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Application of the method of fundamental solutions and the generalized Lagally theorem to the interaction of solid body and external singularities in an inviscid fluid. (English) Zbl 1284.76061
Summary: This paper proposes a method that can calculate the hydrodynamic force of a non-circular object in an inviscid, irrotational, and incompressible flow with the presence of external flow singularities. In order to handle irregular object, the method of fundamental solutions (MFS) is employed to numerically construct the singularity system that describes the body and the flow motion and meets the boundary condition. The obtained singularity system is then integrated into the generalized Lagally theorem to compute the instantaneous hydrodynamic force via algebraic calculations and to describe the unsteady interaction of the object and its ambient flow. The proposed method is validated by simulating the interaction of a circular cylinder with an external free vortex and the numerical solutions are compared to the literature theoretical descriptions. The time history of the cylinder and the vortex trajectory can be exactly reproduced. The current method is then employed to study the axisymmetric approach of a vortex pair-two free vortices with opposite strengths-towards a neutrally buoyant ellipse. We show how the vortex pair and the ellipse trajectory changes with respect to different vortex configurations and ellipse aspect ratios. This example demonstrates the capability of the current method in dealing with fluid-body interaction problem, especially for irregular body shape.

MSC:
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
70E99 Dynamics of a rigid body and of multibody systems
65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
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