An efficient finite difference technique for computing incompressible viscous flows

Numerical solutions of 2‐D steady incompressible flow in a driven skewed cavity

“…In order to do this we compare our results with the results found in the literature. At this point, we would like to note that in the literature among the studies that have solved the skewed cavity flow ( [5], [17], [13], [20], [31], [28], [32], [27], [3], [18], [25], [11] and [22]), only Demirdžiü et al [5], Oosterlee et al [17], Shklyar and Arbel [22] and Louaked et al [13] have presented tabulated results therefore we will mainly compare our results with those studies.…”

“…As mentioned earlier, Demirdžiü et al [5] [17], Louaked et al [13] and Shklyar and Arbel [22]. The results of this study and the results of Demirdžiü et al [5] and also those of Oosterlee et al [17], Shklyar and Arbel [22] and Louaked et al [13] agree well with each other, although we believe that our results are more accurate since in this study a very fine grid mesh is used.…”

“…The results of this study and the results of Demirdžiü et al [5] and also those of Oosterlee et al [17], Shklyar and Arbel [22] and Louaked et al [13] agree well with each other, although we believe that our results are more accurate since in this study a very fine grid mesh is used. Figure 5 to Figure 8 show the streamline and also vorticity contours for Re=100 , in order to demonstrate the accuracy of the numerical solutions we presented, a good mathematical check would be to check the continuity of the fluid, as suggested by Aydin and Fenner [1].…”

TVD-interpolating matrix method prediction of flow with heat transfer

“…Unfortunately, the Leith scheme is a two-dimensionally unstable method arising from the interaction of two one-dimensional methods, each of which is stable. In our previous work Journal of Computational Physics 193 (2003) [226][227][228][229][230][231][232][233][234][235][236][237][238][239][240][241][242] www.elsevier.com/locate/jcp [18], we showed how to modify the method to get a stable and accurate TVD-IMM scheme. Different tools have been developed.…”

“…The resulting version of the IMM, by its flexibility, not only makes it possible to solve the fluid flow equations in curvilinear configurations, but it is also easily adaptable to the most recent and gravitational high resolution schemes for conservation law equations. The TVD-IMM is then an approach to obtain difference equations at arbitrary mesh point and coupled to an efficient TVD scheme which consists on reformulating the classical Lax-Wendroff scheme in such a way that it takes into account the non-orthogonality of the mesh, and then updating it to be like TVD form by appending suitable curvilinear terms [9,[16][17][18]. The flexibility is a major benefit of this approach.…”