Further improvement and analysis of CCD scheme: Dissipation discretization and de-aliasing properties

Proper general decomposition (PGD) for the resolution of Navier–Stokes equations

“…These results are different from these obtain by Sengupta et al in [36] who find a period of 2.29 s. This difference could certainly be explain by the choice of the order's discretisation schemes used. In fact, Sengupta et al used an high-order scheme (Combined Compact Difference scheme) while a second order scheme was used in this study.…”

“…In fact, Sengupta et al used an high-order scheme (Combined Compact Difference scheme) while a second order scheme was used in this study. As Sengupta et al mention in [36], the use of low order discretisation scheme and/or the use of an insufficiently refined grid in the case of a lid driven cavity with Reynolds numbers that are higher than a critical Reynolds, leads to instabilities that affect the dynamics of the flow. However, the aim of this work was to show the capacity of PGD to reproduce the results obtained with a standard model.…”

Space-time discretizing optimal DRP schemes for flow and wave propagation problems

“…The matrix [C] can be obtained for different methods, as given in [17] for some representative discretization methods in finite difference, finite volume and finite element. [C] matrix for some compact schemes has been given in [7,16,[20][21][22]. In spectral notation, this derivative is written as [16] …”

“…This problem has well defined computational geometry and boundary conditions and studied by [5,6,14,22]. We have solved this problem for Re = 1000 and 10,000.…”

“…Most notable results in Botella and Peyret [5] were obtained using Chebyshev collocation spectral method with N = 160 terms Chebyshev polynomial representation. Validation of the proposed numerical schemes for the unsteady case of Re = 10,000 has been done by comparing high accuracy results of [22] which show presence of time varying polygonal structures at the core of the cavity. We have used different uniform grids to solve Eqs.…”