셀 기반 유한 차분법을 이용한 효율적인 3차원 음향파 파동 전파 모델링

박병경,하완수 한국지구물리.물리탐사학회 2019 지구물리와 물리탐사 Vol.22 No.2

In this paper, we studied efficient modeling strategies when we simulate the 3D time-domain acoustic wave propagation using a cell-based finite difference method which can handle the variations of both P-wave velocity and density. The standard finite difference method assigns physical properties such as velocities of elastic waves and density to grid points; on the other hand, the cell-based finite difference method assigns physical properties to cells between grid points. The cell-based finite difference method uses average physical properties of adjacent cells to calculate the finite difference equation centered at a grid point. This feature increases the computational cost of the cell-based finite difference method compared to the standard finite different method. In this study, we used additional memory to mitigate the computational overburden and thus reduced the calculation time by more than 30 %. Furthermore, we were able to enhance the performance of the modeling on several media with limited density variations by using the cell-based and standard finite difference methods together. 셀 기반 유한 차분법을 사용하여 P파 속도와 밀도 변화를 고려한 3차원 시간 영역 음향 파동 전파 모델링에서성능을 향상시킬 수 있는 방법을 살펴보았다. 일반적인 유한 차분법에서는 격자점에 탄성파 속도 또는 밀도와 같은 물성을 할당하고 계산하지만 셀 기반 유한 차분법에서는 이러한 물성을 격자점 사이의 셀에 할당한다. 격자점에서의 차분식계산을 위해서는 주변 셀의 물성 평균값을 이용하는데 이로 인해 일반적인 유한 차분법에 비해 계산량이 증가하게 된다. 이 연구에서는 이러한 계산량 문제를 개선하기 위해 메모리를 추가로 사용하여 모델링 시간을 30 % 이상 줄일 수 있었다. 또한 밀도가 제한적으로 변화하는 매질에서 셀 기반 유한 차분법과 일반 유한 차분법을 함께 사용하여 모델링 성능을 추가로 향상시킬 수 있었다.

Numerical Method for Exposure Assessment of Wireless Power Transmission under Low-Frequency Band

Minhyuk Kim,SangWook Park,Hyun-Kyo Jung 한국자기학회 2016 Journal of Magnetics Vol.21 No.3

In this paper, an effective numerical analysis method is proposed for calculating dosimetry of the wireless power transfer system operating low-frequency ranges. The finite-difference time-domain (FDTD) method is widely used to analyze bio-electromagnetic field problems, which require high resolution, such as a heterogeneous whole-body voxel human model. However, applying the standard method in the low-frequency band incurs an inordinate number of time steps. We overcome this problem by proposing a modified finite-difference time-domain method which utilizes a quasi-static approximation with the surface equivalence theorem. The analysis results of the simple model by using proposed method are in good agreement with those from a commercial electromagnetic simulator. A simulation of the induced electric fields in a human head voxel model exposed to a wireless power transmission system provides a realistic example of an application of the proposed method. The simulation results of the realistic human model with the proposed method are verified by comparing it with the conventional FDTD method.

Time-varying meshing stiffness calculation of an internal gear pair with small tooth number difference by considering the multi-tooth contact problem

Guangjian Wang,Qing Luo,Shuaidong Zou 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.9

Due to the multiple tooth contact problem involving internal gear pair with small tooth number difference (IGPSTND), the existing analytical methods applied for standard spur or helix gear pairs to calculate the time-varying meshing stiffness (TVMS) are not suitable. In this paper, two methods are proposed for calculating the time-varying meshing stiffness in internal gear pairs with small tooth difference. In the first method, an analytical model is established by using the potential energy method, considering the clearance of initial contact tooth and the external load. The second method proposes the application of a hybrid finite elementanalytical method. The proposed two methods are validated by the application of the finite element method. By taking the results of finite element analysis as a comparative reference, the results show that the finite element - analytical method is closer to the reference results than the results obtained by the analytical method, and both methods are less computationally expensive than finite element analysis.

FRACTIONAL CHEBYSHEV FINITE DIFFERENCE METHOD FOR SOLVING THE FRACTIONAL BVPS

Khader, M.M.,Hendy, A.S. The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.1

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

HYDROPLANING SIMULATIONS FOR TIRES USING FEM, FVM AND AN ASYMPTOTIC METHOD

Kim, T.W.,Jeong, H.Y. 한국자동차공학회 2010 International journal of automotive technology Vol.11 No.6

Hydroplaning tires have been frequently simulated using commercial explicit FEM (Finite Element Method) codes. However, these simulations are slow, and the result of the lift force is so oscillatory that the hydroplaning speed cannot be accurately determined. Thus, in the author's previous study, a new methodology using FDM (Finite Difference Method) code and an FE tire model iteratively was proposed. However, this full iteration method still required a long computation time, especially for patterned tires. Thus, in this study, the full iteration methodology was modified such that no iteration or only one additional iteration was needed at each speed. Then, by applying the full iteration method, no iteration method and one iteration method, the hydroplaning speeds of a straight-grooved tire were determined, and it was noted that the hydroplaning speed obtained from the one iteration method was almost the same as that obtained from the full iteration method. Moreover, the hydroplaning speeds of two patterned tires were determined using the one iteration method, and they were compared with the hydroplaning speeds obtained experimentally.

A fourth order finite difference method applied to elastodynamics: Finite element and boundary element formulations

Souza, L.A.,Carrer, J.A.M.,Martins, C.J. Techno-Press 2004 Structural Engineering and Mechanics, An Int'l Jou Vol.17 No.6

This work presents a direct integration scheme, based on a fourth order finite difference approach, for elastodynamics. The proposed scheme was chosen as an alternative for attenuating the errors due to the use of the central difference method, mainly when the time-step length approaches the critical time-step. In addition to eliminating the spurious numerical oscillations, the fourth order finite difference scheme keeps the advantages of the central difference method: reduced computer storage and no requirement of factorisation of the effective stiffness matrix in the step-by-step solution. A study concerning the stability of the fourth order finite difference scheme is presented. The Finite Element Method and the Boundary Element Method are employed to solve elastodynamic problems. In order to verify the accuracy of the proposed scheme, two examples are presented and discussed at the end of this work.

Fractional Chebyshev finite difference method for solving the fractional BVPs

M. M. Khader,A. S. Hendy 한국전산응용수학회 2013 Journal of applied mathematics & informatics Vol.31 No.1

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

A Comparison between 3-D Analytical and Finite Difference Method for a Trapezoidal Profile Fin

Lee, Sung-Joo,Kang, Hyung-Suk 江原大學校 産業技術硏究所 2001 産業技術硏究 Vol.21 No.A

A comparison is made of the temperature distribution and heat loss from a trapezoidal profile fin using two different 3-dimensional methods. These two methods are analytical and finite difference methods. In the finite difference method 78 nodes are used for a fourth of the fin. A trapezoidal profile fin being the height of the fin tip is half of that of the fin base is chosen arbitrarily as the model. One of the results shows that the relative error in the total convection heat loss obtained by using 78 nodes in the finite difference method as compared to the heat conduction through the fin root obtained by analytic method seems to be good (i.e., -3.5% <relative error< 1.0%) for the following range ; Bi<0.3, L<2 and 0.4<w<10.

A Comparison between 3-D Analytical and Finite Difference Method for a Trapezoidal Profile Fin

이성주(Lee Sung Joo),강형석(Kang Hyung Suk) 강원대학교 산업기술연구소 2001 産業技術硏究 Vol.21 No.1

A comparison is made of the temperature distribution and heat loss from a trapezoidal profile fin using two different 3-dimensional methods. These two methods are analytical and finite difference methods. In the finite difference method 78 nodes are used for a fourth of the fin. A trapezoidal profile fin being the height of the fin tip is half of that of the fin base is chosen arbitrarily as the model. One of the results shows that the relative error in the total convection heat loss obtained by using 78 nodes in the finite difference method as compared to the heat conduction through the fin root obtained by analytic method seems to be good (i.e., -3.5% <relative error< 1.0%) for the following range ; Bi<0.3, L<2 and 0.4<w<10.

고차 셀 기반 유한 차분법을 이용한 음향파 파동 전파 모델링

조준현,하완수 한국자원공학회 2021 한국자원공학회지 Vol.58 No.4

We propose high-order finite-difference methods for acoustic wave propagation modeling considering the P-wave velocity and density. We can simulate wave propagation without directly differentiating discontinuous medium parameters using the cell-based finite-difference method. However, a limitation of the conventional cell-based finite-difference method using the second-order scheme is that it requires a large number of grids per wavelength to obtain an accurate result. We improve the conventional cell-based method to exploit arbitrary high-order schemes. In a numerical example, we compare results of the proposed methods with that of the analytic solution, and show that we can obtain accurate results with small number of grids per wavelength using the high-order cell-based methods. 이 연구에서는 P파 속도와 밀도를 고려한 음향파 파동 전파 모델링을 위한 고차 셀 기반 유한 차분법을 제안하였다. 셀 기반 유한 차분법을 사용하면 불연속적인 매질 특성을 직접 미분하지 않고도파동 전파를 모델링할 수 있다. 그러나 기존의 2차 차분식을 사용하는 셀 기반 유한 차분법에서는정확한 결과를 얻기 위해 파장당 격자수가 커야 한다는 한계가 있었다. 이 연구에서는 임의의 고차차분식을 사용할 수 있도록 기존 기법을 개선하였다. 수치 예제에서 해석해와의 비교를 통해 고차셀 기반 유한 차분법을 이용하면 파장당 격자수가 작아도 정확한 결과를 얻을 수 있음을 보였다.