A low communication and large time step explicit finite-volume solver for non-hydrostatic atmospheric dynamics

An explicit finite-volume solver is proposed for numerical simulation of non-hydrostatic atmospheric dynamics with promise for efficiency on massively parallel machines via low communication needs and large time steps. Solving the governing equations with a single stage lowers communication, and using the method of characteristics to follow information as it propagates enables large time steps. Using a non-oscillatory interpolant, the method is stable without post-hoc filtering. Characteristic variables (built from interface flux vectors) are integrated upstream from interfaces along their trajectories to compute time-averaged fluxes over a time step. Thus we call this method a Flux-Based Characteristic Semi-Lagrangian (FBCSL) method. Multidimensionality is achieved via a second-order accurate Strang operator splitting. Spatial accuracy is achieved via the third- to fifth-order accurate Weighted Essentially Non-Oscillatory (WENO) interpolant.We implement the theory to form a 2-D non-hydrostatic compressible (Euler system) atmospheric model in which standard test cases confirm accuracy and stability. We maintain stability with time steps larger than CFL = 1 (CFL number determined by the acoustic wave speed, not advection) but note that accuracy degrades unacceptably for most cases with CFL > 2. For the smoothest test case, we ran out to CFL = 7 to investigate the error associated with simulation at large CFL number time steps. Analysis suggests improvement of trajectory computations will improve error for large CFL numbers.     

Realizable high-order finite-volume schemes for quadrature-based moment methods

Dilute gas–particle flows can be described by a kinetic equation containing terms for spatial transport, gravity, fluid drag and particle–particle collisions. However, direct numerical solution of kinetic equations is often infeasible because of the large number of independent variables. An alternative is to reformulate the problem in terms of the moments of the velocity distribution. Recently, a quadrature-based moment method was derived for approximating solutions to kinetic equations. The success of the new method is based on a moment-inversion algorithm that is used to calculate non-negative weights and abscissas from the moments. The moment-inversion algorithm does not work if the moments are non-realizable, which might lead to negative weights. It has been recently shown [14] that realizability is guaranteed only with the 1st-order finite-volume scheme that has an inherent problem of excessive numerical diffusion. The use of high-order finite-volume schemes may lead to non-realizable moments. In the present work, realizability of the finite-volume schemes in both space and time is discussed for the 1st time. A generalized idea for developing realizable high-order finite-volume schemes for quadrature-based moment methods is presented. These finite-volume schemes give remarkable improvement in the solutions for a certain class of problems. It is also shown that the standard Runge–Kutta time-integration schemes do not guarantee realizability. However, realizability can be guaranteed if strong stability-preserving (SSP) Runge–Kutta schemes are used. Numerical results are presented on both Cartesian and triangular meshes.     

A high-order low-dispersion symmetry-preserving finite-volume method for compressible flow on curvilinear grids

A new high-order finite-volume method is presented that preserves the skew symmetry of convection for the compressible flow equations. The method is intended for Large-Eddy Simulations (LES) of compressible turbulent flows, in particular in the context of hybrid RANS–LES computations. The method is fourth-order accurate and has low numerical dissipation and dispersion. Due to the finite-volume approach, mass, momentum, and total energy are locally conserved. Furthermore, the skew-symmetry preservation implies that kinetic energy, sound-velocity, and internal energy are all locally conserved by convection as well. The method is unique in that all these properties hold on non-uniform, curvilinear, structured grids. Due to the conservation of kinetic energy, there is no spurious production or dissipation of kinetic energy stemming from the discretization of convection. This enhances the numerical stability and reduces the possible interference of numerical errors with the subgrid-scale model. By minimizing the numerical dispersion, the numerical errors are reduced by an order of magnitude compared to a standard fourth-order finite-volume method.     

A nonlinear dynamical model for atmospheric boundary layer turbulence

Using the qualitative theory of nonlinear dynamical systems and the ergodic theory of chaos and strange attractors, we study a truncated-spectrum model of dynamical equations of the atmosphere. In the parameter plane (Re, Ri), the atmospheric motion states can be divided into four regions: O (basic), P (periodic), T (turbulent or chaotic), and T-P (transition of T and P). We analyze the routes to turbulence during the day and at night. Finally, we discuss the physical aspects of the occurrence of turbulence.     

A perspective on high-order methods in computational fluid dynamics

There has been an intensive international effort to develop high-order Computational Fluid Dynamics(CFD) methods into design tools in aerospace engineering during the last one and half decades. These methods offer the potential to significantly improve solution accuracy and efficiency for vortex dominated turbulent flows. Enough progresses have been made in algorithm development, mesh generation and parallel computing that these methods are on the verge of being applied in a production design environment. Since many review papers have been written on the subject, I decide to offer a personal perspective on the state-of-the-art in high-order CFD methods and the challenges that must be overcome.     

A nonlocal Burgers equation in atmospheric dynamical system and its exact solutions

From a two-vortex interaction model in atmospheric and oceanic systems, a nonlocal counterpart with shifted parity and delayed time reversal is derived by a simple AB reduction. To obtain some approximate analytic solutions of this nonlocal system, the multi-scale expansion method is applied to get an AB-Burgers system. Various exact solutions of the AB-Burgers equation, including elliptic periodic waves, kink waves and solitary waves, are obtained and shown graphically.To show the applications of these solutions in describing correlated events, a simple approximate solution for the two-vortex interaction model is given to show two correlated dipole blocking events at two different places. Furthermore, symmetry reduction solutions of the nonlocal AB-Burgers equation are also given by using the standard Lie symmetry method.     

A horizontal atmospheric temperature sounder: Applications to remote sensing of atmospheric hazards

Several atmospheric hazards, including wind shear, clear-air turbulence, and wake vortices cause special problems for aircraft. These phenomena are usually characterized by a change in temperature relative to ambient, which may be detected by a millimeter wave radiometer operating on an absorption line in the atmosphere. Because of available componentry with excellent performance and relative freedom from interference by water vapor, the family of oxygen absorptions centered near 60 GHz is considered the best atmospheric feature on which the design of such an instrument could be based. This paper describes a multi-channel radiometer operating near 60 GHz which should be capable of detecting the hazards mentioned above as well as other potential dangers such as the passage of strong fronts and other severe weather. It is shown that a carefully designed instrument will be capable of measuring range to a hazard to an accuracy of about 5 percent and temperature difference to an accuracy of approximately half the actual measured difference, depending on range and temperature. An actual design is proposed, and graphs of expected performance are included.     

Preequilibrium emission in heavy ion collisions: A dynamical approach

A coupled treatment of both dynamics and G.D.H. Model is proposed to treat “prior equilibration” phase in heavy ion collisions. Assumptions and coupling effects are discussed in details, and a numerical procedure is developped. Comparison with²⁷A1(¹⁴N,X) at energies standing from 7–30 MeV/nucleon is presented. Proton and helium 4 productions, angle integrated spectra and angular distributions are compared. Incomplete fusion to fusion ratio is correctly reproduced in the intermediate incident energy region. A part of the linear momentum lost can be explained and a non negligeable transverse momentum is predicted for the fusion events. Differents types of experimental data are needed to test the validity of this approach and further developments are discussed.     

Continuous and discontinuous Galerkin methods for a scalable three-dimensional nonhydrostatic atmospheric model: Limited-area mode

This paper describes a unified, element based Galerkin (EBG) framework for a three-dimensional, nonhydrostatic model for the atmosphere. In general, EBG methods possess high-order accuracy, geometric flexibility, excellent dispersion properties and good scalability. Our nonhydrostatic model, based on the compressible Euler equations, is appropriate for both limited-area and global atmospheric simulations. Both a continuous Galerkin (CG), or spectral element, and discontinuous Galerkin (DG) model are considered using hexahedral elements. The formulation is suitable for both global and limited-area atmospheric modeling, although we restrict our attention to 3D limited-area phenomena in this study; global atmospheric simulations will be presented in a follow-up paper. Domain decomposition and communication algorithms used by both our CG and DG models are presented. The communication volume and exchange algorithms for CG and DG are compared and contrasted. Numerical verification of the model was performed using two test cases: flow past a 3D mountain and buoyant convection of a bubble in a neutral atmosphere; these tests indicate that both CG and DG can simulate the necessary physics of dry atmospheric dynamics. Scalability of both methods is shown up to 8192 CPU cores, with near ideal scaling for DG up to 32,768 cores.     

Venus atmospheric waves: A challenge for nonlinear dynamics

Planetary-scale cloud patterns seen in ultraviolet images of Venus are produced by atmospheric waves traveling slowly with respect to the cloud-top winds. The cloud features often combine to produce a dark horizontal “Y” shape that encircles the planet. Linear wave theory and detailed observations of the waves show that the “Y” is a combination of two components-a midlatitude wave traveling somewhat slower than the winds and an equatorial wave moving slightly faster. However, nonlinear effects must be invoked in order to couple the two modes in such a way as to reproduce the observations.     

Finite-time rotation number: A fast indicator for chaotic dynamical structures

Lagrangian coherent structures are effective barriers, sticky regions, that separate chaotic phase space regions of different dynamical behavior. The usual way to detect such structures is by calculating finite-time Lyapunov exponents. We show that similar results can be obtained for time-periodic systems by calculating finite-time rotation numbers, which are faster to compute. We illustrate our claim by considering examples of continuous- and discrete-time dynamical systems of physical interest.     

Doping induced disorder in trans-polyacetylene: A spectroscopic and dynamical study

The results of lattice dynamical calculations on pristine and doped trans- polyacetylene are summarized and a reinterpretation of the vibrational spectrum is suggested. The possibility of the existence in the doped system of a centrosymmetrical molecular defect, consistent with the infrared spectrum, alternative to the soliton defect is discussed.     

离子与生物分子相互作用的微观动力学理论

对X射线、γ射线、电子、中子、质子和重离子等对生物体系的辐照研究现状进行了评论。重离子辐照中特有的倒转深度剂量分布,即Bragg峰,成为放射治疗的理想工具。通过对重离子辐照生物组织物理过程的分析,提出了重离子与生物分子相互作用的三步物理过程,即核相互作用导致的核碎裂、库仑相互作用的电子激发和生物分子在周围环境相互作用下的弛豫,最终导致生物分子新结构的形成。由于物理过程是后期辐照化学过程、生物过程的基础,因此建立描述离子与生物分子相互作用物理过程的微观动力学理论是十分迫切的。The status of studying biology system therapy with X-rays, γ-rays, neutron, proton, and heavy ions is reviewed. The depth dose profile, called Bragg profile, makes heavy ion an ideal tool for radiotherapy. The physical process of therapy with heavy ions is analyzed and a 3-step interaction processes of heavy ions with biomolecules is proposed, that is, nuclear fragmentation in nuclear interaction, electron excitation in Coulomb interaction, and the biomolecules relaxation in surroundings, finally leads to a new structure of biomolecule. Since this physical process is the base of the following chemical process and biological process, a dynamical microscopic approach is strongly demanded to be built.     

A general fractional-order dynamical network: synchronization behavior and state tuning

A general fractional-order dynamical network model for synchronization behavior is proposed. Different from previous integer-order dynamical networks, the model is made up of coupled units described by fractional differential equations, where the connections between individual units are nondiffusive and nonlinear. We show that the synchronous behavior of such a network cannot only occur, but also be dramatically different from the behavior of its constituent units. In particular, we find that simple behavior can emerge as synchronized dynamics although the isolated units evolve chaotically. Conversely, individually simple units can display chaotic attractors when the network synchronizes. We also present an easily checked criterion for synchronization depending only on the eigenvalues distribution of a decomposition matrix and the fractional orders. The analytic results are complemented with numerical simulations for two networks whose nodes are governed by fractional-order Lorenz dynamics and fractional-order Ro?ssler dynamics, respectively.     

Heat pulse propagation in a crystal: A molecular dynamical calculation

The propagation of a heat pulse into a perfect bcc crystal is studied by means of molecular dynamical calculations. We observe second sound waves associated with the heat pulse as well as with longitudinal and transverse elastic pulses. Our results explain a number of features observed in second sound experiments and suggest that second sound is a phenomenon of general occurrence.     

Mott-Hubbard transition and Anderson localization: A generalized dynamical mean-field theory approach

The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition. The text was submitted by the authors in English.     

Phonon dispersion of d and f shell metals: A dynamical treatment

The effective pair potential is written as the sum of s-s, d-d, s-d, f-f and s-f contributions. The free electron part of the pair potential is obtained in second-order perturbation theory using rational dielectric function (RDF) in conjunction with Heine-Abarenkov model pseudopotential (HAMP). The exchange-correlation corrections due to Taylor are inherent to RDF. The overlap between d states and f states on different ions and the effect of sd and hybridization are included in an approximate manner, as has been suggested by Wills and Harrison [Phys. Rev. B 28 (1983) 4363], and Harrison [ibid., 550]. An approximate temperature dependence has been included in the effective potential through an asymptotic factor. The ion-ion interaction so defined is used to calculate the phonon dispersion curves for hcp metals Tb and Ho. The calculated phonon frequencies are found to be real and in reasonably good agreement with the neutron inelastic scattering measurements which establishes the validity of the effective pair potential for rare earths.