Comparison of different approaches to calculating pointwise traction in flow

Abstract

For an incompressible Newtonian fluid flowing around an obstacle we are interested in the pointwise traction acting on it. To determine the local deformation of a solid obstacle, an accurate traction calculation is required. Besides the classical approach that concerns a direct calculation of the traction from the Cauchy stress tensor, we investigate the Poincaré-Steklov method based on calculating a dual problem and it seems to provide more accurate results. Indeed, we show a better convergence rate of the latter method with respect to the direct approach. The method is applied to the Turek benchmark, which considers a flow past a rigid cylinder. We also consider a rigid square prism as an obstacle. In this benchmark the total drag and lift acting on the cylinder is computed. We extended the benchmark and computed the point-wise traction for different mesh resolutions and Reynolds numbers.