Flnite-difierence Method Research Articles

Thermal Analyses and Experimental Validation of External Cooling Method for a Gun Barrel

In order to analyze the performance of the external cooling method for the rapid flring gun barrel, an accurate numerical simulation modeling is important. A mathematical model of heat transfer for external cooling gun barrel was established by using flnite difierence method. The temperature history of gun barrel with natural cooling and external cooling method were calculated. The in∞uence of the coolant vaporization on cooling efiect was considered in the calculation. The results show that the temperature gradient in the barrel wall is very large. Through the contrast analysis of calculation results it can be seen that the cooling efiect of the external cooling method is more and more remarkable as the shooting number is increasing. Especially, the gun tube temperature drop is the most obvious in the flring interval. A series of experiments were performed for the gun barrel. The calculation results were discovered to agree with the experimental data. From the results can be concluded that the external cooling method is an efiective means of thermal control for rapid flring gun barrel. Under reasonable flring controlled schedule, the gun barrel life can be efiectively improved by using external cooling method.

HIGH-ORDER UNCONDITIONALLY-STABLE FOUR-STEP ADI-FDTD METHODS AND NUMERICAL ANALYSIS

High-order unconditionally-stable three-dimensional (3-D) four-step alternating direction implicit flnite-difierence time-domain (ADI-FDTD) methods are presented. Based on the exponential evolution operator (EEO), the Maxwell's equations in a matrix form can be split into four sub-procedures. Accordingly, the time step is divided into four sub-steps. In addition, high-order central flnite-difierence operators based on the Taylor central flnite-difierence method are used to approximate the spatial difierential operators flrst, and then the uniform formulation of the proposed high-order schemes is generalized. Subsequently, the analysis shows that all the proposed high-order methods are unconditionally stable. The generalized form of the dispersion relations of the proposed high-order methods is carried out. Finally, in order to demonstrate the validity of the proposed methods, numerical experiments are presented. Furthermore, the efiects of the order of schemes, the propagation angle, the time step, and the mesh size on the dispersion are illustrated through numerical results. Speciflcally, the normalized numerical phase velocity error (NNPVE) and the maximum NNPVE of the proposed schemes are lower than that of the traditional ADI-FDTD method.

ANALYSIS OF ELECTROMAGNETIC PLANE WAVE SCATTERING FROM 2-D PERIODIC ARRANGEMENTS OF POSTS

In the paper, the analysis of electromagnetic wave scattering from frequency selective surface is presented. The surface is composed of periodically arranged posts. The multimodal scattering matrix of such structure is derived and the transmission and re∞ection characteristic for the structure with arbitrary plane wave illumination are calculated. The exact full-wave theory based on the mode-matching method is applied to develop an e-cient theory to analyze such structures. The validity and accuracy of the approach are verifled by comparing the results with those obtained from alternative methods. The analysis of plane wave scattering form the frequency selective surface (FSS) composed of periodic arrangements of scatterers is conducted in this paper. The constructive elements of this structure are comparable in size to the operation wavelength and are composed of conducting and dielectric material. FSSs when multilayered can be utilized as an electromagnetic band structure (EBG) in microwave wavelength range or photonic band structure (PBG) in optical range. Recently, EBGs and PBGs are of great interest due to their extraordinary properties and potential applications, e.g., fllters, polarizers, substrates for radiating elements, or optical switches (1{14). Many numerical techniques have been utilized to investigate band gap structures. The most popular are the cylindrical-harmonic expansion method (15), the flnite element method (16), the flnite difierence method (17), and Fourier modal method (18). FSSs can also flnd application in polarizers

EFFICIENT MULTISCALE FINITE DIFFERENCE FREQUENCY DOMAIN ANALYSIS USING MULTIPLE MACROMODELS WITH COMPRESSED BOUNDARIES

In this paper, a novel idea of reducing numerical complexity of flnite difierence method using multiple macromodels is presented. The e-ciency of the macromodeling technique depends on the number of ports of a model. To enhance the e-ciency of the algorithm the fleld samples at the boundary of the macromodel are replaced with amplitudes of discretized Legendre polynomials. Redeflning the problem in such manner results in signiflcant reduction of the analysis time. The validity and e-ciency of the proposed procedure are demonstrated by performing the analysis of two microwave fllters requiring a high density mesh.

VECTOR MODE ANALYSIS OF OPTICAL WAVEGUIDES BY QUADRATIC SPLINE COLLOCATION METHOD

We present an accurate, e-cient numerical analysis for vector modes of dielectric optical waveguide structures with an arbitrary refractive index proflle using a quadratic spline collocation method (QSCM). The unknown weights of the polynomials are determined by forcing the errors at the collocation points to be zero. Consequently, the original second order difierential equation is converted to a set of algebraic equations which can be solved by matrix techniques. The proposed QSCM method demonstrates better performance than the standard flnite-difierence method of the same convergence rate in terms of grid size with the same degree of computational complexity.

DESIGN AND OPTIMIZATION OF A PERMANENT MAGNET ROTATING MACHINE FOR POWER COOLING GENERATION

Magnetic refrigeration is an innovative, revolutionary, e-cient and environmentally friendly cooling technology which is on the threshold of commercialization. The essential components of magnetic refrigeration system are the magnetic fleld generator and the magnetocaloric material. The two main goals of this paper are to design and to optimize a permanent magnet magnetic refrigeration machine for power cooling generation, where an initial conflguration is studied and based on this study two other conflgurations are presented. Both electromagnetic and thermal studies are explored. The electromagnetic design part has been accomplished by using the flnite elements method and the thermal design part has been achieved using the flnite difierence method.

Variable Mesh Finite Difference Method for Self-Adjoint Singularly Perturbed Two-Point Boundary Value Problems

A numerical method based on flnite difierence method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameteruniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to its normal form and the reduced problem is solved by flnite difierence method taking variable mesh. To support the e‐ciency of the method, several numerical examples have been considered.

FULL-WAVE MODELING OF MULTIPLE VIAS USING DIFFERENTIAL SIGNALING AND SHARED ANTIPAD IN MULTILAYERED HIGH SPEED VERTICAL INTERCONNECTS

A 3D full-wave approach, based on the Foldy-Lax multiple scattering equations, is successfully extended to model massively- coupled multiple vias using difierential signaling and shared antipad in high speed vertical interconnects. For the flrst time, this method has been used and tested on via-pair with shared antipad in multilayered structure. The magnetic frill current source on the port is calculated by using the flnite difierence method. Banded matrix iterative method is applied to accelerate the flnite difierence calculation. Numerical example of 15 signal via-pairs and 20 ground shielding vias in 6- layer board demonstrates that this approach is able to model the via-pair with shared antipad and to include all the coupling efiects among multiple vias. The electrical performances of difierent signal driving schemes are provided and discussed. The coupling crosstalk on various via-pairs is compared. The improvement of signal integrity is shown by using difierential signaling and shared antipad for via-pair in multilayered structure. The results are compared with HFSS and SIwave in accuracy and CPU. The CPU using Foldy-Lax approach is three orders of magnitude faster than using HFSS, and two orders of magnitude faster than using SIwave. The accuracy of Foldy-Lax is within 2% difierence from HFSS up to 20GHz, and outperforms SIwave in accuracy.

Domain decomposition algorithm for the parabolic equation with variable coefficient

In this paper, we design a domain decomposition algorithm for the two-dimensional parabolic equation with variable coe-cient by using a larger spacing at interface points and the implicit scheme at the interior points, hence get an algorithm with the relaxed stability bounds. Then we prove the stability and analyze the accuracy of the algorithm by using the idea of maximum principle. Some results of numerical experiments are also provided. cal explicit scheme by m 2 times. (2) has developed some techniques for the linear parabolic equation by using smaller time step ¢t=¢t=m in Saul'yev schemes at the interface points. The algorithm designed with the technique can increase the sta- bility bound of the classical explicit scheme by 2m times. The algorithm in (3) can increase the stability bound of the classical explicit scheme by 2m 2 times for the lin- ear parabolic equation, using the larger spacing in the x-direction implicit scheme and the y-direction implicit scheme at the interface points. The parallel e-ciency is not very high, because the algorithm needs the global communication while solving the tridiagonal linear algebraic equations. (4) has proposed a parallel flnite difierence method for parabolic PDEs, using either a high-order explicit scheme or a multistep explicit scheme with an intermediate mesh size H lying inside (h;HD) at the interface points. There are some other algorithms, see (5,6,7,8,9) for related discussions. However, much of the work has been directed at the linear parabolic equation, and the proof technique is a constructive method, which is unflt for the parabolic equation with variable a coe-cient. In this paper, we design a domain decomposition algorithm which can increase the stability bound of the classical explicit scheme by 4m 2 times for the parabolic equation with a variable coe-cient, and prove the stability and analyze the accuracy of the algorithm by using the idea of maximum principle. The framework of the paper is as follows. In the next section, a domain decompo- sition algorithm for the parabolic equation with a variable coe-cient is constructed. We use a larger spacing at interface points and the implicit scheme at the interior