A new perspective of higher order compact nonuniform Padé approximation based finite difference scheme for solving incompressible flows directly on polar grids

“KAP” MATERIAL USED FOR VOLUNTARY BLOOD DONATION IN TEZPUR MEDICAL COLLEGE AND HOSPITAL, TEZPUR, ASSAM, INDIA (A RETROSPECTIVE STUDY & PERSONAL EXPERIENCE)

“…Further, at Re=3000 a tertiary vortex is seen to form at the top left corner of the cavity. It is to be mentioned that all the findings are in accordance with those available in the literature[16,9,10,17,11] both experimentally and numerically. Additionally, at higher Re values the vorticity contours move away from the center of the cavity toward the cavity walls thereby developing very strong vorticity gradients in the vicinity of the cavity walls.…”

“…This particular problem was first studied experimentally and numerically by Fuchs and Tillmark [15] and since then it has been used extensively by researchers to validate numerical schemes, particularly for physical domains with circular arc as boundaries [16,9,10,17,11]. values are set to be zero at all the boundaries (ψ = 0).…”

“…Additionally, a valid discretization at singularity r = 0 is necessary. Subsequently, considerable efforts could be found in the literature on HOC discretization of N-S equations in the body-fitted polar coordinate system [7,8,9,10,11]. In the year 2005 Sanyasiraju and Manjula [7] proposed a higher order semicompact scheme to solve the flow past an impulsively started circular cylinder.…”

“…The scheme developed therein is of second order accuracy and carries streamfunction and its first derivatives as the unknown variables. Of late Das et al [11] also worked with steady second order equation with variable coefficients in polar coordinates and introduced a third order accurate HOC scheme. The scheme claimed to be implemented on a nonuniform grid used an implicit form of first order derivatives and was successful in simulating steady incompressible flows.…”