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The unsteady flow within a simplified 3D centrally-actuated type artificial heart was investigated numerically using moving boundary technique. The velocities on the inlet and outlet were determined according to the motion of the diaphragm. The case with heart beat rate of 75 beats per minute (bpm) was simulated. Two models were studied. It is found that, in the diastolic cycle, a vortex ring forms in the conjunction of the blood chamber and the inlet tube. This vortex ring can provide good wash-out on the wall.

A lattice Boltzmann model (LBM) for a moving body in shallow waters is developed. Three different schemes, FH's, Guo's and MMP's schemes, for a curved boundary condition at second-order accuracy are used in the study and compared in detail. The multiple-relaxation-time (MRT) is adopted for better stability. In order to deal with the moving body boundary, a certain momentum is added to reflect the interaction between the fluid and the solid; and a refill method for new wetted nodes moving out from solid nodes has been proposed. The described method is applied to simulate static and moving cylinders in shallow waters. The corresponding experiments are further performed for validation of the present model. It is found that all of the three schemes produce similar results that agree well with the experimental data for the static cylinder. However, for the moving boundary, MMP's scheme performs best. Overall, the proposed modeling approach is able to simulate both, static and moving cylinders in shallow water flows at acceptable accuracy.

A modified ghost fluid (MGF) method for reducing the spurious pressure oscillations in moving boundaries is proposed on the lattice Boltzmann method (LBM). The primary cause of these oscillations is the violation of the boundary geometric conservation law for sharp-interface immersed boundary. We introduce a simple weight strategy into GF method to strictly enforce geometric conservation. The weight strategy reduces the abrupt change of the distribution function on the boundary node when passing through the moving boundary. Some simulations are shown to test the validity of the method. The results illustrate that the modified method maintains the same validity as the GF and reduces the spurious pressure oscillations near the boundaries.

We use Lewis and Riesenfeld's quantum invariant theory to calculate the Lewis–Riesenfeld phases for a time-dependent frequency harmonic oscillator that is confined between a fixed boundary and a moving one. We also discuss the Berry phase for the system with a sinusoidally oscillating boundary.

Particle dissolution is an important process that occurs during heat treatment in the transportation process. We present a one-dimensional model of spherical wax particle dissolution in a fluid. The model includes a nonlinear equation at the free boundary, which was established to describe the dissolution rate of a wax particle assuming a diffusion process. At the moving boundary, we compute the concentration distributions of partial solutions. To estimate wax dissolution in solution and related expressions for the dissolved radius, an analytical solution of a mathematical model for spherical particle dissolution in flow is used.

This paper depicts a ghost cell method to solve the three dimensional compressible time-dependent Euler equations using Cartesian grids for static or moving bodies. In this method, there is no need for special treatment corresponding to cut cells, which complicate other Cartesian mesh methods, and the method avoids the small cell problem. As an application, we present some numerical results for a special moving body using this method, which demonstrates the efficiency of the proposed method.

Aiming at extremely large deformation, a novel predictor–corrector-based dynamic mesh method for multi-block structured grid is proposed. In this work, the dynamic mesh generation is completed in three steps. At first, some typical dynamic positions are selected and high-quality multi-block grids with the same topology are generated at those positions. Then, Lagrange interpolation method is adopted to predict the dynamic mesh at any dynamic position. Finally, a rapid elastic deforming technique is used to correct the small deviation between the interpolated geometric configuration and the actual instantaneous one. Compared with the traditional methods, the results demonstrate that the present method shows stronger deformation ability and higher dynamic mesh quality.

Recent advancement of bio-inspired underwater vehicles has led to a growing interest in understanding the fluid mechanics of fish locomotion, which involves complex interaction between the deforming structure and its surrounding fluid. Unlike most natural swimmers that undulate their body and caudal fin, manta rays employ an oscillatory mode by flapping their large, flattened pectoral fins to swim forward. Such a lift-based mode can achieve a substantially high propulsive efficiency, which is beneficial to long-distance swimming. In this study, numerical simulations are carried out on a realistic manta ray model to investigate the effect of pectoral fin kinematics on the propulsive performance and flow structure. A traveling wave model, which relates a local deflection angle to radial and azimuthal wavelengths, is applied to generate the motion of the pectoral fins. Hydrodynamic forces and propulsive efficiency are reported for systematically varying kinematic parameters such as wave amplitude and wavelengths. Key flow features, including a leading edge vortex (LEV) that forms close to the tip of each pectoral fin, and a wake consisting of interconnected vortex rings, are identified. In addition, how different fin motions alter the LEV behavior and hence affect the thrust and efficiency is illustrated.

A deterministic model of polymer crystallization, derived from a previous stochastic one, is considered. The model describes the crystallization process of a rectangular sample of a material cooled at one of its sides. It is a reaction–diffusion system, composed of a PDE for the temperature and an ODE for the phase change of a polymer melt from liquid to crystal. The two equations are strongly coupled since the evolution of temperature depends on a source term, due to the latent heat developed during the phase change, the nucleation and growth rates are functions of the local (in time and space) temperature. The main difference with respect to the previous model is the introduction of a critical temperature of freezing in these functions. The paper does not contain detailed analytical aspects, that are left to subsequent investigations. A qualitative analysis of the proposed model is carried out, based on numerical simulations. An interesting feature shown by the simulations is that the solution exhibits an advancing moving band of crystallization in the mass distribution, as well as a moving boundary in the temperature field, both advancing with the same decreasing velocity. For some values of the parameters, which are typical of the physical problem, the advance takes place by jumps due to regular stops of the most advanced point of crystallization. The duration of these halts increases as the applied temperature decreases. This may indicate that the crystallization time is not a monotone function of the applied temperature. A simplified mathematical model is eventually proposed which reproduces the same patterns.

A reaction–diffusion equation is studied in a time-dependent interval whose length varies with time. The reaction term is either linear or of KPP type. On a fixed interval, it is well known that if the length is less than a certain critical value then the solution tends to zero. When the domain length may vary with time, we prove conditions under which the solution does and does not converge to zero in long time. We show that, even with the length always strictly less than the ‘critical length’, either outcome may occur. Examples are given. The proof is based on upper and lower estimates for the solution, which are derived in this paper for a general time-dependent interval.

In order to model nonlinear breaking waves with moving boundary and coastal sandbar migration; we presented a morphodynamic model, where hydrodynamic equations (free surface flows) and sediment transport equation are solved in a coupled manner. The originality lies in the development of an innovative approach, in which, we project the horizontal velocity onto a basis functions depending only on the variable z and we calculate analytically the vertical velocity and the nonhydrostatic pressure. The choice of basis depends on the problem under consideration. This model is numerically stable because there is no mesh in the vertical direction. This model is accurate because we can directly introduce functions that best fits the physical nature of the flow. Our model is validated through laboratory measurements carried out by Dingemans [1994, J. Comput. Phys. 231, 328–344], Cox and Kobayashi [2000, J. Geophys. Res. 105(c6), 223–236. and Dette et al. [2002, Coast. Eng.47, 137–177].

The paper proposes a general formulation for simulating unsteady state heat transfer problem with moving boundaries. The method is equipped with a correction term based on the finite element method. In dealing with the unsteady behavior, forward time marching is performed using the finite difference method. We introduce a correction term to effectively deal with the moving boundary effects, which directly uses the nodal temperature at the previous step in the time marching process. A mathematical study has been conducted to examine the theoretical basis. Finally, intensive numerical experiments are conducted to demonstrate effectiveness and stability of the proposed procedure.

An improved momentum-exchanged immersed boundary-based lattice Boltzmann method (MEIB-LBM) for incompressible viscous thermal flows is presented here. MEIB-LBM was first proposed by Niu et al, which has been shown later that the non-slip boundary condition is not satisfied. Wang. et al. and Hu. et al overcome this drawback by iterative method. But it needs to give an appropriate relaxation parameter. In this work, we come back to the intrinsic feature of LBM, which uses the density distribution function as a dependent variable to evolve the flow field, and uses the density distribution function correction at the neighboring Euler mesh points to satisfy the non-slip boundary condition on the immersed boundary. The same idea can also be applied to the thermal flows with fluid-structure interference. The merits of present improvements for the original MEIB-LBM are that the intrinsic feature of LBM is kept and the flow penetration across the immersed boundaries is avoided. To validate the present method, examples, including forced convection over a stationary heated circular cylinder for heat flux condition, and natural convection with a suspended circle particle in viscous fluid, are simulated. The streamlines, isothermal contours, the drag coefficients and Nusselt numbers are calculated and compared to the benchmark results to demonstrate the effective of the present method.

Realistic acoustic problems often involve interactions between arbitrary-shaped moving objects at the interface with a fluid domain. The present work aims at developing numerical methods to take into account moving boundaries for acoustic problems, with a high order of convergence. The reference problem considered in this work is the solution of the non-linear Euler equations by a finite-difference time-domain method, describing the formation of one-dimensional waves created by a moving piston. The most suitable class of methods to solve this type of problem in the case of complex moving boundaries is the ghost-point method for sharp interface with 4th order reconstruction.¹ In order to accurately formulate the immersed boundaries with ghost points, the boundary conditions are formulated in terms of characteristic waves of the non-linear equations. The proposed approach is also extended to represent moving boundaries with a prescribed acoustic impedance. This is achieved by coupling a time-domain acoustic impedance model to the immersed boundary technique. The method is also applied to a two-dimensional example, where an acoustic pulse is reflected by a moving wall.