Simulation Of Nonlinear Interaction Research Articles

Simulations of nonlinear interaction between beta-induced Alfvén eigenmode and tearing mode

The nonlinear interaction between the beta-induced Alfvén eigenmode (BAE) and the tearing mode (TM) observed in the HL-2A experiment is systematically studied with the hybrid kinetic-magnetohydrodynamic code M3D-K. It is found that the nonlinear growth of TM can lead to a gradient buildup on the magnetic island (MI) edge, and then triggers the destabilization of the linearly-stable BAE. Then, the triggered BAE together with TM can produce a significant redistribution of energetic particles. For BAE linearly-dominant-unstable case, the TM activity results in the inward motion of BAE mode structure, and the BAE can have a delay effect on the MI saturation. Furthermore, a high-frequency axisymmetric ‘breathing’ mode is generated by the mode coupling of BAE and TM, agreeing well with the experimental observation, and causes the synchronized periodic oscillation of MI width.

Nonlinear Simulation of Interaction between Water and Free Floating Ship

Based on fluid-solid two-phase coupling numerical model, this paper utilized velocity potential function theory to investigate the nonlinear interaction of water and free floating body. Meanwhile, multi-time step integral method and Overall numerical solution method, which are suitable for finite element dynamic analysis, and free surface boundary condition, not moving boundary conditions and the water-solid coupling boundary conditions are adopted to analyze the dynamic responses of water and free floating body with different dimensions. Numerical results show that the change of floating body sizes can obviously affect the dynamic characteristics of the fluid-solid coupling system, especially in the aspects of the stress responses of the floating body and the pressure responses of the water model.

Quasi ALE finite element method for nonlinear water waves

This paper presents a newly developed quasi arbitrary Lagrangian–Eulerian finite element method (QALE-FEM) for simulating water waves based on fully nonlinear potential theory. The main difference of this method from the conventional finite element method developed by one of authors of this paper and others (see e.g. [Q.W. Ma, G.X. Wu, R. Eatock Taylor, Finite element simulation of fully non-linear interaction between vertical cylinders and steep waves. Part 1: Methodology and numerical procedure and Part 2: Numerical results and validation, Int. J. Numer. Methods Fluids, 36 (2001) 265–308.] and [G.X. Wu, Z.Z. Hu, Simulation of nonlinear interactions between waves and floating bodies through a finite-element-based numerical tank, Proc. R. Soc. A 460 (2004) 2050, 3037–3058.]) is that the complex mesh is generated only once at the beginning and is moved at all other time steps in order to conform to the motion of the free surface and structures. This feature allows one to use an unstructured mesh with any degree of complexity without the need of regenerating it every time step, which is generally inevitable and very costly. Due to this feature, the QALE-FEM has high potential in enhancing computational efficiency when applied to problems associated with the complex interaction between large steep waves and structures since the use of an unstructured mesh in such a case is likely to be necessary. To achieve overall high efficiency, the numerical techniques involved in the QALE-FEM are developed, including the method to move interior nodes, technique to re-distribute the nodes on the free surface, scheme to calculate velocities and so on. The model is validated by water waves generated by a wavemaker in a tank and the interaction between water waves and periodic bars on the bed of tank. Satisfactory agreement is achieved with analytical solutions, experimental data and numerical results from other methods.

Simulation of nonlinear interactions between waves and floating bodies through a finite-element-based numerical tank

Fully nonlinear water–wave interactions with a floating structure are investigated through a numerical towing tank. A wave maker is installed on one end of the tank while a numerical beach based on a combination of damping zone and Sommerfeld condition is adopted on the other side of the tank. A floating body is placed at a location in the tank, where it will be set into motion by the waves generated by the wave maker. The simulation is based on the velocity potential theory together with the finite–element method. The mesh used follows the deformation of the free surface and the body motion. Its structure is adjusted and the distribution of elements is completely rearranged when the motion is big to avoid an over–distorted grid. Auxiliary functions are introduced to decouple the nonlinear mutual dependence between the hydrodynamic force and the body motion. Extensive numerical results are provided for vertical circular cylinders and a simplified floating production, storage and offloading, for which meshes are obtained through an efficient scheme based on a two–dimensional tri–tree method.

Stochastic Simulations and Discreteness of Light

The stochastic simulations of nonlinear interactions are frequently employed method in quantum optics [1, 2]. The simulations use the continuous stochastic variables and one can put a question, whether it is possible to generate the effects of discreteness of light in the nonlinear systems. In addition, it is well known that for large variety of the nonlinear systems, the stochastic simulations exhibit an instability and generate invalid solutions [3] if the boundary terms in the phase-space become non-negligible. On the other hand, it will be presented here on an illustrative example that this instability is closely related to the omitting of a quantum discreteness in the continuous stochastic simulations. Because, if the discrete character is incorporated in a proper way, the stochastic simulations offer the correct results in agreement with the exact solutions. In summary, we suggest that the continuous stochastic simulations are not able to correctly describe a discreteness of light in the quantum nonlinear systems [4]. To illustrate this. we use the nonlinear photonic interaction (anharmonic oscillator) described by the interaction Hamiltonian, where κ is a real nonlinear constant and  is the annihilation operator of the light mode. An evolution of mean-value of the quadrature operator for initial coherent state |α〈 exhibits well-known periodical behavior with revival period Δt = κ/2π, as can be seen in Fig. 1(b), which is an exhibition of the interference between the discrete eigenstates of the photon-number operator [5].

Nonlinear interaction simulation of low-frequency electrostatic waves in the F-region of the highlatitude ionosphere

Nonlinear interaction processes of three and more low frequency electrostatic waves in the ionospheric F-region are numerically and analytically investigated. It is shown that these processes cannot be described without taking into account the ion inertia. Considering the ion inertia, the increase of disturbances is limited to the level of a few per cent. The fluctuation spectrum of plasma concentration becomes approximately exponential and does not depend on the initial type of the disturbances.