Time-domain Boundary Condition Research Articles

Simulation of water entry into shallow water based on boundary element method

The problem of a two-dimensional wedge entering into shallow water is investigated with the boundary element method based on the potential flow theory, and fully nonlinear boundary conditions in time domain are imposed. A stretched coordinate system is used at the initial stage of water entry to avoid the numerical problems originated from extremely small wetted surface. An auxiliary function is used to calculate the pressure on the body surface. The free surface is updated through the fourth order Runge-Kutta scheme. Particularly, a jet cut model is used to avoid the numerical difficulties when the thin and high jet forms. Detailed results through the free surface, pressure distribution and hydrodynamic load at constant speed and prescribed time-varying speed are provided, the comparison with the results from experiments, Wagner theory, semi-analytic method are made and effects of water depth are investigated in detail. It is found that the bottom of the shallow water domain would exert a noticeable effect on the pressure distribution and force of the wedge, especially when the tip of wedge is close to the domain bottom.

Investigations of an Effective Time-Domain Boundary Condition for Quiescent Viscothermal Acoustics

Investigations of an Effective Time-Domain Boundary Condition for Quiescent Viscothermal Acoustics

An iterative time-marching scheme for the investigation of hydrodynamic interaction between multi-ships during overtaking

An iterative time-marching scheme is developed to investigate the hydrodynamic interactions between multiple ships. Such an unsteady interactive effect could be magnified in restricted waterways, e.g., a channel or harbor area. To the author’s knowledge, nearly all the research on the ship-to-ship interaction neglecting the free surface effects. The free surface is usually treated as a rigid wall. This assumption is only reasonable when the speed of the ships is very low in deep water condition, due to the hydrodynamic interaction between the ships is mainly induced by near-field disturbances. However, when the moving speeds are moderately higher, especially with a small lateral separation between ships, the far-field effects arising from the ship waves become important. The main objective of the present paper is to develop an iterative time-matching algorithm to solve the hydrodynamic interaction between high-speed ships taking into account the nonlinear free surface boundary condition in time domain.

Wave energy extraction for an array of dual-oscillating wave surge converter with different layouts

Array configuration of oscillating wave surge converter (OWSC) devices in nearshore is a preferable option for realizing a cost-balance of extracting wave energy and reducing installation expense due to closer installed place to coastline. The goal of the present work is to assess energy extraction of an array of dual-OWSC system with different layout schemes in comparison with an isolated OWSC, which can be regarded as a guideline for multi-array configuration in realistic wave farm. The coupled three-dimensional (3-D) hydrodynamic model is established based on the potential flow theory with fully nonlinear boundary condition in time domain. A non-dimensional approach is conducted to focusing on the accurate effects of multi-body interaction, wave nonlinearity, wave resonance, mechanical damping, layout scheme and oblique incidence as optimization design. For a front-back array system, wave resonance in dual-module gap enhances significantly the energy extraction of the front OWSC but does not contribute much to that of the back OWSC. Furthermore, wave resonance in wide gap has a positive effect on the capture efficiency in large wave periods. An in-line array system has a beneficial performance in small wave periods, while a staggered array system realizes more energy extraction in resonance region. A strong wave disturbance between flap sides of an in-line and staggered system, leads to the increase of energy extraction for the back OWSC with imposing small incident wave heading. Therefore, the combination of multi-triple-array OWSC with different gap distances will provide a desirable configuration which is independent on oblique wave conditions.

Efficient Interpolation Method for Wireless Communications and Signal Processing Applications

Interpolation involves the process of estimating values at positions in between the adjacent samples, which has very fundamental and applied implications in signal processing and communication systems. In this work, a new method of cubic spline interpolation (CSI) is proposed and derived mathematically from the input samples respecting the time-domain boundary conditions, and the corresponding piecewise polynomials are optimized in the frequency domain to achieve good spectral properties. A comparative analysis of several prior arts, including arbitrary frequency response polynomial (AFRP) and basis spline (B-spline) is also presented, giving a clear overview of the advantages associated with the proposed technique in terms of implementation complexity, latency, and in-band and out-of-band spectral performance. The measurement results with three different radio frequency (RF) power amplifier (PA) prototypes using an input stimulus comprised of different instantaneous bandwidth (iBW) carrier aggregated 5G new radio (NR) waveform are demonstrated to highlight the improved performance in the context of digital predistortion (DPD) correction. Finally, the architecture of the proposed method is illustrated, which is suitable for real-time high-speed digital implementation.

Finite-Difference Time-Domain Modeling of Periodic Structures: A review of constant wave vector techniques

This article reviews state-of-the-art periodic boundary conditions (PBCs) in finite difference time-domain (FDTD) simulations that operate by enforcing constant wave vector components. The mathematical principles and 3D FDTD implementation details are systematically outlined. Techniques for extracting scattering parameters, Brillouin diagrams, and attenuation constants are presented along with the array scanning method (ASM) used to model the interaction of nonperiodic sources with periodic structures. Through these techniques, the robustness, utility, and efficiency of PBCs are demonstrated and a unified view of the various approaches to the FDTD implementation of PBCs is presented.

Multilayer Topology Optimization of Wideband SIW-to-Waveguide Transitions

This article utilizes a topology optimization approach to design planar multilayer transitions between substrate integrated waveguides (SIWs) and rectangular waveguides (RWGs). The optimization problem is formulated based on the modal field analyses and Maxwell’s equations in the time domain solved by the finite-difference time-domain (FDTD) method. We present a time-domain boundary condition based on the Klein–Gordon equation to split traveling waves at homogeneous waveguide ports. We employ the boundary condition to compute portal quantities and to devise an adjoint-field system that enabled an efficient computation of the objective function gradient. We solve design problems that include more than 105 000 design variables by using less than 400 solutions of Maxwell’s equations. Moreover, a new formulation that effectively combats the development of in-band resonances in the design is presented. The transition configuration allows the direct mount of conventional RWG sections on the circuit board and aims to cover the entire K-band. The guiding structure of the optimized transition requires blind vias, which is realized by a simple and cost-efficient technique. In addition, the transition is optimized for three different setups that can be used to provide different field polarizations. The proposed transitions show less than 1-dB insertion loss and around 15-dB return loss over the frequency interval 18–28 GHz. Several prototypes are fabricated with an excellent match between the simulation and measurement results.

Analysis of Time-domain Electromagnetic Scattering Problem by Multiple Cavities

The time-domain multiple cavity scattering problem, which arises in diverse scientific areas, has significant industrial and military applications. The multiple cavities, embedded in an infinite ground plane, is filled with inhomogeneous media characterized by variable dielectric permittivities and magnetic permeabilities. Corresponding to the transverse electric, the scattering problem can be studied by the Helmholtz equation in frequency domain and wave equation in time-domain respectively. A novel transparent boundary condition in time-domain is developed to reformulate the cavity scattering problem into an initial-boundary value problem in a bounded domain. The well-posedness and stability of the reduced problem are established. Moreover, a priori energy estimates for the electric field is obtained with minimum regularity requirement for the data and an explicit dependence on the time by studying the wave equation directly.

Light-scattering model for aerosol particles with irregular shapes and inhomogeneous compositions using a parallelized pseudo-spectral time-domain technique**Project supported by the National Natural Science Foundation of China (Grant Nos. 41575025 and 41575024).

To improve the modeling accuracy of radiative transfer, the scattering properties of aerosol particles with irregular shapes and inhomogeneous compositions should be simulated accurately. To this end, a light-scattering model for nonspherical particles is established based on the pseudo-spectral time domain (PSTD) technique. In this model, the perfectly matched layer with auxiliary differential equation (ADE-PML), an excellent absorption boundary condition (ABC) in the finite difference time domain generalized for the PSTD, and the weighted total field/scattered field (TF/SF) technique is employed to introduce the incident light into 3D computational domain. To improve computational efficiency, the model is further parallelized using the OpenMP technique. The modeling accuracy of the PSTD scheme is validated against Lorenz–Mie, Aden–Kerker, T-matrix theory and DDA for spheres, inhomogeneous particles and nonspherical particles, and the influence of the spatial resolution and thickness of ADE-PML on the modeling accuracy is discussed as well. Finally, the parallel computational efficiency of the model is also analyzed. The results show that an excellent agreement is achieved between the results of PSTD and well-tested scattering models, where the simulation errors of extinction efficiencies are generally smaller than 1%, indicating the high accuracy of our model. Despite its low spatial resolution, reliable modeling precision can still be achieved by using the PSTD technique, especially for large particles. To suppress the electromagnetic wave reflected by the absorption layers, a six-layer ADE-PML should be set in the computational domain at least.

Time domain simulation of porous surfaces for comparison with the ANSI impedance measurement

This study is to investigate sound propagation with different porous ground conditions. Sound propagations are simulated using finite difference time domain methods (FDTD). The ground materials are modeled as porous media. Two types of models are used in simulating the porous ground: (1) the original Zwikker-Kosten (ZK) model coupled with the immersed boundary method and (2) a modified ZK impedance model, as proposed by Wilson et al. (2006, 2007), as a time-domain boundary condition (TDBC) derived from the frequency-domain impedance boundary condition. The first method directly calculates the wave propagation inside porous media, while the second method only specifies the ground surface as a porous boundary condition. Both methods are based on the ZK-type models but have different responses in the frequency domain. Sound pressure levels in different frequency ranges are studied and discussed. Simulation results from both of the models are compared with the measurement data in ANSI S1.18 standard.

Piecewise linear recursive convolution (PLRC) implementation of convolution perfectly matched layer (CPML) in finite-difference time-domain (FDTD)

Convolutional perfectly matched layer (CPML) is an important absorbing boundary condition (ABC) in finite-difference time-domain (FDTD). The formulation of CPML needs no modification for any kind of media theoretically. This paper presents a novel implementation of CPML using piecewise linear recursive convolution (PLRC) to improve the absorbing performance. Compared to the classical CPML that the field in the convolution integral is approximated by a piecewise constant function, the PLRC implementation approximates the field in the convolution integral as a piecewise linear function. Numerical experiments of one-dimensional planar wave’s absorbance were performed and the reflected field is recorded at every time step. The frequency response of the reflection is achieved via Fourier transform The results show that the PLRC implementation of CPML has good absorbing effect at a broad frequency band and can achieve better absorbing performance than classical implementation of CPML at higher frequency. The CPML’s constitutive parameters’ influence on the absorbing performance is studied via sweeping the parameters and the results are illustrated by contour plots which are very helpful in appropriate parameters choice. At last, the proper parameters in truncating one-dimensional planar waves in free space are advised.

Broadband liner impedance eduction for multimodal acoustic propagation in the presence of a mean flow

A new broadband impedance eduction method is introduced to identify the surface impedance of acoustic liners from in situ measurements on a test rig. Multimodal acoustic propagation is taken into account in order to reproduce realistic conditions. The present approach is based on the resolution of the linearized 3D Euler equations in the time domain. The broadband impedance time domain boundary condition is prescribed from a multipole impedance model, and is formulated as a differential form well-suited for high-order numerical methods. Numerical values of the model coefficients are determined by minimizing the difference between measured and simulated acoustic quantities, namely the insertion loss and wall pressure fluctuations at a few locations inside the duct. The minimization is performed through a multi-objective optimization thanks to the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The present eduction method is validated with benchmark data provided by NASA for plane wave propagation, and by synthesized numerical data for multimodal propagation.

Numerical Simulation of time domain wall impedance on circular and annular ducts using the immersed boundary method

In this work, time domain boundary conditions of wall impedance are simulated on circular and annular ducts of constant cross section. The discretization technique used here is the immersed boundary method in the framework of finite volume formulation. It has fourth order of precision in space and uses a third order Runge-Kutta method for time stepping. Several boundary conditions for wall impedance are tested and then compared with the analytical results of the one-dimensional resonating chamber for code validation. The impedance boundary conditions are simulated on a circular duct with wall treatment and with a synthetic sound source. Mean flow conditions include constant axial velocity and swirling flows of rigid body rotation and potential flow. The results are then compared with a fourth order eigensystem method of linearized governing equations. The results of the immersed boundary methodology are assessed along with the wall impedance boundary condition models and their linear validity is compared with the results of the eigensystem method.

Time-domain implementation of an impedance boundary condition with boundary layer correction

A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley (2011) [25]. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.

Mathematical modeling for solute transport in aquifer

Groundwater pollution may occur due to human activities, industrial effluents, cemeteries, mine spoils, etc. This paper deals with one-dimensional mathematical modeling of solute transport in finite aquifers. The governing equation for solute transport by unsteady groundwater flow is solved analytically by the Laplace transform technique. Initially, the aquifer is subjected to the spatially dependent source concentration with zero-order production. One end of the aquifer receives the source concentration and is represented by a mixed-type boundary condition in the splitting time domain. The concentration gradient at the other end of the porous media is assumed to be zero. The temporally dependent velocity and the dispersion coefficients are considered. A numerical solution is obtained by using an explicit finite difference scheme and compared with the analytical result. Accuracy of the solution is discussed by using the root mean square error method. Truncation error is also explored for the parameters like numerical dispersion and velocity terms. The impact of Peclet number is examined. For graphical interpretation, unsteady velocity expressions (i.e., such as exponential, sinusoidal, asymptotic, and algebraic sigmoid) are considered. The work may be used as a preliminary predictive tool for groundwater resource and management.

Surface Impedance Boundary Conditions in Time Domain for Guided Structures of Arbitrary Cross Section With Lossy Dielectric Walls

This paper presents a procedure to implement the concept of surface impedance boundary condition (SIBC) for lossy dielectrics in time domain. The SIBC formulation, validation, and results are obtained with a time domain numerical method, namely the transmission-line matrix (TLM). The formulation of surface impedance in frequency domain is converted to the time domain using a rational approximation followed by a bilinear transform with a canonical representation in the state-space. This surface impedance formulation has been implemented in TLM. Simulations show that the proposed model is valid for interfaces between air and a lossy dielectric, and arbitrary conductivity $\sigma$. An application that concerns mode propagation in a rectangular tunnel with lossy dielectric walls is shown. A comparison with an approximate method proposed by Marcatilli is presented. It confirms that the propagation in electrically large guided structures, such as tunnels with lossy dielectric walls, can be efficiently modeled by this approach.

Broadband surface impedance boundary conditions for higher order time domain discontinuous Galerkin method

Purpose – The purpose of this paper is to present a time domain discontinuous Galerkin (DG) approach for modeling wideband frequency dependent surface impedance boundary conditions. Design/methodology/approach – The paper solves the Maxwellian initial value problem in a computational domain, which is spatially discretized by the higher order DG method. On the boundary of the computational domain the paper applies a suitable impedance boundary condition (IBC). The frequency dependency of the impedance function is modeled by auxiliary differential equations (ADE). Findings – The authors will study the resonance frequency and the Q factor of different types of cavity resonators including lossy materials. The lossy materials are modeled by means of IBCs. The authors will compare the results with analytical results, as well as numerical results obtained by direct calculations where lossy materials are included explicitly into the numerical model. Several convergence studies are performed which demonstrate the accuracy of the approach. Originality/value – Modeling of frequency dependent boundary conditions in time domain with finite difference time domain method (FDTD) method is considered in numerous papers, as well as in frequency domain finite element method (FEM), and in a few papers also time domain FEM. However, FDTD method is only first order accurate and fails in modeling of complicated surfaces. FEM allows for high order accuracy, but time domain modeling is numerically extremely expensive. In frequency domain, broadband modeling of frequency dependent boundary conditions requires several simulations as opposed to the time domain, where a single simulation is needed. The time domain DG method proposed in this paper allows to overcome the difficulties. The authors introduce a broadband surface impedance formulation based on the ADE approach for the higher order DG method.

Time-domain solver in curvilinear coordinates for outdoor sound propagation over complex terrain

The current work aims at developing a linearized Euler equations solver in curvilinear coordinates to account for the effects of topography on sound propagation. In applications for transportation noise, the propagation environment as well as the description of acoustic sources is complex, and time-domain methods have proved their capability to deal with both atmospheric and ground effects. First, equations in curvilinear coordinates are examined. Then time-domain boundary conditions initially proposed for a Cartesian coordinate system are implemented in the curvilinear solver. Two test cases dealing with acoustic scattering by an impedance cylinder in a two-dimensional geometry and by an impedance sphere in a three-dimensional geometry are considered to validate the boundary conditions. Accurate solutions are obtained for both rigid and impedance surfaces. Finally, the solver is used to examine a typical outdoor sound propagation problem. It is shown that it is well-suited to study coupled effects of topography, mixed impedance ground and meteorological conditions.

Reconstruction of time-domain impedance boundary condition considering the incident intensity effect on perforated-plate acoustic liner

Based on impedance prediction methods for a perforated plate acoustic liner, time-domain impedance boundary conditions are en- hanced with consideration of incident intensity. The impedance coefficient of the time-domain boundary condition is re-derived using parameters of the liner structure, and is classified by physical characteristics. To show the capability of the reconstructed impedance boundary condition, two numerical calculations are performed with comparison to analytical results. The first considers the one- dimensional wave propagation problem to account for the reflection wave due to an incident intensity variation on the acoustic liner. The second considers the excess attenuation of impedance surface. The numerical simulation is performed using the linearized Euler equa- tions (LEEs). Dispersion-relation-preserving finite difference scheme and optimized Adams-Bashforth time-integration method are used spatial discretization / time integration, respectively. The numerical results show excellent agreement with analytical results. Moreover, a reconstruction method of impedance boundary condition can easily obtain the impedance coefficients under environments of variant magnitudes of incident waves.

EFFICIENT SIMULATIONS OF PERIODIC STRUCTURES WITH OBLIQUE INCIDENCE USING DIRECT SPECTRAL FDTD METHOD

A simple and e-cient joint algorithm of flnite difierence time domain (FDTD) and periodic boundary condition (PBC), called as the direct spectral FDTD method, has been investigated to study three-dimensional (3D) periodic structures with oblique incidence, where both the azimuth angleand the elevation angle µ are varying. The number of sampling points for the horizontal wave number can be determined by using an adaptive approach. As numerical results, the transmission and re∞ection coe-cients from split-ring resonators (SRRs) and a dielectric grating slab are computed to validate the accuracy and e-ciency of the direct spectral FDTD method. The computed results are in good agreement to the published ones obtained by other methods.