On the Calculation of Two-Dimensional Added Mass Coefficients by the Taylor Theorem and the Method of Fundamental Solutions

This work integrates the Taylor theorem and the method of fundamental solutions to develop a numerical tool for estimating the added mass coefficient tensor for a solid object of any convex shape moving in potential flow. In potential flow theory, the Taylor theorem calculates the added mass coefficient tensor for a Rankine body with algebraic manipulations of the properties of the internal singularities employed to generate the corresponding flow. To apply this theorem for objects in other shapes, the singularity strength and locations are required information which is facilitated numerically in this work by the method of fundamental solutions (MFS). The developed scheme is tested on a circle, an ellipse, a square, and a rhombus and the numerical results are in good agreement with the corresponding analytical values. A final example of a Cassini oval is also considered to show the potential applications on bio-engineering problems.