Application of a 2D harmonic polynomial cell (HPC) method to singular flows and lifting problems

Abstract

Abstract:Further developments and applications of the 2D harmonic polynomial cell (HPC) method proposed by Shao and Faltinsen [22] are presented. First, a local potential flow solution coupled with the HPC method and based on the domain decomposition strategy is proposed to cope with singular potential flow characteristics at sharp corners fully submerged in a fluid. The results are verified by comparing them with the analytical added mass of a double-wedge in infinite fluid. The effect of the singular potential flow is not dominant for added mass and damping, but the error is non-negligible when calculating mean wave loads using direct pressure integration. Then, the double-layer nodes technique is used to simulate a thin free shear layer shed from lifting bodies, across which the velocity potential is discontinuous. The results are verified by comparing them with analytical results for steady and unsteady lifting problems of a flat plate in infinite fluid. The latter includes the Wagner problem and the Theodorsen functions. Satisfactory agreement with other numerical results is documented for steady linear flow past a foil and beneath the free surface.

Local and global properties of the harmonic polynomial cell method: In‐depth analysis in two dimensions

“…Generally, it is natural to choose N HP = N node as done in the previous studies, and in this case …”

“…Recent studies have tried to modify the original HPC method in different contexts, showing that it has the potential to deal with various complicated problems. Liang et al coupled the HPC method with a local corner‐flow solution based on a domain decomposition (DD) strategy to account for the singular‐flow characteristics due to sharp corners. They also introduced a double‐layer node technique to simulate a thin free shear layer shed from lifting bodies.…”

Generalized HPC method for the Poisson equation

“…This implies that the HPC solver cannot capture singular solutions of the Laplace equation (e.g. in a domain with a sharp corner [11], or at the intersection between the free surface and the tank wall when it is non-vertical at the waterline [12] and the free-surface condition is linear). A strategy consists in matching an inner non-analytical solution for the singularity and an outer solution through the HPC solver.…”

The Harmonic Polynomial Cell Method for Moving Bodies Immersed in a Cartesian Background Grid

“…It is expected that the convergence of the velocity potential shown in FIGURE 7 also applies for other types of geometries where the body-curvature varies smoothly. In case of sharp corners, where the potential-flow solution becomes singular, additional measures such as the local analytical solution proposed by Liang et al [10] would be necessary to retain an accurate solution.…”

“…Generally, their results were in good agreement with experiments. Liang et al [10] applied the HPC method to study several additional problems relevant for marine hydrodynamics, including violent (nonlinear) sloshing in a two-dimensional tank. Very good agreement with experimental results was achieved indicating that, as long as the underlying assumptions of potential flow are valid, the method is capable of handling strongly nonlinear free-surface flows.…”