Polynomial interpolation methods for viscous flow calculations

The lid-driven square cavity flow: numerical solution with a 1024 x 1024 grid

“…For all variables of interest, the discretization error estimated (U) with Eqs. (13) and (14) The main focus of this work was to solve the problem of laminar flow inside a square cavity of which lid moves at a constant velocity and analytical solution is unknown (Kawaguti, 1961;Burggraf, 1966;Rubin and Khosla, 1977;Benjamin and Denny, 1979;Ghia, Ghia and Shin, 1982). Results were presented for 42 variables of interest (φ), and their estimated discretization errors (U) on a grid of 1024 x 1024 nodes and Reynolds numbers (Re) = 0.01, 10, 100, 400 and 1000.…”

“…1 This work addresses the classical problem (Kawaguti, 1961;Burggraf, 1966;Rubin and Khosla, 1977;Benjamin and Denny, 1979;Ghia, Ghia and Shin, 1982) of laminar flow inside a square cavity of which lid moves at constant velocity: Fig. 1; where u and v are the components of the velocity vector in x and y directions, ρ and µ are fluid density and viscosity.…”

Derivation of New Staggered Compact Schemes with Application to Navier-Stokes Equations

“…This representation is in general not unique. It is well known, for instance, that in the particular case of the Padé scheme, the classical third-degree cubic spline gives a consistent interpolation, in the sense that its analytical first derivative at node x j returns Equation (1) [10]. In what follows, we will consider a different set of local interpolations which is consistent with the compact scheme in Equation (1).…”

“…In these early years the focus was not only on the applications of compact schemes, but also on the development of a theoretical framework in which new schemes could be derived. In a series of papers, Rubin and co-workers [8][9][10] firstly estabilished that many compact schemes can be derived by employing the theory of spline interpolation. They showed, for example, that the classical Padé fourth-order formula for first derivative can be obtained by analytically differentiating the cubic spline interpolation, thus recognizing that compact schemes could be derived through a theory of polynomial interpolation in physical space, which has to be necessarily implicit.…”

Analysis of local defect correction and high-order compact finite differences

“…They are also known as Padé differencing approximation [12]. In the 70-80's a large number of applications for solving fluid-mechanics equations have been developed in [11,13,19,20]. From the more recent papers the works [14] and [16] should be mentioned.…”