analytical study of the potential flow around the ship’s hull using the finite element method - محمد نسرين (Latakia University Journal -Engineering Sciences Series, 2023)
Solving the flow equations around the ship’s hull helps in analyzing many phenomena related to the hydrodynamic interaction between ships and the flow. Considering that these equations are differential and non-linear, it is often difficult to find their mathematical solution. In this paper, a method is presented to find a numerical solution for the equations of the potential flow around the ship’s hull in highly restricted waterways. The open source gmsh program is used to generate the finite elements around the ship’s hull, and then a weak mathematical expression is obtained for the equation of the potential flow by applying the weighted residual method using a function test of the Gallerkin type. In addition, the method for generating elemental matrixes is explained, after obtaining the nodal values ​​of the velocity potential in the flow field, the proposed numerical solution is validated by verifying the orthogonality of streamlines with equal values ​​of the velocity potential. Then the results of the velocity potential are used in calculating the velocity field in the flow; this enables evaluating the pressure field based on the energy conservation equation.