Finite-volume Time-domain Method Research Articles

Verification of frequency-dependent impedance boundaries for the Finite-Volume Time-Domain scheme

Numerical simulation methods are widely used to approximate solutions to the wave-equation, taking into account the initial condition ('initial sources') and boundary conditions ('wall materials'). Trustworthy simulations are essential; a primary step is to ensure the correctness of the implementation through a process known as code verification. In this work, we do code verification by studying the convergence of the known finite-volume time-domain (FVTD) method with a frequency-dependent boundary condition modeled as an inductance/resistance/capacitance (LRC) termination. Due to the difficulties of obtaining an analytical solution for frequency-dependent impedance boundaries, we thoroughly derive and implement The Method of Manufactured Solutions tailored to the wave-equation inside a rectangular room for uniform frequency- dependent wall impedance. Asymptotic estimates are found empirically based on a convergence study compared against the manufactured ground truth solution. We investigate the impact of the frequency-dependent boundaries on the convergence affected by the total sum of numerical errors and validate the theoretical properties of the FVTD scheme for various LRC model configurations. The method should also serve as a useful resource for others to verify the correctness of their code implementations.

Analysis of electromagnetic scattering from hypersonic vehicle coated with non-uniform plasma sheath based on FVTD method

The finite volume time domain (FVTD) method is proposed to accurately calculate the electromagnetic (EM) scattering of hypersonic vehicles coated with non-uniform plasma sheath. The plasma sheath in the actual flight environment is accurately established by solving the Navier–Stokes equations and combining appropriate thermochemical models. The radar cross section (RCS) of metal and uniform medium coated metal targets calculated by FVTD are in good agreement with those simulated by the software FEKO (MoM) and the Mie series. The calculated RCS of the vehicle under the reentry condition is consistent with the flight test data, too. The calculated electron number density distribution is consistent with the flight experiment results. The body fitted structure EM grid is adopted. The EM grid independence of the target coated with plasma sheath is studied. Then, the scattering and plasma EM parameters of the vehicle during the actual reentry are studied. The reentry altitude is from 78 to 55 km, and the reentry velocity is from 6406 to 6350 m/s. With the reentry altitude decreasing, the plasma angular frequency and collision frequency increased gradually. The scattering of different incident conditions and different wall catalytic conditions is analyzed in depth. This paper provides a valuable reference for vehicles' detection, recognition, and stealth during reentry flights.

Direct synthesis of time domain pseudo-random 3D electromagnetic response with a band-limited source

Methods based on pseudo-random coded emission technology can effectively suppress the noise in electromagnetic exploration and improve the depth and resolution of the detection. Additionally, the synthesis of electromagnetic response signals excited by pseudo-random code sources can provide not only theoretical data for data processing but also intermediate results for evaluations of field data. Currently, pseudo-random signal simulations ignore the presence of source effects generated by band-limited sources in the Earth's impulse response. Furthermore, the simulation methods are mainly completed based on one-dimensional and two-dimensional formats and thus cannot accurately reflect the pseudo-random response of three-dimensional geoelectric structures. In this paper, 3D pseudo-random electromagnetic signals with a band-limited source were synthesized according to the propagating routine of the electromagnetic field. First, Maxwell's Equations were solved using a three-dimensional time-domain finite volume method. To avoid the singularity of the source and incorporate source effect response, the Gaussian function was introduced to simulate the band-limited impulse sources. The Earth's impulse response was obtained, which contained source effects under three-dimensional geoelectric structures. Then, ideal pseudo-random electromagnetic signals could be composed by convoluting the Earth's impulse response with a pseudo-random source waveform. Since the transmitter and receiver instruments were band-limited, a low-pass filter with a Blackman window was introduced to simulate the instrument's system response. The simulated pseudo-random signals were obtained by adding noise and the ideal pseudo-random electromagnetic signals were filtered using a low-pass filter. By comparison with signals acquired in the field, the correctness of the pseudo-random signal synthesis with source effects was successfully verified.

Automated adaptive TFSF method for solving time domain Maxwell's equations

AbstractThe total field–scattered field (TFSF) formulation is quite popular for solving Maxwell's equations in finite difference time domain (FDTD) and finite volume time domain (FVTD) methods. Here a fixed TFSF interface around the scattering body is employed to separate the total field (TF) cells and scattered field (SF) cells. This interface is selected based on experience as it is assigned prior to the solution, and, therefore, the solution accuracy may not be optimal. In the present work, a novel automated adaptive total field–scattered field (ATFSF) method is proposed for accurately computing the electromagnetic scattering by complex‐shaped metal objects excited by an external plane wave. In the proposed method, an algorithm is devised to dynamically identify the TF cells and the SF cells, to be solved using TF and SF methods, respectively, using intensity of electromagnetic (EM) wave. The algorithm is tested in a 2‐D spectral volume time domain (SVTD) framework for solving electromagnetic scattering, and the predicted surface current/radar cross section is compared against the SF, TF, and the conventional TFSF methods. It is seen that the present method improves the solution accuracy significantly.

A comparative study of several boundary conditions on the body surface for the meshless electromagnetic scattering method

In order to accurately calculate the radar cross sections (RCS) of stealth aircrafts by using the meshless method, several typical body surface boundary conditions from finite-volume time-domain (FVTD) methods, which are suitable for the meshless method, have been compared. The bistatic RCS of a 2-D cylinder irradiated by transverse magnetic wave (TM wave) or transverse electric wave (TE wave) and a 3-D sphere irradiated by different polarization waves are calculated by the meshless method based on different boundary conditions. The numerical results show that the bistatic RCS calculated by the first boundary condition is closest to the series solution, which indicates that the scattering electric field on the surface of perfect conductors is only related to the incident electric field, and the scattering magnetic field is related to the scattering magnetic field near the body surface and the variation of the normal scattering electric field on the body surface. Finally, based on the selected optimal body surface boundary condition, the paper present the electromagnetic scattering field and the bistatic RCS for a 3-D stealth aircraft model, which shows the ability of the meshless method in dealing with 3-D practical problems to a certain extent.

A Hybrid Asymptotic-FVTD Method for the Estimation of the Radar Cross Section of 3D Structures

The Finite Volume Time-Domain (FVTD) method is an effective full-wave technique which allows an accurate computation of the electromagnetic field. In order to analyze the scattering effects due to electrically large structures, it can be combined with methods based on high-frequency approximations. This paper proposes a hybrid technique, which combines the FVTD method with an asymptotic solver based on the physical optics (PO) and the equivalent current method (ECM), allowing the solution of electromagnetic problems in the presence of electrically large structures with small details. Preliminary numerical simulations, aimed at computing the radar cross section of perfect electric conducting (PEC) composite objects, are reported in order to evaluate the effectiveness of the proposed method.

Finite Volume Time Domain with the Green Function Method for Electromagnetic Scattering in Schwarzschild Spacetime**Supported by the National Natural Science Foundation of China under Grant No 61601105.

The finite volume time domain (FVTD) algorithm and Green function algorithm are extended to Schwarzschild spacetime for numerical simulation of electromagnetic scattering. The FVTD method in Schwarzschild spacetime is developed by filling the flat spacetime with an equivalent medium. The Green function in Schwarzschild spacetime is acquired by solving initial value problems. Both the FVTD code and the Green function code are validated by numerical results. Scattering in Schwarzschild spacetime is simulated with these methods.

Predictive calculation of ion current environment of dc transmission line based on ionised flow model of embedded short‐term wind speed

The predictive calculation and wind effect on the ion flow environment of dc transmission line are evaluated by embedded short-term wind speed based ionised flow model. The wind has a major impact on the electric field and ion current density profiles. In the ionised flow model of embedded short-term wind speed, the short-term wind speed is calculated by using time series model and Kalman filter algorithm. The ionised field considering short-term wind speed is solved by finite-element method with acceleration technique and time-domain finite volume method. The algorithm is validated by the coaxial cylinder electrode configuration and practical bipolar dc transmission configuration. Computational results are made to provide a physical understanding of wind effect on the corona formation process. In the timescale of long-term prediction, the time evolution behaviour of ground-level ion current density and electric field with time-varying wind speed is estimated.

Computing with large time steps in time-domain electromagnetics

ABSTRACTThe finite volume time-domain method is recast in a large time step (LTS) version to solve the time-domain Maxwell's equations. The LTS method allows the use of time steps much larger than that dictated by the Courant–Friedrich–Lewy criteria for numerical stability in a Godunov-based finite volume framework. Solutions can be obtained much faster and sometimes with higher accuracy compared to conventional time-stepping methods. Results are analyzed for electromagnetic wave propagation in 1D and 2D. Solutions are shown to remain unconditionally stable with an increase in the Courant number.

A time-domain finite volume method for the prediction of water muffler transmission loss considering elastic walls

This work extends the application of the finite volume method to predict the acoustic performance of the water muffler with the consideration of elastic walls. The three-dimensional time-domain finite volume method and the improved time-domain impulse method are employed to predict the acoustic attenuation characteristics of mufflers. The present results agree well with analytical solutions and numerical results obtained by finite element method with commercial codes. The effects of different thicknesses of elastic end cavity wall, elastic tube, and cavity walls on acoustic characteristics of a water-filled Helmholtz resonator are investigated. An attempt to simplify the present method with the effective sound speed has been implemented and discussed.

Space and Time Domain Finite Volume Method for Numerical Simulation of Negative Corona Discharge in Air

In this paper, a space and time domain finite volume method is proposed to study the characteristics of space charges on a bar-to-plate geometry. Three ionic species, namely, positive ions, negative ions, and electrons, are considered. A finite element method is used to solve Poisson’s equation, and a finite volume method is used to solve charge transport equation. Different time steps based on space domain and time domain are applied to improve computational efficiency when solving the charge transport equation. Four points are marked to indicate the characteristics of a Trichel pulse. Density distributions of three ionic species and electrical field strength along the axis are presented. Trichel pulses on a bar-to-plate geometry are simulated and compared with the experimental results. Good agreements are obtained, thereby confirming the validity of the proposed method.

Finite Volume Time Domain Room Acoustics Simulation under General Impedance Boundary Conditions

In room acoustics simulation and virtualization applications, accurate wall termination is a perceptually crucial feature. It is particularly important in the setting of wave-based modeling of 3D spaces, using methods such as the finite difference time domain method or finite volume time domain method. In this paper, general locally reactive impedance boundary conditions are incorporated into a 3D finite volume time domain formulation, which may be specialized to the various types of finite difference time domain method under fitted boundary termination. Energy methods are used to determine stability conditions for general room geometries, under a large family of nontrivial wall impedances, for finite volume methods over unstructured grids. Simulation results are presented, highlighting in particular the need for unstructured or fitted cells at the room boundary in the case of the accurate simulation of frequency-dependent room mode decay times.

An effective 3D leapfrog scheme for electromagnetic modelling of arbitrary shaped dielectric objects using unstructured meshes

In computational electromagnetics, the advantages of the standard Yee algorithm are its simplicity and its low computational costs. However, because of the accuracy losses resulting from the staircased representation of curved interfaces, it is normally not the method of choice for modelling electromagnetic interactions with objects of arbitrary shape. For these problems, an unstructured mesh finite volume time domain method is often employed, although the scheme does not satisfy the divergence free condition at the discrete level. In this paper, we generalize the standard Yee algorithm for use on unstructured meshes and solve the problem concerning the loss of accuracy linked to staircasing, while preserving the divergence free nature of the algorithm. The scheme is implemented on high quality primal Delaunay and dual Voronoi meshes. The performance of the approach was validated in previous work by simulating the scattering of electromagnetic waves by spherical 3D PEC objects in free space. In this paper we demonstrate the performance of this scheme for penetration problems in lossy dielectrics using a new averaging technique for Delaunay and Voronoi edges at the interface. A detailed explanation of the implementation of the method, and a demonstration of the quality of the results obtained for transmittance and scattering simulations by 3D objects of arbitrary shapes, are presented.

A Finite Volume Time Domain Method for In-Plane Vibration on Mixed Grids

A finite volume time domain method is developed for in-plane vibration based on mixed triangular and quadrilateral elements. Here the linear quadrilateral element shape function is introduced instead of the constant one to improve the accuracy of the present method. The improvement is validated to be vital to avoid violent numerical oscillation of displacement fields when applying to the point–source problem. The present method is proposed to analyze the transient responses and the natural characteristics of several in-plane problems. The results show good agreement with the commercial code solutions and the analytical solutions. In order to demonstrate the capability of the present method for multiexcitation problems, an example with sources containing different frequencies and phase angles, concentrated and uniform distributions, and impulse and continuous forms is analyzed.

Time domain finite volume method for three-dimensional structural–acoustic coupling analysis

This work extends the application of finite volume method (FVM) to structural–acoustic problems. A three-dimensional time domain FVM (TDFVM) is proposed to predict the transient response and natural characteristics of structural–acoustic coupling systems. Acoustic wave equation in heterogeneous medium and structural dynamic equation are solved in fluid and solid sub-domains respectively. The structural–acoustic coupling is implemented according to normal components of particle acceleration continuity condition and normal traction equilibrium condition at the interface. The computational domain is discretized with four-node tetrahedral grid which is generated easily and has strong adaptability to complicated geometries. Numerical experiments are carried out to examine the accuracy of the method in both time domain and frequency domain. The results show good agreement with analytical solutions and numerical results. For structural–acoustic problem, TDFVM has the capability to consider the heterogeneity of both fluid and solid.

An Unstructured Finite-Volume Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

An unstructured finite-volume time-domain method (UFVTDM) is developed to solve two-dimensional transient heat conduction in multilayer functionally graded materials (FGMs). A four-node quadrilateral grid and a three-node triangular grid are employed to deal with mixed-grid problems. The accuracy of the method is improved by treating the quadrilateral grid as a bilinear element with consideration of both the linear term and the constant term. The improvement is validated to be vital to avoid violent numerical oscillation when applying the method to heat point-source problems. The accuracy and capability of the UFVTDM are validated by numerical tests.

A Monte Carlo Method for Simulating Scattering From Sea Ice Using FVTD

A scattering model based on a Monte Carlo method and the finite-volume time-domain (FVTD) method has been created for sea ice scattering simulations. Statistical methods were used to generate a Gaussian-distributed randomly rough surface. The Polder-Van Santen-de Loor (PVD) model was used to estimate the sea ice dielectric values with inputs based upon actual measured physical variables obtained during field-based experiments and well-known parameterizations. Scattering simulations were performed through an application of the scattered-field (SF) formulation invoked in an FVTD computational engine. Simulated SFs were compared with C-band scatterometer measurements and showed good agreement for copolarized signals in a series of case studies. The developed simulation method has the potential to be used for a variety of sea ice types under different physical conditions.

Finite Volume Time Domain modelling of microwave breakdown and plasma formation in a metallic aperture

The modelling of plasma formation during microwave breakdown is a difficult task because of the strong non-linear coupling between Maxwellʼs equations and plasma equations, and of the large plasma density gradients that form during breakdown. An original Finite Volume Time Domain (FVTD) method has been developed to solve Maxwellʼs equations coupled with a simplified fluid plasma model and is described in this paper. This method is illustrated with the study of the shielding of a metallic aperture by the plasma generated by an incident high power electromagnetic wave. Typical results obtained with the FVTD method for this shielding problem are shown.

Time-domain finite volume method for ion-flow field analysis of bipolar high-voltage direct current transmission lines

In this study, a highly stable time-domain approach for analysing the ion-flow field of the bipolar high-voltage direct current transmission lines is proposed. The influence of the space charges generated by corona on the electric field is taken into account. Usually, the steady state of this electric field space charge coupled problem is directly solved and the transient process is ignored. However, the complete time-domain analysis of this problem may provide a deep look at the formation process of the direct current ion-flow field. In this work, the charge simulation method is used to solve the space-charge-free electric field, the finite element method is employed to solve the electric field in the presence of space charges, and the finite volume method is applied to solve the current continuity equation. Crank–Nicolson method is introduced to separate the governing equations in time domain and overcome the time-step limitation. Good agreement is obtained between the calculated and experimental results, verifying the validity of the approach.

An Efficient Scattered-Field Formulation for Objects in Layered Media Using the FVTD Method

A technique for efficiently simulating the scattering from objects in multilayered media is presented. The efficiency of the formulation comes from the fact that the sources for the scattered fields (SFs) only occur at the inhomogeneities and, therefore, the SFs impinging on the boundaries are more easily absorbed. To demonstrate the technique, a 1-D-finite-difference time-domain solution to the plane-wave propagation through a multilayered medium is used as an incident-field source for an SF formulation of the finite-volume time-domain method. Practical aspects of the application are discussed and numerical examples for scattering from canonical objects are presented to show the validity of the proposed technique. The simulation scheme described herein can be used for simulations of geophysical media with appropriate specifications of the dielectric properties of the media and the inhomogeneities.