ERROR IN NUMERICAL SIMULATION OF EXTERNAL FLOW AROUND AN IMMSERD BODY

A posteriori error estimation is usually adopted in numerical simulations of external flow around an immersed body, where the body is located in a channel of “sufficient size”. During the error estimation, both the channel size and grid resolution are varied in large ranges so as to achieve the converged solution. In this work, a simple technique of a priori error estimation is developed for such simulations. The effect of the channel size is investigated by the superposition of image solutions for Stokes flow or potential flow depending on the actual Reynolds number. The effect of grid resolution is investigated through applying the well-known error estimation in polynomial approximation to specific simple flows, i.e., boundary layer, far-field potential flow, and the Rankine vortex. The global error estimation for external flow simulations is obtained by assembling the results obtained under these three simple characteristic flow models. In order to verify the theoretical findings, numerical simulations of flow around an air foil (2D) and around a sphere (3D) are carried out in a large range of Reynolds numbers. The numerical simulations agree with the theoretical predictions extremely well. Both theoretical and numerical results demonstrate that the channel size needs to be of around 100 folds of the characteristic size of the immersed body in Stokes flows so as to exhibit a discrepancy around 1% from the external flow problem of infinite domain. However, for flows of Reynolds number larger than 100, the channel size only needs to be 10 (for 2D) or 5 (for 3D) in unit of the body size so as to achieve the same precision. The technique of a priori error estimation can be used for simulations of external flow around an arbitrary body other than the air foil or sphere investigated here.