Numerical solution of incompressible flows by discrete singular convolution

Abstract

SUMMARYA discrete singular convolution (DSC) solver is developed for treating incompressible ows. Three di erent two-dimensional benchmark problems, the Taylor problem, the driven cavity ow, and a periodic shear layer ow, are utilized to test the accuracy, to explore the reliability and to demonstrate the e ciency of the present approach. Solution of extremely high accuracy is attained in the analytically solvable Taylor problem. The results of treating the other problems are in excellent agreement with those in the literature.

Discussions on driven cavity flow

“…[14], the obtained false periodic numerical solutions looked so real and fascinating with certain frequencies and periodicity. We believe that the studies that presented unsteady solutions of driven cavity flow using Direct Numerical Simulations ( [4,32,44,34,10,24,46,31]) have experienced the same type of numerical oscillations because they have used a small grid mesh. We would like to note that in all of the Direct Numerical Simulation studies on the driven cavity flow found in the literature ( [4,32,44,34,10,24,46,31]), the maximum number of grid points used is 257×257.…”

“…We believe that the studies that presented unsteady solutions of driven cavity flow using Direct Numerical Simulations ( [4,32,44,34,10,24,46,31]) have experienced the same type of numerical oscillations because they have used a small grid mesh. We would like to note that in all of the Direct Numerical Simulation studies on the driven cavity flow found in the literature ( [4,32,44,34,10,24,46,31]), the maximum number of grid points used is 257×257. We believe that because of the course grids used in [4,32,44,34,10,24,46,31], their periodic solutions resemble the false periodic solutions observed in Erturk et.…”

“…We would like to note that in all of the Direct Numerical Simulation studies on the driven cavity flow found in the literature ( [4,32,44,34,10,24,46,31]), the maximum number of grid points used is 257×257. We believe that because of the course grids used in [4,32,44,34,10,24,46,31], their periodic solutions resemble the false periodic solutions observed in Erturk et. al.…”

“…In the third category, the following two dimensional Direct Numerical Simulation studies on driven cavity flow, Auteri, Parolini & Quartepelle [4], Peng, Shiau & Hwang [32], Tiesinga, Wubs & Veldman [44], Poliashenko & Aidun [34], Cazemier, Verstappen & Veldman [10], Goyon [24], Wan, Zhou & Wei [46] and Liffman [31] can be found in the literature as an example.…”

A Family of Stationary Solutions to the Euler Equations and Generalized Solutions

“…Equivalent vector fields to those ones treaties in this work have been studied as application of high order essentially no oscillatory (ENO) schemes for smooth solutions of NavierStokes and Euler equations, (see [14]), in problems involving the Taylor-Green vortex, (see [8], [3] and [10]) and to explore a discrete singular convolution algorithm (DSC) for solving certain mechanics problems, (see [16] and [17]). …”