Reference values for drag and lift of a two‐dimensional time‐dependent flow around a cylinder

Abstract

SUMMARYThis paper presents a numerical study of a two-dimensional time-dependent ow around a cylinder. Its main objective is to provide accurate reference values for the maximal drag and lift coe cient at the cylinder and for the pressure di erence between the front and the back of the cylinder at the ÿnal time. In addition, the accuracy of these values obtained with di erent time stepping schemes and di erent ÿnite element methods is studied.

Stable and accurate pressure approximation for unsteady incompressible viscous flow

“…In [18], this boundary condition is derived in section 3 and appears two lines below (15). Equation (4) of [18] is a discretized version of (32) with q n+1 replaced by ∆t φ n+1 .…”

“…The computational mesh is shown in Figure 7 and the contour plot of the stream function at t= [2,4,5,6,7,8] is shown in Figure 11. For comparison with [15] we also calculate the drag and lift coefficients, denoted by c d (t) and c l (t), which are the x and y components of the quantity…”

On the impact of the scheme for solving the higher dimensional equation in coupled population balance systems

“…We will use the Q 2 finite element for the velocity and the P disc 1 (discontinuous linears) finite element for the pressure. This pair of finite element spaces has been proven to be among the best performing ones for discretizing the incompressible Navier-Stokes equations [6,9,10,13]. Since laminar flows will be considered in the numerical studies, a stabilization of the spatial discretization of the Navier-Stokes equations, [1], or the application of a turbulence model, [26], is not necessary.…”

“…In numerical studies for incompressible flows, the Crank-Nicolson scheme has shown a good relation of accuracy to efficiency [15]. In particular, it was considerably more accurate than the backward Euler scheme (θ 1 = θ 4 = 1, θ 2 = θ 3 = 0), see also [9]. Next, the system (12), (13) is linearized by a fixed point iteration: Given (u…”

Two‐level finite element method with a stabilizing subgrid for the incompressible Navier–Stokes equations

“…The unsteady flow around a cylinder problem [33] is governed by the unsteady Navier-Stokes equations with Re = 100 and f = 0. The problem is given with homogeneous initial value u(x, y, 0) = 0 and boundary conditions at inflow (x = 0) and outflow (x = 2.2) boundaries as u(0, y, t) = u(2.2, y, t) = 0.41 −2 sin( t/8)(6y(0.41− y), 0), 0 y 0.41 (24) No-slip boundary conditions are described at the other boundaries (y = 0, 0.41 and around the cylinder).…”