Finite element analysis of viscous flow - Solid body interaction

This paper describes preliminary development work on extending the finite element method to cover interaction between viscous flow and a moving solid body. The analysis uses the stream function-high precision triangular finite element representation for two-dimensional incompressible flow. The interactive forces and constraints between the fluid and body are developed from surface traction and compatibility conditions. This yields a set of coupled equations for the fluid-body system. Results are obtained for the linearized case of uni-directional motion of a spring-mass (of square shape) body system surrounded by still fluid and excited by a harmonic external force. Numerical results are obtained for the response and phase angle of the body as functions of frequency. At the same time, results for the associated flow fields are also obtained. As a by-product, results are obtained for the added mass and damping coefficients as a function of frequency.