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A radial basis function (RBF)-based ghost cell method is presented to simulate flows around a rigid or flexible moving hydrofoil on a Cartesian grid. A compactly supported radial basis function (CSRBF) is introduced to the ghost cell immersed boundary method to treat the complex flexible boundaries in the fluid. The results indicate that this RBF representation method can accurately track tempo-spatially varied interfaces and avoid the identification failure encountered in original RBF. In addition, an interface cell interpolation method is developed to treat the irregular boundaries such as sharp points and thin boundaries. Solution quality is improved by constructing the interface cells along the local irregular boundaries, instead of the ghost cells. To validate the proposed method, uniform flows around stationary and pitching hydrofoils are simulated. Then, a flexible hydrofoil undulating in the fluid is simulated. Good agreements are obtained by comparing the present results with the reference results. Furthermore, the relationship between the oscillation frequency and the force coefficient is studied. Also, generation mechanism of the thrust force is explained.

The problem of a particle confined in a box with moving walls is studied, focusing on the case of small perturbations which do not alter the shape of the boundary (‘pantography’). The presence of resonant transitions involving the natural transition frequencies of the system and the Fourier transform of the velocity of the walls of the box is brought to the light. The special case of a pantographic change of a circular box is analyzed in depth, also bringing to light the fact that the movement of the boundary cannot affect the angular momentum of the particle.

This paper investigates the fluid–solid interaction in an electrostatic microvalve to control the flow rate. A double clamped microbeam which has been considered as a microvalve by imposing a DC voltage on it in a capacitive system, is deflected and hence changes the boundary conditions of the fluid domain. So, in each step of increasing the voltage, the Navier–Stokes and Euler–Bernoulli equations have been solved simultaneously. To overcome the difficulties of the finite element solution in moving boundaries of the fluid domain, after each step, a mapping approach has been accomplished. Silicon and dielectric elastomer (DE) have been adopted as the microbeam’s material and capability of them to control the flow rate has been compared. The results have shown that DE can be an attractive candidate for microvalve instead of silicon due to the decreasing required applied voltage for achievement for a certain flow rate. The presented results can be also useful for modeling the FSI problems with moving boundaries in the fluid domain, especially in the microvalve design applications.

A frequency-domain formulation is proposed to compute the far-field noise generated by flows with periodically oscillating or rotating boundaries. The proposed formulation significantly enhances the efficiency of the frequency-domain method in handling the multi-frequency sources with nonrectilinear motion. The novelty of the proposed method is that the frequency- and time-dependent components of the Ffowcs Williams and Hawkings (FW-H) integral are separated by using the far-field asymptotic Green’s function. The separation of the frequency- and time-dependent components avoids the need for an expensive time integration in computing the multi-frequency noise generated by flows with periodically moving boundaries. They proposed only one Fourier transform computation in obtaining the noise at different frequencies. The efficiency of the proposed formulation is investigated by analyzing the required number of floating-point operations. Its validity is examined by computing the noise from rotating or oscillating permeable boundaries around composite monopoles and a flapping wing. The proposed formulation is applicable to the FW-H integral with periodically oscillating or rotating boundaries when the maximum velocity on the moving boundary is subsonic.

We consider the solvability of the Fokker–Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker–Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulting ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker–Planck equations are presented.