An adaptive continuation-multigrid method for the balanced vortex model

Obtaining solutions of the Eliassen balanced vortex model requires solving an invertibility relation, which is a nonlinear elliptic problem of the Monge-Ampere type. Multigrid techniques for this problem are investigated. An adaptive algorithm which combines the full multigrid method with continuation in a parameter related to the strength of the forcing is developed. Numerical results demonstrate the efficiency and robustness of this algorithm.     

Simulation of viscous flows with undulatory boundaries. Part I: Basic solver

A numerical method for the simulation of viscous flows with undulatory walls and free surfaces is presented. The simulation domain is discretized by a boundary-fitted and time-dependent grid. The Navier–Stokes equations, subject to fully nonlinear kinematic and dynamic boundary conditions at the free surface and no-slip boundary condition at the wall, are simulated by a hybrid pseudo-spectral and finite difference method in space and a semi-implicit fractional-step method in time. The performance of the method is demonstrated by a series of test cases including flows over wavy boundaries, various surface waves, and interaction between vortices and free surfaces. Validation by convergence test and extensive comparisons with previous theoretical, experimental, and numerical studies indicate the accuracy and efficiency of the method. Finally, a simulation example of turbulence and free surface interaction is presented. Results show that the rich features of the free surface such as surface waves, splats, anti-splats, dimples, and scars are captured accurately. Characteristic vortical structures and variation of turbulence statistics in the near-surface region are also elucidated.     

A multi-scale simulation method for high Reynolds number wall-bounded turbulent flows

We present an assessment and enhancement of the hybrid two-level large-eddy simulation method (A.G. Gungor and S. Menon, A new two-scale model for large eddy simulation of wall-bounded flows, Prog. Aerosp. Sci. 46 (2010), pp. 28–45), a multi-scale formulation for simulation of high Reynolds number wall-bounded turbulent flows. The assessment of the method is performed by examining role of static and dynamic blending functions used to perform hybridisation of two-level simulation (K. Kemenov and S. Menon, Explicit small-scale velocity simulation for high-Re turbulent flows, J. Comput. Phys. 220 (2006), pp. 290–311; K. Kemenov and S. Menon, Explicit small-scale velocity simulation for high-Re turbulent flows. Part 2: Non-homogeneous flows, J. Comput. Phys. 222 (2007), pp. 673–701) and large-eddy simulation methods. The sensitivity of first- and second-order turbulence statistics to the type of blending functions is investigated by simulating a fully developed turbulent flow in a channel at a friction Reynolds number Re_τ = 395 and comparing the results with those obtained using a direct numerical simulation. The first-order statistics do not show any significant differences for different blending functions, but the second-order statistics show some minor differences. The dynamic evaluation of the hybrid region and the blending function is necessary for non-equilibrium and complex flows where use of a static blending function can lead to inaccurate results. We propose two criteria for the dynamic evaluation; first evaluates extent of the hybrid region based on the subgrid turbulent kinetic energy and the second estimates the blending function based on a characteristic length scale. The computational efficiency of the method is enhanced by incorporating a hybrid programming paradigm where a standard domain decomposition by the message-passing-interface library is combined with the open multi-processing based parallelisation. A further enhancement of the method is achieved by incorporating a closure model for the unclosed hybrid terms in the governing equations, which appear due to hybridisation of two-level- and large-eddy-simulation methods. The model is based on an order of magnitude approximation and a preliminary assessment of the model shows improvement of turbulence statistics when used to simulate turbulent flow in a periodic channel. The assessment and improvements to the multi-scale method make it more suitable for simulation of practical wall-bounded turbulent flows at higher Reynolds number than a conventional large-eddy simulation. This is demonstrated by simulating two representative cases; turbulent flow at high Reynolds number in a periodic channel and flow over a bump placed on the lower surface of a channel, where a relatively coarser computational grid is found to be sufficient for reasonably accurate results.     

A comparison of vortex and pseudo-spectral methods for the simulation of periodic vortical flows at high Reynolds numbers

We present a validation study for the hybrid particle-mesh vortex method against a pseudo-spectral method for the Taylor–Green vortex at Re_Γ = 1600 as well as in the collision of two antiparallel vortex tubes at Re_Γ = 10,000. In this study we present diagnostics such as energy spectra and enstrophy as computed by both methods as well as point-wise comparisons of the vorticity field. Using a fourth order accurate kernel for interpolation between the particles and the mesh, the results of the hybrid vortex method and of the pseudo-spectral method agree well in both flow cases. For the Taylor–Green vortex, the vorticity contours computed by both methods around the time of the energy dissipation peak overlap. The energy spectrum shows that only the smallest length scales in the flow are not captured by the vortex method.In the second flow case, where we compute the collision of two anti-parallel vortex tubes at Reynolds number 10,000, the vortex method results and the pseudo-spectral method results are in very good agreement up to and including the first reconnection of the tubes. The maximum error in the effective viscosity is about 2.5% for the vortex method and about 1% for the pseudo-spectral method. At later times the flows computed with the different methods show the same qualitative features, but the quantitative agreement on vortical structures is lost.     

A hybrid method for hydrodynamic-kinetic flow Part I: A particle-grid method for reducing stochastic noise in kinetic regimes

In this work we present a hybrid particle-grid Monte Carlo method for the Boltzmann equation, which is characterized by a significant reduction of the stochastic noise in the kinetic regime.     

Correlation algorithm for computing the velocity fields in microchannel flows with high resolution

A cross-correlation algorithm, which enables the obtaining of the velocity field in the flow with a spatial resolution up to a single pixel per vector, has been realized in the work. It gives new information about the structure of microflows as well as increases considerably the accuracy of the measurement of the flow velocity field. In addition, the realized algorithm renders information about the velocity fluctuations in the flow structure. The algorithm was tested on synthetic data at a different number of test images the velocity distribution on which was specified by the Siemens star. The experimental validation was done on the data provided within the international project “4th International PIV Challenge”. Besides, a detailed comparison with the Particle Image Velocimetry algorithm, which was realized previously, was carried out.     

Dichromated gelatin for volume holographic recording with high sensitivity. Part I

Dichromated gelatin would be the most suitable irreversible medium for holographic recording but for its low sensitivity. The efficiency of the photoinduced reduction of the chromium ion increases considerably if superfine grains of silver halide crystals are present in the layer. The light sensitivity achieved is about 10 times better than that of dichromated gelatin layers, obtained and processed in the conventional way.     

航空图像高分辨率放大的小波方法研究

航空图像由于航空CCD相机距景物较远,所以图像分辨率较低。为了获得较高分辨率的数字图像,传统的方法就是要对原数字图像进行插值放大。提出了一种基于二维离散小波的图像放大方法,与传统插值方法相比,此方法既放大了图像、提高了分辨率,同时又保持了原始图像的细节特征。从实验结果来看,此方法是一种较好的提高航空图像分辨率的方法。     

A Physicist for All Seasons: Part I

The first part of this interview covers Frank Oppenheimer’s childhood, family background, and early education in New York City; his deep lifelong bond to his older brother Robert; his undergraduate years at Johns Hopkins University (1930–1933); his stays at the Cavendish Laboratory in Cambridge, England, and at the University of Florence, Italy (1933–1935); his graduate studies at the California Institute of Technology (1935–1939); his postdoctoral assistantship at Stanford University (1939–1941); and the frequent summers he spent in New Mexico with his brother, family, and friends.     

A special class of stationary flows for two-dimensional euler equations: A statistical mechanics description. Part II

We continue and conclude our analysis started in Part I (see [CLMP]) by discussing the microcanonical Gibbs measure associated to a N-vortex system in a bounded domain. We investigate the Mean-Field limit for such a system and study the corresponding Microcanonnical Variational Principle for the Mean-Field equation. We discuss and achieve the equivalence of the ensembles for domains in which we have the concentration at (–8)⁺ in the canonical framework. In this case we have the uniqueness of the solutions of the Mean-Field equation. For the other kind of domains, for large values of the energy, there is no equivalence, the entropy is not a concave function of the energy, and the Mean-field equation has more than one solution. In both situations, we have concentration when the energy diverges. The Microcanonical Mean Field Limit for the N-vortex system is proven in the case of equivalence of ensembles.Communicated by J.L. Lebowitz     

A high resolution sonar for sea-bed imaging

A sonar system for making three-dimensional topographic images of the sea-bed is described. The system applies a sectorial scan within each range cell by electronic beam forming. It is designed to resolve 128 beams each separated by 0.5° to cover a 64° sector. The beam forming is facilitated by a real-time Fourier transform of the signal samples from the multielement receiving transducer array. The Fourier transform is implemented as a chirp transform using surface acoustic wave reflective array devices.The design and measured performance of the transducers, and the beam former are discussed in some detail.     

hp-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel analysis

The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space–time discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the p-multigrid. The performance of the hp-MGS algorithm is further improved using semi-coarsening in combination with a new semi-implicit Runge–Kutta method as smoother. A detailed multilevel analysis of the hp-MGS algorithm is presented to obtain more insight into the theoretical performance of the algorithm. As model problem a fourth order accurate space–time discontinuous Galerkin discretization of the advection–diffusion equation is considered. The multilevel analysis shows that the hp-MGS algorithm has excellent convergence rates, both for steady state and time-dependent problems, and low and high cell Reynolds numbers, including highly stretched meshes.     

A fourth-order divergence-free method for MHD flows

This paper extends our previous third-order method [S. Li, High order central scheme on overlapping cells for magneto-hydrodynamic flows with and without constrained transport method, J. Comput. Phys. 227 (2008) 7368–7393] to the fourth-order. Central finite-volume schemes on overlapping grid are used for both the volume-averaged variables and the face-averaged magnetic field. The magnetic field at the cell boundaries falls within the dual grid and is naturally continuous so that our method eliminates the instability triggered by the discontinuity in the normal component of the magnetic field. Our fourth-order scheme has much smaller numerical dissipation than the third-order scheme. The divergence-free condition of the magnetic field is preserved by our fourth-order divergence-free reconstruction and the constrained transport method. Numerical examples show that the divergence-free condition is essential to the accuracy of the method when a limiter is used in the reconstruction. The high-order, low-dissipation, and divergence-free properties of this method make it an ideal tool for direct magneto-hydrodynamic turbulence simulations.     

一种异步非正交跳频网台盲分选方法

提出了一种新体制跳频网台盲分选方法,针对跳频通信异步非正交组网方式,将基于最大信噪比算法的盲源分离技术应用于跳频网台分选。建立了跳频网台盲分选仿真数学模型并进行了多跳频网台分选仿真。仿真结果验证了盲源分离技术应用在跳频网台分选中的可行性和有效性,得出了跳频网台盲分选方法对异步非正交组网方式的分选性能。     

Stabilized finite element method for incompressible flows with high Reynolds number

In the following paper, we discuss the exhaustive use and implementation of stabilization finite element methods for the resolution of the 3D time-dependent incompressible Navier–Stokes equations. The proposed method starts by the use of a finite element variational multiscale (VMS) method, which consists in here of a decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales. This choice of decomposition is shown to be favorable for simulating flows at high Reynolds number. We explore the behaviour and accuracy of the proposed approximation on three test cases. First, the lid-driven square cavity at Reynolds number up to 50,000 is compared with the highly resolved numerical simulations and second, the lid-driven cubic cavity up to Re = 12,000 is compared with the experimental data. Finally, we study the flow over a 2D backward-facing step at Re = 42,000. Results show that the present implementation is able to exhibit good stability and accuracy properties for high Reynolds number flows with unstructured meshes.     

A linear nonconforming finite element method for Maxwell’s equations in two dimensions. Part I: Frequency domain

We suggest a linear nonconforming triangular element for Maxwell’s equations and test it in the context of the vector Helmholtz equation. The element uses discontinuous normal fields and tangential fields with continuity at the midpoint of the element sides, an approximation related to the Crouzeix–Raviart element for Stokes. The element is stabilized using the jump of the tangential fields, giving us a free parameter to decide. We give dispersion relations for different stability parameters and give some numerical examples, where the results converge quadratically with the mesh size for problems with smooth boundaries. The proposed element is free from spurious solutions and, for cavity eigenvalue problems, the eigenfrequencies that correspond to well-resolved eigenmodes are reproduced with the correct multiplicity.     

High order multi-moment constrained finite volume method. Part I: Basic formulation

A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests.     

A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part I: On a rectangular collocated grid system

A consistent, conservative and accurate scheme has been designed to calculate the current density and the Lorentz force by solving the electrical potential equation for magnetohydrodynamics (MHD) at low magnetic Reynolds numbers and high Hartmann numbers on a finite-volume structured collocated grid. In this collocated grid, velocity (u), pressure (p), and electrical potential (φ) are located in the grid center, while current fluxes are located on the cell faces. The calculation of current fluxes on the cell faces is conducted using a conservative scheme, which is consistent with the discretization scheme for the solution of electrical potential Poisson equation. A conservative interpolation is used to get the current density at the cell center, which is used to conduct the calculation of Lorentz force at the cell center for momentum equations. We will show that both “conservative” and “consistent” are important properties of the scheme to get an accurate result for high Hartmann number MHD flows with a strongly non-uniform mesh employed to resolve the Hartmann layers and side layers of Hunt’s conductive walls and Shercliff’s insulated walls. A general second-order projection method has been developed for the incompressible Navier–Stokes equations with the Lorentz force included. This projection method can accurately balance the pressure term and the Lorentz force for a fully developed core flow. This method can also simplify the pressure boundary conditions for MHD flows.     

A multi-moment vortex method for 2D viscous fluids

In this paper we introduce simplified, exact, combinatorial formulas that arise in the vortex interaction model found in [33]. These combinatorial formulas allow for the efficient implementation and development of a new multi-moment vortex method (MMVM) using a Hermite expansion to simulate 2D vorticity. The method naturally allows the particles to deform and become highly anisotropic as they evolve without the added cost of computing the non-local Biot–Savart integral. We present three examples using MMVM. We first focus our attention on the implementation of a single particle, large number of Hermite moments case, in the context of quadrupole perturbations of the Lamb–Oseen vortex. At smaller perturbation values, we show the method captures the shear diffusion mechanism and the rapid relaxation (on Re^1/3 time scale) to an axisymmetric state. We then present two more examples of the full multi-moment vortex method and discuss the results in the context of classic vortex methods. We perform numerical tests of convergence of the single particle method and show that at least in simple cases the method exhibits the exponential convergence typical of spectral methods. Lastly, we numerically investigate the spatial accuracy improvement from the inclusion of higher Hermite moments in the full MMVM.     

A simple extended source for high resolution holography

As a simple realization of an extended source in high resolution holography spheres made of homogeneous glass are treated experimentally and theoretically. A matrix of such glass balls has been used for producing point holograms for multiple imaging systems. Using spatially incoherent light in the imaging process, the squared absolute value of the autocorrelation function of the wave front in the focus of the spheres determines the image resolution. The measured resolution of about 1.5 μm agrees with the value expected from the measured and calculated autocorrelation width.