超声速、高超声速粘性气体分离流动的显隐式差分解法

本文利用反扩散的两步显、隐式差分方法,求解了超声速、高超声速粘性气体绕二维、三维压缩拐角的层流和湍流分离运动.结果表明,它既能获得很好的精度,又能大大缩短计算机时.     

Acceleration of Plasma in Coaxial Channels with Preshaped Electrodes and Longitudinal Magnetic Field

The paper presents a mathematical model and results of numerical simulation of axisymmetric plasma flows in nozzle-type channels formed by two coaxial electrodes. Transonic accelerated flows, which are of interest for the development of plasma accelerators, are considered. The mathematical apparatus of the models are two-dimensional MHD problems solved numerically, the steady-state solutions of which are obtained in the process of relaxation. Some characteristics of the flow in narrow tubes between close trajectories are considered in the quasi-one-dimensional approximation. The main attention is paid to the influence of the longitudinal magnetic field and the curvilinear geometry of the electrodes on the properties of accelerated flows.     

<Emphasis Type="Italic">R</Emphasis>-function method in boundary-value problems of magnetic hydrodynamics with a small parameter at higher derivatives

Using the R -function method, we construct mathematical and computer models of magnetohydrodynamic flows for different types of boundary conditions in an electromagnetic pump. Numerical experiments are performed. The representation of the geometric information and physical constants in the form of literal parameters enables us to perform multivariant computations and investigate their influence on the field pattern.     

BEM-based numerical study of three-dimensional compressible bubble dynamics in stokes flow

The dynamics of compressible gas bubbles in a viscous shear flow and an acoustic field at low Reynolds numbers is studied. The numerical approach is based on the boundary element method (BEM), which is effective as applied to the three-dimensional simulation of bubble deformation. However, the application of the conventional BEM to compressible bubble dynamics faces difficulties caused by the degeneration of the resulting algebraic system. Additional relations based on the Lorentz reciprocity principle are used to cope with this problem. Test computations of the dynamics of a single bubble and bubble clusters in acoustic fields and shear flows are presented.     

Numerical algorithm for moving-boundary fluid dynamics problems and its testing

A new Eulerian algorithm is proposed for computing incompressible flows with moving boundaries of arbitrary geometry. The algorithm can be regarded as an extension of Hirt’s classical volume-of-fluid method. The results of its implementation and testing are presented. A comparison of the numerical results with experimental data and computations of other authors reveals good agreement.     

Hydrodynamic action functional and absorption of electromagnetic waves in plasma

The path integration method is used to study the absorption of waves in plasma. The absorption is considered of longitudinal electromagnetic waves as a consequence of scattering on the transverse waves, which requires the introduction of an integration with respect to a supplementary field of the vector potential. The scattering on the transverse waves becomes the determining one for a one-component plasma in the long wavelength limit. The hydrodynamic action functional is constructed for a magnetized electron-ion plasma by the method of successive integration, first with respect to “fast” fields and, next, with respect to “slow” fields. The absorption of the longitudinal waves is computed with the aid of this functional. The domains of frequencies of the order of the plasma frequency and of the order of the cyclotron frequency are considered. In comparison with the case of a free plasma, here the Coulomb logarithm is varied.     

Application of the particle method to simulate one-dimensional bounded plasma with a distributed sources

We consider the behavior of a plasma bounded in the longitudinal direction by absorbing walls. The model contains charged particles (electrons and ions) moving in the direction of an external magnetic field with two velocity components: longitudinal and transverse. The charged particles are created in pairs by a distributed source. The working model is based on the electrostatic “particles in a cell” method augmented by Emmert's model for a volume source and a model of binary Coulomb particle collisions using the Monte Carlo method. Calculation results are reported for a model with electron-ion collisions and for a collisionless plasma model. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996, pp. 100–109.     

浅水流动与污染物扩散的高分辨率计算模型

将组合型TVD格式应用于守恒型的浅水方程和污染物扩散方程，建立了二者耦合求解的高分辨率有限体积计算模型。给出了溃坝水流、明渠突扩流和污染物输运计算的典型算例，并与实验数据或其它数值结果进行了比较，证实了该模型的有效性，表明它不但能处理有激波的非恒定流问题，也能较好地计算具有任意边界的一般的浅水流动和污染物扩散问题，为浅水流动和水环境模拟提供了精度高、稳定性好、普适性强的数值方法。     

Some applications of a galerkin-collocation method for boundary integral equations of the first kind

Here we apply the boundary integral method to several plane interior and exterior boundary value problems from conformal mapping, elasticity and fluid dynamics. These are reduced to equivalent boundary integral equations on the boundary curve which are Fredholm integral equations of the first kind having kernels with logarithmic singularities and defining strongly elliptic pseudodifferential operators of order - 1 which provide certain coercivity properties. The boundary integral equations are approximated by Galerkin's method using B-splines on the boundary curve in connection with an appropriate numerical quadrature, which yields a modified collocation scheme. We present a complete asymptotic error analysis for the fully discretized numerical equations which is based on superapproximation results for Galerkin's method, on consistency estimates and stability properties in connection with the illposedness of the first kind equations in L₂. We also present computational results of several numerical experiments revealing accuracy, efficiency and an amazing asymptotical agreement of the numerical with the theoretical errors. The method is used for computations of conformal mappings, exterior Stokes flows and slow viscous flows past elliptic obstacles.     

Generation of a longitudinal current by a transverse electromagnetic field in collisional degenerate plasma

From the Vlasov–Boltzmann kinetic equation for a collisional degenerate plasma, the electron distribution function is constructed in the quadratic approximation in the electric field strength. A formula for calculating the electric current is derived. It is shown that nonlinearity leads to the rise of a longitudinal electric current directed along the wave vector. The longitudinal current is orthogonal to the known transverse classical current obtained in the linear analysis. When the collision frequency tends to zero, all results obtained for a collisional plasma pass into the corresponding results for a collisionless plasma. The case of small wavenumbers is considered. It is shown that, when the collision frequency tends to zero, the expression for the current passes into the corresponding expression for the current in a collisionless plasma. Graphic analysis of the real and imaginary parts of the current density is performed. The dependence of the electromagnetic field oscillation frequency and electron–plasma-particle collision frequency on the wavenumber is studied.     

Virtual Tokamak library software

We describe the concept of the Virtual Tokamak library, its functionality, major components, and method of use. The library is designed to predict, support, and interpret experiments as well as handle measurements on tokamak instruments implementing the idea of energy production on the basis of controlled thermonuclear fusion. The library software consists of an interactive graphic shell and a number of interrelated computer codes simulating various processes in the tokamak plasma, its structural elements, diagnostics and control system. This is a specific implementation of advanced information technologies including Internet technologies and approaches of distributed computations in the field of the mathematical modeling of plasma. The Virtual Tokamak is unique in terms of combined application and system software.     

Modified fully discretized projection method for the incompressible Navier–Stokes equations

The stability and convergence of a second-order fully discretized projection method for the incompressible Navier–Stokes equations is studied. In order to update the pressure field faster, modified fully discretized projection methods are proposed. It results in a nearly second-order method. This method sacrifices a little of accuracy, but it requires much less computations at each time step. It is very appropriate for actual computations. The comparison with other methods for the driven-cavity problem is presented.     

Regularized shallow water equations for numerical simulation of flows with a moving shoreline

A numerical algorithm for simulating free-surface flows based on regularized shallow water equations is adapted to flows involving moving dry-bed areas. Well-balanced versions of the algorithm are constructed. Test computations of flows with dry-bed areas in the cases of water runup onto a plane beach and a constant-slope beach are presented. An example of tsunami simulation is given.     

Acoustic radiation force of attraction,cancellation and repulsion on a circular cylinder near a rigid corner space

The purpose of this study is to derive exact partial wave series expansions for the longitudinal and transverse radiation force components, for a circular cylinder in the proximity of a rigid corner space, and illuminated by incident plane waves with arbitrary orientation in the polar plane. Based on the multipole expansion method in cylindrical coordinates, the method of images as well as the translational addition theorem, an effective incident field (resulting from the primary waves as well as the multiple scattered fields from the image sources) is determined first, and used subsequently with the scattered field to derive the mathematical expressions for the radiation force components, stemming from the integration of the radiation stress in a non-viscous fluid. Numerical computations illustrate the analysis for rigid and soft cylinders with particular emphasis on the distances from the particle edges to the neighbouring walls, the size of the cylinder and the angle of incidence. Depending on the choice of these parameters, the radiation force components can vanish, rendering complete “invisibility”; i.e., the cylinder becomes unresponsive to the transfer of linear momentum carried by the incident effective field. Moreover, the radiation force components alternate between positive and negative values, suggesting a force of repulsion or attraction. The results find potential applications in acoustofluidics design and optimization as they shed light on the anechoic radiation force effect on a particle nearby a rigid corner. Other applications in noise and vibration control could also benefit from the results of the present investigation along with further related topics.     

Improved asymptotic predictions for the effective slip over a corrugated topography

Accurate analytical prediction of the effective slip boundary condition in shear-driven Stokes flows directed longitudinally and transversely to a one-dimensional sinusoidal no-slip topography is explored. First, the domain perturbation technique is extended through spectral analysis and symbolic computations to obtain polynomial approximations (Taylor polynomials) of arbitrary specifiable order for the effective slip length. However, when assessed for numerical accuracy against fully-resolved numerical simulations using the finite-element-method, higher order Taylor polynomials give progressively inferior predictions in comparison to lower-order ones, unless the product of amplitude and wave-number is restricted below unity. From Domb–Sykes plots, the reason for the poor accuracy of higher order Taylor polynomials is assessed to be the finite convergence radii, approximately equaling unity, of the asymptotic power series for both longitudinal and transverse flows. For either of the flows, application of Euler transformation to the expansion parameter provide polynomial-form approximations that are accurate for amplitude values exceeding the convergence radius. The slow convergence of the Euler-transformed series can be remedied through Shanks transformation, at the cost of losing the convenience of closed forms. Finally, Padé approximants are shown to provide even more accurate but still closed-form alternatives to polynomials that work accurately at amplitudes much exceeding the above-identified convergence radii.     

Fast Legendre spectral method for computing the perturbation of a gradient temperature field in an unbounded region due to the presence of two spheres

The temperature distribution around two spheres is considered when the main field has a constant gradient at infinity. Bispherical coordinates are used, together with a transformation of the dependent variable that leads to separation of variables. Then the solution can be sought in Legendre series with respect to one of the bispherical coordinates. An important element of the proposed work is the effective way to reduce an essentially 3D problem to a set of three 2D problems. The Legendre spectral method is shown to have an exponential convergence which is confirmed by the computations. The efficiency is so high that even for the hard cases of two closely situated spheres, an accuracy of 10^?10 is achieved with as few as 20 terms in the expansion. Solutions with both longitudinal and transverse gradients at infinity are obtained, and the contour lines of the temperature field are presented graphically. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

A kinetic scheme for unsteady pressurised flows in closed water pipes

The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel system of equations, and then we recall how to obtain the corresponding kinetic formulation. Then we build the kinetic scheme ensuring an upwinding of the source term due to the topography performed in a close manner described by Perthame and Simeoni (2001) [1] and Botchorishvili et al. (2003) [2] using an energetic balance at microscopic level. The validation is lastly performed in the case of a water hammer in an uniform pipe: we compare the numerical results provided by an industrial code used at EDF-CIH (France), which solves the Allievi equation (the commonly used equation for pressurised flows in pipes) by the method of characteristics, with those of the kinetic scheme. It appears that they are in a very good agreement.     

Three dimensional electromagnetic scattering T-matrix computations

The infinite T-matrix method is a powerful tool for electromagnetic scattering simulations, particularly when one is interested in changes in orientation of the scatterer with respect to the incident wave or changes of configuration of multiple scatterers and random particles, because it avoids the need to solve the fully reconfigured systems. The truncated T-matrix (for each scatterer in an ensemble) is often computed using the null-field method. The main disadvantage of the null-field based T-matrix computation is its numerical instability for particles that deviate from a sphere. For large and/or highly non-spherical particles, the null-field method based truncated T-matrix computations can become slowly convergent or even divergent. In this work, we describe an electromagnetic scattering surface integral formulation for T-matrix computations that avoids the numerical instability. The new method is based on a recently developed high-order surface integral equation algorithm for far field computations using basis functions that are tangential on a chosen non-spherical obstacle. The main focus of this work is on the mathematical details required to apply the high-order algorithm to compute a truncated T-matrix that describes the scattering properties of a chosen perfect conductor in a homogeneous medium. We numerically demonstrate the stability and convergence of the T-matrix computations for various perfect conductors using plane wave incident radiation at several low to medium frequencies and simulation of the associated radar cross of the obstacles.     

Longitudinal electric current generated by a transverse electromagnetic field in a collisional plasma

We consider a collisional plasma with an arbitrary degree of degeneration of the electron gas. The plasma is located in an external electromagnetic field. We calculate the electric current generated in the plasma by the electromagnetic field. We show that the electric current has two nonzero components. One component is a transverse current, obtained by a linear analysis. The second component is a longitudinal current directed along the wave vector and orthogonal to the transverse current. We consider the case of small wave numbers. As the collision rate tends to zero, all the derived formulas pass into formulas for a collisionless plasma. We perform a graphical investigation of the dimensionless current density depending on the wave number, the oscillation frequency of the electromagnetic field, and the rate of electron collisions with plasma particles.