A distributed force element method with matching of fundamental solutions

Quantifying the contribution of vortex structures to wall forces is essential for identifying the primary sources of forces. The traditional force-element method focuses on the contribution of flow structures to the resultant force. However, the contribution of flow structures to the distributed force cannot be identified. This work proposes a distributed force element method to address this issue. Inspired by the framework of matched asymptotic expansions, the method resolves the surface pressure by matching the fundamental solutions of the outer wave and inner flow regions. The pressure is thus decomposed into contributions from a convective acceleration term, a boundary acceleration term and a boundary vorticity term. The method is implemented by solving the resulting linear system with singular value decomposition. The volume source is further decomposed into direct radiation and boundary scattering components. It is found that compared with the direct radiation component, the boundary scatter component decays fast in the wake. Consequently, the direct radiation component is dominant in the far wake. A finite-domain pressure correction is proposed based on the direct radiation component. The distributed force element method is validated using several benchmark cases: two-dimensional configurations including laminar flow around stationary and oscillating circular cylinders; three-dimensional cases comprising laminar flow past a sphere, subcritical flow past a sphere and laminar flow over an inclined spheroid. The results suggest that the proposed distributed force element method enables the precise quantification of how flow structures in the wake and around the bluff bodies contribute to the surface pressure.