Numerical Dispersion Analysis Research Articles

Numerical analysis of dispersion and self-phase modulation for elimination of chaotic time delay

We mainly investigate the influence of group velocity dispersion (GVD) and self-phase modulation (SPM) in single-mode fiber on chaotic time delay signature (TDS) of single feedback semiconductor laser. In the simulation, the second-order dispersion coefficient and the average input optical power in fibers are adjusted to control GVD and SPM. The results show that after the fiber length reaches the dispersion length of the chaotic laser, the chaotic TDS caused by single optical feedback begins to be suppressed due to the significant enhancement of GVD, and then the value of the autocorrelation coefficient at the chaotic TDS descends at the fastest suppression rate of 0.5 dB/km. When chaos laser propagates about 20 km in the fibers, duo to the accumulation of SPM to the significant range of action, the chaotic TDS achieves the best stable suppression state, and the suppression effect can reach 11.6 dB.

Numerical analysis of particle dispersion and deposition in coal combustion using large-eddy simulation

High-fidelity modeling provides a useful approach to investigate the particle dispersion and deposition mechanism in pulverized coal combustion. To be able to analyze these detailed mechanisms, this work couples detailed multiphysics models for poly-dispersed turbulent, particle-laden flow, particle and gas phase reaction chemistry, convective, conductive and radiative heat transfer, ash formation and deposition with a Large-Eddy Simulation (LES) approach to numerically simulate coal combustion in a downfired self-sustained oxy-fuel combustor (OFC). It is necessary to explicitly capture all but the highest frequency dynamics of the turbulence and its coupling with each of the other physical phenomena using LES. Effects of subgrid-scale unresolved turbulence on the particle motions are also analyzed by a novel Stokes number analysis. Due to the inherent relation ship between coal combustion and ash deposition, this study integrates the improved ash deposition model into the numerical simulation. Overall simulation results are compared with experimentally measured data from the OFC. The simulation and measured data for the averaged gas temperature and deposition rates agree with 5% and 28%. This study shows that high-fidelity LES coupled with other detailed multiphysics models running on a exascale computing facility can provide a good representation of complex coal combustion and deposition in a laboratory-scale furnace.

Classical and Multisymplectic Schemes for Linearized KdV Equation: Numerical Results and Dispersion Analysis

We construct three finite difference methods to solve a linearized Korteweg–de-Vries (KdV) equation with advective and dispersive terms and specified initial and boundary conditions. Two numerical experiments are considered; case 1 is when the coefficient of advection is greater than the coefficient of dispersion, while case 2 is when the coefficient of dispersion is greater than the coefficient of advection. The three finite difference methods constructed include classical, multisymplectic and a modified explicit scheme. We obtain the stability region and study the consistency and dispersion properties of the various finite difference methods for the two cases. This is one of the rare papers that analyse dispersive properties of methods for dispersive partial differential equations. The performance of the schemes are gauged over short and long propagation times. Absolute and relative errors are computed at a given time at the spatial nodes used.

Design and Dispersion Control of Microstructured Multicore Tellurite Glass Fibers with In-Phase and Out-of-Phase Supermodes

High nonlinearity and transparency in the 1–5 μm spectral range make tellurite glass fibers highly interesting for the development of nonlinear optical devices. For nonlinear optical fibers, group velocity dispersion that can be controlled by microstructuring is also of great importance. In this work, we present a comprehensive numerical analysis of dispersion and nonlinear properties of microstructured two-, four-, six-, and eight-core tellurite glass fibers for in-phase and out-of-phase supermodes and compare them with the results for one-core fibers in the near- and mid-infrared ranges. Out-of-phase supermodes in tellurite multicore fibers are studied for the first time, to the best of our knowledge. The dispersion curves for in-phase and out-of-phase supermodes are shifted from the dispersion curve for one-core fiber in opposite directions; the effect is stronger for large coupling between the fields in individual cores. The zero dispersion wavelengths of in-phase and out-of-phase supermodes shift to opposite sides with respect to the zero-dispersion wavelength of a one-core fiber. For out-of-phase supermodes, the dispersion can be anomalous even at 1.55 μm, corresponding to the operating wavelength of Er-doped fiber lasers.

An optimal method for a staggered-grid finite-difference solution of elastic wave equations including rotational deformation

The staggered-grid finite-difference (SGFD) method is one of the most popular means used in seismic numerical modelling because of its computational efficiency and it is easy to implement. However, it will lead to serious numerical errors while using coarse grids or wavelet with high-frequency. In this work, we proposed an optimal spatial SGFD method based on a new improved particle swarm optimization (PSO) algorithm. Then the dispersion of numerical solution of the first-order spatial derivatives is analyzed. Meanwhile, numerical modelling of elastic wave equations and elastic wave equations including rotational deformation are performed with the optimal spatial SGFD method based on the improved PSO algorithm. Numerical dispersion analysis and numerical modeling results indicate that the optimal spatial SGFD method based on the improved PSO algorithm has high modeling accuracy and can efficiently suppress the numerical dispersion.

Implicit highly-coupled single-ion Hall-MHD formulation for hybrid particle-in-cell codes

The rudiments of a particle-based single-fluid two-temperature magnetohydrodynamic (MHD) algorithm have been outlined in Thoma et al. (2013). The extension of this algorithm to include the effect of Hall physics is described in this paper. An implicit leapfrog version of the algorithm, which allows timesteps large compared to the resistive decay time and other relevant timescales, has recently been added to a hybrid particle-in-cell code. In standard MHD the Hall term in the generalized Ohm’s law can often be neglected when the Hall parameter is small. This term must, however, be retained in regimes where it is non-negligible. The retention of displacement current in Maxwell’s equations avoids the numerical difficulties associated with the whistler mode, which are encountered in standard explicit Hall-MHD codes, and allows the algorithm to be incorporated into hybrid particle-in-cell codes, for which particles may migrate from a kinetic to fluid to MHD description based upon local ambient plasma conditions. A highly-coupled implicit Hall-MHD formalism is presented, in which displacement current can either be retained or neglected. Even when displacement current is neglected, the highly-coupled implicit formalism avoids the restrictive timesteps for the whistler mode in explicit Hall-MHD codes. A comparison of numerical and analytic dispersion analysis demonstrates the feasibility of this approach and establishes relevant constraints to assure numerical stability. The implementation of the algorithm is described, and test simulation results in 1D and 2D in both linear and nonlinear regimes are presented.

Survey of cubic B-spline implicit time integration methodin computational wave propagation

Recently an implicit time integration method based-on Cubic B-spline has been presented for solving the problems in structural dynamics. This method benefits from high accuracy and desire stability. In this paper, the presented method is developed for analyzing the wave propagation problems and the results are compared to the methods in the literature including a series of Bathe family methods (Noh-Bathe, Standard Bathe p1/B2-Bathe and pq-Bathe methods) and Newmark trapezoidal rule method. A numerical dispersion analysis is presented to evaluate the method in one and two wave propagation problems. Results indicate that the method under study has adequate performance in wave propagation as good as structural dynamic problems.

Numerical analysis of hydrogen release, dispersion and combustion in a tunnel with fuel cell vehicles using all-speed CFD code GASFLOW-MPI

Hydrogen energy is expanding world-widely in recent years, while hydrogen safety issues have drawn considerable attention. It is widely accepted that accidental hydrogen release in an open-air environment will disperse quickly, hence not causing significant hydrogen hazards. A hydrogen hazard is more likely to occur when hydrogen is accidentally released in a confined place, i.e. parking garages and tunnels. Prediction the main accident process, including the hydrogen release, dispersion, and combustion, is important for hydrogen safety assessment, and ensuring the safety installations during accidents. Hence, a postulated accident scenario induced by the operation of Thermal Pressure Relief Device in a tunnel is analysed for hydrogen fuel cell vehicles with GASFLOW-MPI in this study. GASFLOW-MPI is a well validated parallel CFD code focusing on the transport, combustion, and detonation of hydrogen. It solves compressible Navier-Stokes equations with a powerful all-speed Arbitrary-Lagrangian-Eulerian (ALE) method; hence can cover both the non-compressible flow during the hydrogen release and dispersion phases, and the compressible flow during deflagration and detonation. In this study, a 3D model of real-scaled tunnel is modelled, firstly. Then the hydrogen dispersion in the tunnel is calculated to evaluate the risk of Flame acceleration and the Deflagration-Detonation Transient (DDT). The case with jet fire is analysed with assuming that the hydrogen is ignited right after being injected forming a jet fire in the tunnel, the consequence of this case is limited considering the small hydrogen inventory. The detonation in the tunnel is calculated by assuming a strong ignition at the top of the tunnel at an unfavourable time and location. The pressure loads are calculated to evaluate the consequence of the hazard. The analysis shows that the GASFLOW-MPI is applicable at a widely range for tunnel accidents, meanwhile, the safety issues related to tunnel accidents is worthy further study considering the complexity of tunnels.

An Efficient Numerical Formulation for Wave Propagation in Magnetized Plasma Using PITD Method

A modified precise-integration time-domain (PITD) formulation is presented to model the wave propagation in magnetized plasma based on the auxiliary differential equation (ADE). The most prominent advantage of this algorithm is using a time-step size which is larger than the maximum value of the Courant–Friedrich–Levy (CFL) condition to achieve the simulation with a satisfying accuracy. In this formulation, Maxwell’s equations in magnetized plasma are obtained by using the auxiliary variables and equations. Then, the spatial derivative is approximated by the second-order finite-difference method only, and the precise integration (PI) scheme is used to solve the resulting ordinary differential equations (ODEs). The numerical stability and dispersion error of this modified method are discussed in detail in magnetized plasma. The stability analysis validates that the simulated time-step size of this method can be chosen much larger than that of the CFL condition in the finite-difference time-domain (FDTD) simulations. According to the numerical dispersion analysis, the range of the relative error in this method is 10−6 to 5×10−4 when the electromagnetic wave frequency is from 1 GHz to 100 GHz. More particularly, it should be emphasized that the numerical dispersion error is almost invariant under different time-step sizes which is similar to the conventional PITD method in the free space. This means that with the increase of the time-step size, the presented method still has a lower computational error in the simulations. Numerical experiments verify that the presented method is reliable and efficient for the magnetized plasma problems. Compared with the formulations based on the FDTD method, e.g., the ADE-FDTD method and the JE convolution FDTD (JEC-FDTD) method, the modified algorithm in this paper can employ a larger time step and has simpler iterative formulas so as to reduce the execution time. Moreover, it is found that the presented method is more accurate than the methods based on the FDTD scheme, especially in the high frequency range, according to the results of the magnetized plasma slab. In conclusion, the presented method is efficient and accurate for simulating the wave propagation in magnetized plasma.

Improved direct integration auxiliary differential equation FDTD scheme for modeling graphene drude dispersion

In this communication, an improved direct-integration auxiliary differential equation (IM-DI-ADE) scheme is introduced for incorporating graphene's Drude dispersion into the finite difference time domain (FDTD) simulations in the GHz and THz frequency ranges. Stability analysis is performed and it is shown that the time-step stability limit of the presented IM-DI-ADE scheme coincides with the conventional non-dispersive FDTD Courant–Friedrichs–Lewy (CFL) limit and removes the additional stability stringent of the classical DI-ADE counterpart. In addition, the presented scheme does not increase the memory storage overhead. Numerical dispersion analysis is also addressed and it is shown that the presented scheme provides high accuracy. The formulation is validated by numerical tests that investigate the tunneling of electromagnetic wave through a graphene sheet and the existence of the surface plasmon polaritons (SPPs) waves created at the interface between the graphene sheet and a dielectric material.

Numerical Analysis of Large Negative Dispersion and highly Birefringent Photonic Crystal Fiber

This article deals with a study of proposed PCF in which a fiber core is surrounded by square shaped air holes arranged in circular rings in the cladding region. Parametric variation of proposed fiber is measured by varying the square air hole number in the core region, length of square air hole and also for hole packing density ratio (HPD) variation from visible to near-infrared (NIR) wavelength range. The parametric analysis shows that zero dispersion wavelength (ZDW) varies for all possible parametric variations mentioned above. The maximum negative dispersion value of −810 ps/nm/Km is obtained at 1.55 μm for 3 square air holes in fiber core while minimum confinement loss value is 1.23 × 10-5dB/m at the same wavelength. Besides this, the birefringence and nonlinear coefficient values were also found high as 3.6 × 10-3 and 75 W-1 km-1, respectively at 1.55 μm. Hence, the proposed PCF can be better used in four wave mixing, solitons generation, polarization maintaining fiber and optical sensor applications.

Numerical and experimental analysis of flow and particulate matter dispersion in indoor environment

Reducing indoor particulate matter (PM) concentration is an issue of concern from an environmental point of view as the world’s population spend only 4% of their time outdoors. Computational fluid dynamics (CFD) is a fundamental tool for predicting indoor pollutant dispersion and improving knowledge on how indoor and outdoor environments interact in terms of pollutant and momentum exchanges. In this paper, an unsteady CFD simulation has been carried out to investigate the airflow and PM concentration in a classroom of the University of Rome “La Sapienza”. Wind velocity and PM concentration acquired during a field campaign conducted within and outside the building of interest have been used as input for the simulation and to test the model performance as well. The results show a reasonable agreement between measured and simulated concentration within the classroom and emphasize the major role played by the micrometeorology in PM concentration. The importance of the boundary conditions at the room openings has been also discussed.

Numerical analysis of air pollutant dispersion in steam power plant area using the finite volume method

In this research a mathematical model will be developed for the distribution of air pollutants. The model is built on the basis of momentum equations and mass continuity equations solved using the finite volume method. Based on the model obtained, the effect of wind speed and initial concentration on the distribution of pollutants in the air will be analyzed. An air pollutant with a certain concentration released through the chimney into the atmosphere will undergo a process of transportation and transformation. The characteristics of emission sources such as concentration when the emission and wind speed around the chimney really determine the spreading of the concentration. The case study in this research is located in the Paiton-Probolinggo Steam Power Plant area. The analysis of the distribution of pollutants was solved numerically using the Gauss Seidel iteration method assisted by MATLAB software and simulated using a CFD approach assisted by FLUENT software. The results obtained in this research indicated that the greater the wind speed around the chimney, the lower the concentration of SO2 pollutants in the air, while the effect of the initial concentration showed that the greater the initial concentration, the greater the concentration of pollutants scattered in the air.

A new method for numerical dispersion analysis of Laplace-domain 2-D elastic wave equation

Elastic wave modelling in the Laplace domain is the foundation of Laplace-domain elastic wave full waveform inversion. In order to use Laplace-domain numerical modelling schemes efficiently, appropriate grid intervals must be chosen correctly. The determination of grid intervals is based on numerical dispersion analysis of Laplace-domain elastic wave equation. A new method of numerical dispersion analysis is developed for Laplace-domain 2-D elastic wave equation. The novelty of the method lies in two aspects: (1) Based on the concept of the pseudo-wavelength for both P- and S-waves, I introduce a general quantity which is a combination of the Laplace constant, velocity and grid interval. Therefore, the dispersion relations no longer directly depend on the concrete Laplace constant, velocity and grid interval. Just like the frequency-domain dispersion analysis, a general conclusion with regard to the general quantity can be made; (2) The ratio of numerical eigenvalue to analytical eigenvalue can be interpreted as the normalised attenuation propagation velocity. The number of grid points per S-wave pseudo-wavelength is determined by the accuracy of normalised P- and S-wave attenuation propagation velocities. Based on a commonly used finite-element scheme, the numbers of grid points per S-wave pseudo-wavelength are determined for different Poisson ratios and for different ratios of directional grid intervals. These results are important in applying the finite-element scheme to Laplace-domain elastic wave modelling and full waveform inversion. Comparisons with the analytical solution validate the criterion on the numbers of grid points per S-wave pseudo-wavelength.

Study on electromagnetic characteristics of plasma model-based on the symplectic multiresolution time-domain scheme

A novel numerical computation scheme, which is symplectic multiresolution time-domain (S-MRTD) scheme, for modeling plasma model is proposed. The loss plasma dispersive model is taken into account in S-MRTD scheme, and the detailed formulations of the proposed S-MRTD scheme are also provided. A one-dimensional perfectly matched layers (PML) are used to terminate the computational domain. The analyses of stability and numerical dispersion demonstrate that S-MRTD scheme is more efficient than traditional finite-different time-domain (FDTD) and MRTD methods. The energy conservation characteristics of S-MRTD scheme in electromagnetic simulation are proved by the propagation of pulse in free space for long-term simulation. In the end, the S-MRTD formulations are confirmed by computing the electric field intensity, reflection and the transmission coefficients for the pulse wave through an unmagnetized plasma slab. A favorable agreement between the numerical solutions is demonstrated, and the efficiency of the proposed scheme is verified. Meanwhile, numerical results show that plasma frequency, collision frequency and thickness are important factors affecting reflection and transmission coefficients.

A high-precision low-dispersive nearly analytic difference method with its application in frequency-domain seismic waveform inversion

ABSTRACTTo improve the efficiency of seismic waveform inversion, we construct a novel high-order (6th-order) frequency-domain nearly analytic discrete method for forward modelling in inversion processes. Compared with some existing numerical schemes, this method is more powerful in suppressing numerical dispersion and enhancing the accuracy of computational results based on coarse discrete grids. We describe the discretisation of the frequency-domain wave equation, investigate the efficiency of wave-field simulation and perform numerical dispersion analysis. The inversion efficiency can also be improved when the inexact rotated block triangular preconditioned Krylov iteration solvers are incorporated into the corresponding linear system. Moreover, the inversion behaviour of frequency-domain NAD methods is also systematically discussed as one of its important applications. We take three representative media models as examples and the reliable inversion results are obtained reflecting the effectiveness of the proposed methods.

Optimal shape parameter for meshless solution of the 2D Helmholtz equation

The solution of the Helmholtz equation is a fundamental step in frequency domain seismic imaging. This paper deals with a numerical study of solutions for 2D Helmholtz equation using a Gaussian radial basis function-generated finite difference scheme (RBFFD). We analyze the behavior of the local truncation error in approximating partial derivatives of the 2D Helmholtz equation solutions when the shape parameter of RBF varies. For discretization, we performed, by means of a classical numerical dispersion analysis with plane waves, a minimization of the error function to obtain local and adaptive near optimal shape parameters according to the local wavelength of the required solution. In particular, the method is applied to obtain a simple and accurate solver by using stencils which seven nodes on hexagonal regular grids, wich mitigate pollution-effects. We validated numerically that the stability and isotropy are enhanced with respect to Cartesian grids. Our method is tested with standard case studies and velocity models, showing similar or better accuracy than finite difference and finite element methods. This is an efficient way for interacting with inverse and imaging problems such as Full Wave Inversion.

The spatial fourth-order compact splitting FDTD scheme with modified energy-conserved identity for two-dimensional Lorentz model

In this paper, we give the energy conservation for the electromagnetic fields propagating in two-dimensional Lorentz media and develop a new spatial fourth-order compact splitting FDTD scheme to solve the two-dimensional electromagnetic Lorentz system. The spatial compact finite difference technique and the splitting technique are combined to construct the numerical scheme. The advantages of the developed scheme lie in its fourth-order accuracy in space and second-order accuracy in time, modified discrete energy conservation, unconditional stability as well as its easy implementation. These results are demonstrated rigorously in the paper. Numerical dissipation and numerical dispersion analysis are shown and numerical dispersion errors are compared with other schemes. Besides, numerical tests verify the modified discrete energy conservation and convergence ratios in time and space.

Numerical Analysis of Pollutant Concentration Dispersion and Convective Flow in a Two-dimensional Confluent River Model

Numerical Analysis of Pollutant Concentration Dispersion and Convective Flow in a Two-dimensional Confluent River Model

Numerical Prognosis of Dispersion and Transport of Pollutants in Romania, Based on Emissions of Pollutants

Abstract Air pollution is one of the major problems of mankind, transport of pollutants extending far beyond the borders of the countries where they were produced, causing unpredictable, direct and indirect changes of the environment. The main tool for the study of this phenomenon consists of mathematical modeling of complex physical and chemical phenomena involved. In practice, air emissions are estimated on basis of measurements taken from selected sources being representative of the major categories and types. At national level, the Air Quality Evaluation Center (CECA) provides regular reports to the European Environment Agency (EEA) or the European Commission as requirements of Romania’s lawful duties in air quality domain. The registry of emissions TNO/ MACC (Netherlands Organisation for Applied Scientific Research/ Monitoring Atmospheric Composition and Climate) contains emissions inventories which have been homogenized and checked in advance and obtained from emissions officially reported at sectoral level for each country. In this study, for the analysis of the weather numerical dispersion and transport of pollutants, it has been used the numerical air quality model WRF-CHEM version 3.5, centered over Romania, at the spatial resolution of 10 km, using as input data the TNO emission database for 2009. By interpolating values from the regular grid of the TNO database with the WRF-CHEM model 3.5 grid, monthly average values were obtained for each day of the week, for any parameter considered. Preliminary results obtained for different pollutants (for example: PM10, O3) confirm the need to validate these results by implementing and integrating air quality forecasting model by assimilating different types of measurements (data model, gravimetric data observations, etc.).