A detailed and systematic analysis is performed on the local and global properties of the recently developed Harmonic Polynomial Cell (HPC) method, a very accurate and efficient field solver for problems governed by the Laplace equation. At the local cell level, a simple rule is identified for the proper choice of harmonic polynomials in the local representation of the velocity potential in cells with symmetry properties. The local solution error, its convergence rate, its dependence on the cell topology, its distribution inside the cell and its features across cells with different dimensions, are carefully examined with relevant findings for HPC numerical implementations. At the global level, the error convergence rate is analytically estimated in terms of error contributions from the boundary conditions and from inside the liquid domain. In most cases, the error associated with boundary conditions dominates the global error. In order to minimize it, Quadtree grid strategies or high-order local expressions of the velocity potential are proposed for cells near critical boundary portions. To model accurately the boundary conditions on rigid or deformable surfaces with generic geometries, three different grid strategies are proposed by adopting concepts of immersed boundary method and overlapping grids. They are comparatively studied for a circular rigid cylinder in infinite fluid and for the propagation of a free-surface wave. Then, an immersed boundary strategy, using numerical choices suggested in this paper, is successfully compared against a fully nonlinear Boundary Element Method for the case of a surface-piercing circular cylinder heaving in otherwise calm water.

Purpose This paper aims to present an efficient and simplified proportional-integral/proportional-integral and derivative controller design method for the higher-order stable and integrating processes with time delay in the cascade control structure (CCS). Design/methodology/approach Two approaches based on model matching in the frequency domain have been proposed for tuning the controllers of the CCS. The first approach is based on achieving the desired load disturbance rejection performance, whereas the second approach is proposed to achieve the desired setpoint performance. In both the approaches, matching between the desired model and the closed-loop system with the controller is done at a low-frequency point. Model matching at low-frequency points yields a linear algebraic equation and the solution to these equations yields the controller parameters. Findings Simulations have been conducted on several examples covering high order stable, integrating, double integrating processes with time delay and nonlinear continuous stirred tank reactor. The performance of the proposed scheme has been compared with recently reported work having modified cascade control configurations, sliding mode control, model predictive control and fractional order control. The performance of both the proposed schemes is either better or comparable with the recently reported methods. However, the proposed method based on desired load disturbance rejection performance outperforms among all these schemes. Originality/value The main advantages of the proposed approaches are that they are directly applicable to any order processes, as they are free from time delay approximation and plant order reduction. In addition to this, the proposed schemes are capable of handling a wide range of different dynamical processes in a unified way.

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