Distributed force element decomposition with method of fundamental solutions

Abstract: Quantifying the contribution of vortex structures to pressure stress is useful for designing flow control strategies to mitigate low or drag. The traditional force-element method focuses on the contribution of vortex structures to the resultant force. However, the contribution of vortex structures to the distributed force can not be identified. To address this problem, a distributed force element method is proposed. This method projects the Navier-Stokes equation to a divergence-free space and obtain a Poisson equation for pressure. The Green's function is employed to express pressure stress on the solid boundary as a combination of volume and surface integrals. Contributions to the distributed source are divided into acceleration surface elements, vorticity surface elements, convection volume elements. The method of fundamental solutions and singular value decomposition are used to efficiently solve the Green's functions. The distributed force element method is validated using laminar flows around a stationary circular cylinder and oscillating circular cylinder, and three-dimensional laminar and turbulent flows around a sphere. In laminar flow over a circular cylinder, fluctuation of forces mainly originate from volume sources, while in flow over an oscillating circular cylinder, inertial and volume source terms may cancel out, suppressing lift fluctuation. In flows over a sphere, a strong negative volume source in the boundary layer on the sphere creates low-pressure regions, while pressure in the separated shear layer is close to zero.