Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations

Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: firstly, as building blocks in the subcell flux differencing form of Fisher and Carpenter (Technical Report NASA/TM-2013-217971, NASA, 2013; J Comput Phys 252:518–557, 2013) and secondly (enhanced by dissipation) as numerical surface fluxes in finite volume like schemes. The purpose of this article is threefold. Firstly, the flux differencing theory is extended, guaranteeing high-order for general symmetric and consistent numerical fluxes and investigating entropy stability in a generalised framework of summation-by-parts operators applicable to multiple dimensions and simplex elements. Secondly, a general procedure to construct affordable entropy conservative fluxes is described explicitly and used to derive several new fluxes. Finally, robustness properties of entropy stable numerical fluxes are investigated and positivity preservation is proven for several entropy conservative fluxes enhanced with local Lax–Friedrichs type dissipation operators. All these theoretical investigations are supplemented with numerical experiments.     

Tailoring temporal intensities at first- and second-dispersion order

We discuss a method for describing, at fractions of the Talbot length, the evolution of the complex envelope in a first-order dispersive medium, as well as in a second-order dispersive medium. We unveil closed form expressions that are useful for tailoring temporal intensities by using phase-only modulations.     

INV-WATFLX,a code for simultaneous estimation of soil properties and planar vector water flux from fully or partly functioning needles of a penta-needle heat-pulse probe

Soil thermal properties and water fluxes are fundamental for understanding water and heat transport phenomena in the vadose zone. Processes of interest include quantifying infiltration and runoff in addition to solute transport rates, which are of great interest in many scientific and engineering applications where water flux and temperature are key parameters. In this study, INV-WATFLX was developed for simultaneously fitting thermal diffusivity, thermal conductivity and heat velocities in a plane normal to a penta-needle heat-pulse probe (PHPP) using temperature rise measurements in a porous medium. The inverse problem is formulated as the minimization of a generalized least-squares criterion by means of a Gauss–Newton–Levenberg–Marquardt method. Fitted temperature measurements following a heat-pulse injection were calculated from an analytical solution of temperature rise derived at the four thermistor positions of the PHPP. The INV-WATFLX code was tested with a set of synthetic simulations using CORE^2D V4. Relative errors of thermal diffusivity, conductivity, bulk volume heat capacity, and water fluxes estimated in INV-WATFLX to their prescribed values in the synthetic simulations were smaller than 3%. We also evaluated the ability of INV-WATFLX to provide estimation of thermal properties and fluxes from temperature rise measured by a sub-set of the four thermistors. INV-WAFLX was applied to laboratory column flow experiments for water flux estimation using a PHPP. Water fluxes estimated using INV-WATFLX was comparable to independently measured fluxes. The new code provides reliable estimation of soil thermal properties and water fluxes from temperature rise using heat-pulse measurements.     

V.I.T.E.: Short-range modelling of a pollutant input

The VITE software uses a random-walk method to model the dispersive transport of pollutant plumes. Convective currents are calculated by a bidimensional hydrodynamic model and dispersive effects are described by a random velocity that is related to time and turbulent level. The evolution rates of the pollutant are taken into account by a stochastic approach. The VITE software runs on a PC computer and integrates a graphic tool that displays the simulated pollutant patch on the screen. The model is exemplified on the Thau lagoon (French Mediterranean coast).     

Dispersion relations in the nuclear optical model

We have developed a code to calculate integrals arising from the dispersion relation between the real and the imaginary parts of the nuclear optical model potential (OMP). Both, analytical solution for the most common dispersive OMP, and the general numerical solution, are included. In the numerical integration, fast convergence is achieved by means of the Gauss-Legendre integration method, which offers accuracy, easiness of implementation and generality for dispersive optical model calculations. The numerical method is validated versus analytical solution. The use of this package in the OMP parameter search codes allows for an efficient and accurate dispersive analysis.     

Unified Analysis of Leap-Frog Methods for Solving Time-Domain Maxwell’s Equations in Dispersive Media

In this paper, we consider the time dependent Maxwell’s equations resulting from dispersive medium models. First, the stability and Gauss’s law are proved for all three most popular dispersive medium models: the isotropic cold plasma, the one-pole Debye medium and the two-pole Lorentz medium. Then leap-frog mixed finite element methods are developed for these three models. Optimal error estimates are proved for all three models solved by the lowest-order Raviart-Thomas-Nédélec spaces. Extensions to multiple pole dispersive media are presented also. Numerical results confirming the analysis are presented.     

管道长距离超声导波模态频散现象的抑制方法研究

针对超声导波频散特性所导致的信号波包在结构中传播发生展宽及衰减现象，研究了超声导波在2m长管道中以特定频率(77kHz)传播时的频散现象。指出了采用圆周均匀分布传感器在管道中激励导波可以抑制其中弯曲导波模态的产生，同时利用信号重建激励方法以及所建立的实验系统在特定的距离上抑制了超声导波模态的频散现象。结果表明，本文方法有效地抑制了77kHz的L(0，1)导波模态的频散现象。     

A lattice Boltzmann model for electromagnetic waves propagating in a one-dimensional dispersive medium

A first-order extended lattice Boltzmann (LB) model with special forcing terms for one-dimensional Maxwell equations exerting on a dispersive medium, described either by the Debye or Drude model, is proposed in this study. The time dependent dispersive effect is obtained by the inverse Fourier transform of the frequency-domain permittivity and is incorporated into the LB evolution equations via equivalent forcing effects. The Chapman–Enskog multi-scale analysis is employed to ensure that proposed scheme is mathematically consistent with the targeted Maxwell’s equations at the macroscopic limit. Numerical validations are executed through simulating four representative cases to obtain their LB solutions and compare those with the analytical solutions and existing numerical solutions by finite difference time domain (FDTD). All comparisons show that the differences in numerical values are very small. The present model can thus accurately predict the dispersive effects, and demonstrate first order convergence. In addition to its accuracy, the proposed LB model is also easy to implement. Consequently, this new LB scheme is an effective approach for numerical modeling of EM waves in dispersive media.     

Top-of-atmosphere flux retrievals from CERES using artificial neural networks

The Clouds and the Earth's Radiant Energy System (CERES) instruments on the Terra spacecraft provide accurate shortwave (SW), longwave (LW) and window (WN) region top-of-atmosphere (TOA) radiance measurements from which TOA radiative flux values are obtained by applying Angular Distribution Models (ADMs). These models are developed empirically as functions of the surface and cloud properties provided by coincident high-resolution imager measurements over CERES field-of-view. However, approximately 5.6% of the CERES/Terra footprints lack sufficient imager information for a reliable scene identification. To avoid any systematic biases in regional mean radiative fluxes, it is important to provide TOA fluxes for these footprints. For this purpose, we apply a feedforward error-backpropagation Artificial Neural Network (ANN) technique to reproduce CERES/Terra ADMs relying only on CERES measurements. All-sky ANN-based angular distribution models are developed for 10 surface types separately for shortwave, longwave and window TOA flux retrievals. To optimize the ANN performance, we use a partially connected first hidden neuron layer and compact training sets with reduced data noise. We demonstrate the performance of the ANN-based ADMs by comparing TOA fluxes inferred from ANN and CERES anisotropic factors. The global annual average bias in ANN-derived fluxes relative to CERES is less than 0.5% for all ANN scene types. The maximum bias occurs over sea ice and permanent snow surfaces. For all surface types, instantaneous ANN-derived TOA fluxes are self-consistent in viewing zenith angle to within 9% for shortwave, 3.5% and 3% longwave daytime and nighttime, respectively.     

A Numerical Comparison of the Lax–Wendroff Discontinuous Galerkin Method Based on Different Numerical Fluxes

Discontinuous Galerkin (DG) method is a spatial discretization procedure, employing useful features from high-resolution finite volume schemes, such as the exact or approximate Riemann solvers serving as numerical fluxes and limiters. In [(2005). Comput. Methods Appl. Mech. Eng. 194, 4528], we developed a Lax–Wendroff time discretization procedure for the DG method (LWDG), an alternative method for time discretization to the popular total variation diminishing (TVD) Runge–Kutta time discretizations. In most of the DG papers in the literature, the Lax–Friedrichs numerical flux is used due to its simplicity, although there are many other numerical fluxes, which could also be used. In this paper, we systematically investigate the performance of the LWDG method based on different numerical fluxes, including the first-order monotone fluxes such as the Godunov flux, the Engquist–Osher flux, etc., the second-order TVD fluxes and generalized Riemann solver, with the objective of obtaining better performance by choosing suitable numerical fluxes. The detailed numerical study is mainly performed for the one-dimensional system case, addressing the issues of CPU cost, accuracy, non-oscillatory property, and resolution of discontinuities. Numerical tests are also performed for two-dimensional systems.      

Fluxplus, a microcomputer program for interactive calculation of 'in vitro' solute fluxes, uptakes and accumulations in studies of intestinal transport

A new microcomputer program for interactive comparisons, analysis and calculation of in vitro solute transepithelial fluxes and nutrient uptakes and accumulations by intestinal tissues is described. The program is written in Microsoft GWBASIC for the widely distributed IBM-PC. Flux, uptake and accumulation values are obtained by computation from initial sequential data files and stored in sequential or random-orgaized files, depending on the specific process. Computed unidirectional fluxes are saved together with their associate electrical variables. The program calculates univariate statistics for unidirectional and net fluxes, and allows comparisons between selected groups of experiments by using the Student's t-test. An homocedasticity test is also provided. Active uptake or accumulations of solutes are calculated by substracting the predicted diffusive values at a determined concentration to total uptake or accumulation and from this, kinetic parameters are computed. The program was designed to be user-friendly and includes several functions to permit the user to manage and examine stored data. Examples of outputs illustrate applications of the program.     

Transport-independent fairness

The Internet relies on cooperative endpoints to react to signals from the network that congestion is occurring. In particular, TCP interprets packet loss as a signal of congestion. However there are many new non-cooperative protocols in use which attempt to exploit the network aggressively and do not reduce their demands when the network signals congestion. We propose the aggregate control of “fluxes” defined by policies at individual routers. Each router can then calculate an optimal allocation of bandwidth to each flux contending for a given output link. We propose a combined hill climbing and convex programming method for this optimization, which we call HCCP. HCCP is designed to punish greedy fluxes rather than just regulating them: such fluxes may find their bandwidth allocation reduced to zero if they are sufficiently aggressive. Our results show that HCCP is effective at regulating a wide range of rather generally characterized transport protocols. We explore the use of both throughput maximization and proportionally fair allocation and recommend the latter because the former often leads to the situation where one or more fluxes receive zero bandwidth.     

A high-order one-step sub-cell force-based discretization for cell-centered Lagrangian hydrodynamics on polygonal grids

We present a one-step high-order cell-centered numerical scheme for solving Lagrangian hydrodynamics equations on unstructured grids. The underlying finite volume discretization is constructed through the use of the sub-cell force concept invoking conservation and thermodynamic consistency. The high-order extension is performed using a one-step discretization, wherein the fluxes are computed by means of a Taylor expansion. The time derivatives of the fluxes are obtained through the use of a node-centered solver which can be viewed as a two-dimensional extension of the Generalized Riemann Problem methodology introduced by Ben-Artzi and Falcovitz.     

Use of AVHRR-derived surface temperatures in evaluating a land–atmosphere model

The vertical transports of heat and moisture at the Earth's surface provide a critical linkage between meteorological, hydrological and ecological processes. Unfortunately, estimates of energy and water fluxes by land surface–atmosphere models are difficult to validate. This is due to the fine spatial and temporal resolution of the models, as well as a lack of widespread observations of these fluxes and other components of the surface energy budget. However, modelled fluxes of energy and water are often based largely on accurate determination of the modelled soil surface temperature. Land surface temperatures (LSTs) derived from the Advanced Very High Resolution Radiometer (AVHRR) onboard polar-orbiting satellites can be determined over large spatial extents a few times per day. They provide a means by which modelled surface temperatures, and thus modelled fluxes, can be evaluated. In this paper, two versions of the Simulator for Hydrology and Energy Exchange at the Land Surface (SHEELS) model are evaluated using AVHRR-derived LSTs. Model vegetation cover is held constant in the first version, whereas Normalized Difference Vegetation Index (NDVI) data are used to temporally modify vegetation cover in the second version. Inclusion of the NDVI data is found to decrease the bias between modelled and satellite-derived LSTs by 0.5?K. However, even with this improvement in vegetation parametrization, bias remains large (3.7?K).     

Finite-difference time-domain simulation of acoustic propagation in dispersive medium: An application to bubble clouds in the ocean

Accurate modeling of pulse propagation and scattering is a problem in many disciplines (i.e. electromagnetics and acoustics). For the case of an acoustic wave propagating in a two-dimensional non-dispersive medium, a routine 2nd order in time and space Finite-Difference Time-Domain (FDTD) scheme representation of the linear wave equation can be used to solve for the acoustic pressure. However when the medium is dispersive, one is required to take into account the frequency dependent attenuation and phase speed. Until recently to include the dispersive effects one typically solved the problem in the frequency domain and not in the time domain. The frequency domain solutions were Fourier transformed into the time domain. However by using a theory first proposed by Blackstock [D.T. Blackstock, J. Acoust. Soc. Am. 77 (1985) 2050. [1]], the linear wave equation has been modified by adding an additional term (the derivative of the convolution between the causal time-domain propagation factor and the acoustic pressure) that takes into account the dispersive nature of the medium. In the case of acoustic propagation through water, the water environment becomes strongly dispersive due to the presence of air bubbles that are present below the air-water interface.     

Arbitrary High-Order Discontinuous Galerkin Schemes for the Magnetohydrodynamic Equations

In this paper, we propose a discontinuous Galerkin scheme with arbitrary order of accuracy in space and time for the magnetohydrodynamic equations. It is based on the Arbitrary order using DERivatives (ADER) methodology: the high order time approximation is obtained by a Taylor expansion in time. In this expansion all the time derivatives are replaced by space derivatives via the Cauchy-Kovalevskaya procedure. We propose an efficient algorithm of the Cauchy-Kovalevskaya procedure in the case of the three-dimensional magneto-hydrodynamic (MHD) equations. Parallel to the time derivatives of the conservative variables the time derivatives of the fluxes are calculated. This enables the analytic time integration of the volume integral as well as that of the surface integral of the fluxes through the grid cell interfaces which occur in the discrete equations. At the cell interfaces the fluxes and all their derivatives may jump. Following the finite volume ADER approach the break up of all these jumps into the different waves are taken into account to get proper values of the fluxes at the grid cell interfaces. The approach under considerations is directly based on the expansion of the flux in time in which the leading order term may be any numerical flux calculation for the MHD-equation. Numerical convergence results for these equations up to 7th order of accuracy in space and time are shown.     

Spurious caustics of dispersion-relation-preserving schemes

A linear dispersive mechanism leading to a burst in the L _∞ norm of the error in numerical simulation of polychromatic solutions is identified. This local error pile-up corresponds to the existence of spurious caustics, which are allowed by the dispersive nature of the numerical error. From the mathematical point of view, spurious caustics are related to extrema of the numerical group velocity and are physically associated with interactions between rays defined by the characteristic lines of the discrete system. This paper extends our previous work about classical schemes to dispersion-relation preserving schemes.     

Integrated analysis of thermal and visual images for sceneinterpretation

An approach for computer perception of outdoor scenes is presented. The approach is based on integrating information extracted from thermal images and visual images, which provides information not available by processing either type of image alone. The thermal image is analyzed to provide estimates of surface temperature. The visual image provides surface absorptivity and relative orientation. These parameters are used together to provide estimates of heat fluxes at the surfaces of viewed objects. The thermal behavior of scene objects is described in terms of surface heat fluxes. Features based on estimated values of surface heat fluxes are shown to be more meaningful and specific in distinguishing scene components     

Closing horizontal groundwater fluxes with pipe network analysis: An application of the REW approach to an aquifer

The Representative Elementary Watershed (REW) approach for modeling the hydrologic response of watersheds is based on the discretization of a catchment into hydrologically sensitive control volumes. Global balance laws for mass, momentum (and energy) are formulated for the volumes. An implementation of the approach requires closing unknown REW-scale mass fluxes and forces exchanged across the REW-internal control volume boundaries and between REWs. In the present paper we focus exclusively on the horizontal groundwater flow, while neglecting other hydrological processes such as surface runoff, subsurface stormflow and surface-groundwater interaction. Here we describe a simplified groundwater modeling approach, which is based on the parsimonious estimation of mass fluxes exchanged laterally between REWs. The procedure employs principles of mass and energy conservation as stated by the Kirchhoff laws. The problem is reduced to the solution of a coupled system of linear equations in terms of inter-REW groundwater fluxes and a dimensionless ratio Θ between the local saturated zone depths y^s and spatial length scales Λ over which piezometric head gaps are dissipated. The equation system is solved by successive approximation, as suggested by the Cross method, which is used in engineering practice for resolving resistor networks under steady state conditions. The procedure converges rapidly for complex network configurations. It is shown that for given boundary fluxes imposed at the watershed edges, mass fluxes exchanged in-between REWs can be calculated in an unique and consistent fashion. The paper briefly reviews the essential governing equations, introduces the formulation of the problem in terms of the Kirchoff laws and shows the numerical solution of the network. Simulation results for an application to the Hesbaye groundwater system in Belgium are presented.     

Regularisation and the inverse problem

In this paper the task of solving the inverse photon diffusion problem in human tissue will be discussed. In such problems the optical properties of the tissue are to be determined from a knowledge of measured values of the boundary output fluxes. Measurements are, of course, normally corrupted by noise. By using a finite element model of the diffusion process and simulated noise, it is shown that the estimates obtained by minimising the sum of squares of errors in the output fluxes are biased. Alternative objective functions are discussed that overcome this difficulty and are incidentally easier to minimise. A simple upper bound is given for the amount of noise that can be permitted if reliable estimates are to be obtained.