by Oosterlee et al (1993), and the two-box-cavity proposed by Hinatsu & Ferziger (1991), which is still the subject of intense research (e.g. Zhou et al 2003;Nithiarasu & Liu 2005;Ahusborde & Glockner 2010). One of the investigation's closest related with the present work is the analysis of lid-driven cavity flow in a two-dimensional domain of quarter-circular cross-section by Vynnycky & Kimura (1994), who reported steady flow patterns in Re e [0,1000].…”

Numerical solution of the Helmholtz equation with high wavenumbers

“…The unified feature of the DSC formalism was discussed and it was demonstrated that computational methods of Galerkin, collocation, global, local and finite difference types can be derived from a single starting point in the framework of the DSC algorithm [24]. The DSC algorithm may be regarded as a local spectral method [25] and it has been used for the treatment of complex boundary conditions in structural analysis [26,27] and applied to computational hydrodynamics [28]. Certain aspects of the convergence of the DSC algorithm have been discussed [25].…”