Flow around an obstacle: Various approaches to calculate pointwise traction

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. In addition to the classical approach that concerns a direct calculation of the traction from the Cauchy stress tensor, we investigate the Poincaré-Steklov method based on the calculation of a dual problem and it seems to provide more accurate results. Indeed, we show a better convergence rate for 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 to address non-smooth boundaries and singularities in the flow.