Characteristic behaviour of plasma fluctuations inside a plasma bubble in presence of a magnetic field due to the formation of a potential well

Experiments were carried out to observe the effect of a magnetic field and grid biasing voltage in presence of a plasma bubble in a magnetized, filamentary discharge plasma system. A spherical mesh grid of 80% optical transparency was negatively biased and introduced into the plasma for creating a plasma bubble. Diagnostics via an electrical Langmuir probe and a hot emissive probe were extensively used for scanning the plasma bubble. Plasma floating potential fluctuations were measured at three different positions of the plasma bubble. The instability in the pattern showed the dynamic transition from periodic to chaotic for increasing magnetic fields. Time scale analysis using continuous wavelet transform was carried out to identify the presence of non‐linearity from the contour plots. The mechanisms of the low‐frequency instabilities along with the transition to chaos could be qualitatively explained. Non‐linear techniques such as fast Fourier transform, phase space plot, and recurrence plot were used to explore the dynamics of the system appearing during plasma fluctuations. In order to demonstrate the observed chaotic phenomena in this study, characteristics of chaos such as the Lyapunov exponent were obtained from experimental time series data. The experimentally observed potential structure is confirmed with numerical analysis based on fluid hydrodynamics.     

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.     

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

This paper studies an (n+4)-dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infected-susceptible and virus-susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.     

A mixed hp FEM for the approximation of fourth‐order singularly perturbed problems on smooth domains

We consider fourth‐order singularly perturbed problems posed on smooth domains and the approximation of their solution by a mixed Finite Element Method on the so‐called Spectral Boundary Layer Mesh. We show that the method converges uniformly, with respect to the singular perturbation parameter, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrate our theoretical findings.     

The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

A computational method for geometric optimization of enhanced heat transfer devices based upon entropy generation minimization

A computational fluid dynamics‐based optimization methodology is developed, appropriate for the geometric optimization of enhanced heat transfer devices based upon the principle of entropy generation minimization, in which the objective function is evaluated from a flow field obtained by computational simulation. A quasi‐Newton optimization procedure is employed, with computation of the objective function gradients based upon a finite difference approach. The optimization procedure is developed to be general with regard to the choice of objective function, the details of the problem under consideration, and the computational methodology employed in solving the fluid flow and heat transfer problems. A novel implementation of a Taylor series‐based procedure for the fast solution of nearby problems is presented, which is found to greatly benefit the efficiency of the present methodology. Finally, a numerical experiment is presented, illustrating the use of the present method in the geometric optimization of a practical enhanced heat transfer device on the basis of the criterion of entropy generation minimization. The optimization of the fin spacing of a simple plate fin heat sink is considered, and a comparison of the computational results with results obtained by analytical optimization based upon empirical friction factor and Nusselt number correlations is given. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of RBFs for volume data interpolation in CFD

A greedy method for choosing an optimum reduced set of control points is integrated with RBF interpolation and evaluated for the purpose of interpolating large‐volume data sets in CFD. Given a function defined at a set of points, the greedy method selects a small subset of these points that is sufficient to keep the interpolation error at all the remaining points below a chosen bound. This is equivalent to a type of data compression and would have useful storage, post‐processing, and computational applications in CFD. To test the method in terms of both the point selection scheme and the suitability of reduced control point volume interpolation, a trial application of the interpolation to velocity fields in CFD volume meshes is considered. To optimise the point selection process, and attempt to be able to capture multiple length scales, a variable support radius formulation has also been included. Structured and unstructured mesh cases are considered for aerofoils, a wing case and a wing‐body case. For smooth volume functions, the method is shown to work well, producing accurate velocity interpolations using a very small number of the cells in the mesh. For general complex fields including large gradients, the method is still shown to be effective, although large gradients require more interpolation points to be used.Copyright © 2013 John Wiley & Sons, Ltd.     

Exact pressure integrations on submerged bodies in waves using a quadtree adaptive mesh algorithm

The development of an adaptive free surface, mesh cutting, methodology, in order to analytically integrate pressures on varying wet parts of partially submerged surfaces in the presence of waves, is presented. Given a function of free‐surface elevation, the algorithm checks for the intersection of the body with the free surface and, based on user‐defined parameters, modifies the initial mesh, by subdividing the elements where necessary and eliminating others, via a quadtree approach. Redundant sub‐divisions, generated in the quad‐division process, are partially eliminated, but the quadrilateral nature of the elements is always kept. The free‐surface function must be single‐valued and its definition domain simply connected. Hydrostatic and Froude–Krylov forces are computed exactly on each panel by means of analytical formulations, which are derived and presented, based on the theory of linear gravity waves and from applying Green's theorem. Copyright © 2014 John Wiley & Sons, Ltd.     

A high‐order element based adaptive mesh refinement strategy for three‐dimensional unstructured grid

Adaptive mesh refinement (AMR) shows attractive properties in automatically refining the flow region of interest, and with AMR, better prediction can be obtained with much less labor work and cost compared to manually remeshing or the global mesh refinement. Cartesian AMR is well established; however, AMR on hybrid unstructured mesh, which is heavily used in the high‐Reynolds number flow simulation, is less matured and existing methods may result in degraded mesh quality, which mostly happens in the boundary layer or near the sharp geometric features. User intervention or additional constraints, such as freezing all boundary layer elements or refining the whole boundary layer, are required to assist the refinement process. In this work, a novel AMR strategy is developed to handle existing difficulties. In the new method, high‐order unstructured elements are first generated based on the baseline mesh; then the refinement is conducted in the parametric space; at last, the mesh suitable for the solver is output. Generating refined elements in the parametric space with high‐order elements is the key of this method and this helps to guarantee both the accuracy and robustness. With the current method, 3‐dimensional hybrid unstructured mesh of huge size and complex geometry can be automatically refined, without user intervention nor additional constraints. With test cases including the 2‐dimensional airfoil and 3‐dimensional full aircraft, the current AMR method proves to be accurate, simple, and robust.