A new approach for analysis of resonant structures based on the spatial finite-difference and temporal differential formulation

1996 ◽  
Vol 44 (4) ◽  
pp. 631-635 ◽  
Author(s):  
Zhizhang Chen ◽  
A.M.K. Chan
Keyword(s):  
Finite Difference ◽  
New Approach ◽  
Resonant Structures ◽  
Differential Formulation

scholarly journals Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
A. Kazemi Nasab ◽  
A. Kılıçman ◽  
Z. Pashazadeh Atabakan ◽  
S. Abbasbandy
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Finite Difference Methods ◽  
Algebraic Equations ◽  
Chebyshev Wavelets ◽  
New Approach ◽  
Nonlinear Algebraic Equations ◽  
Chebyshev Wavelet ◽  
Fractional Differential

A new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. This method can be considered as a nonuniform finite difference method. Some examples are given to verify and illustrate the efficiency and simplicity of the proposed method.

scholarly journals A Tsunami Ball Approach to Storm Surge and Inundation: Application to Hurricane Katrina, 2005

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Steven N. Ward
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Hurricane Katrina ◽  
Storm Surge ◽  
Volume Density ◽  
Momentum Equation ◽  
Cape Cod ◽  
Laptop Computer ◽  
New Approach ◽  
Advection Term

Most analyses of storm surge and inundation solve equations of continuity and momentum on fixed finite-difference/finite-element meshes. I develop a completely new approach that uses a momentum equation to accelerate bits or balls of water over variable depth topography. The thickness of the water column at any point equals the volume density of balls there. In addition to being more intuitive than traditional methods, the tsunami ball approach has several advantages. (a) By tracking water balls of fixed volume, the continuity equation is satisfied automatically and the advection term in the momentum equation becomes unnecessary. (b) The procedure is meshless in the finite-difference/finite-element sense. (c) Tsunami balls care little if they find themselves in the ocean or inundating land. (d) Tsunami ball calculations of storm surge can be done on a laptop computer. I demonstrate and calibrate the method by simulating storm surge and inundation around New Orleans, Louisiana caused by Hurricane Katrina in 2005 and by comparing model predictions with field observations. To illustrate the flexibility of the tsunami ball technique, I run two “What If” hurricane scenarios—Katrina over Savannah, Georgia and Katrina over Cape Cod, Massachusetts.

Numerical simulation of Sector Bond log and improved cement bond image

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. D95-D104 ◽  
Author(s):  
Ruo-Long Song ◽  
Jin-Xia Liu ◽  
Chun-Hui Hou ◽  
Ke-Xie Wang
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Field Data ◽  
New Approach ◽  
Channel Size ◽  
Well Production ◽  
Well Completion ◽  
Bond Evaluation ◽  
Potential Channels ◽  
Acoustic Responses

The two principal functions of a primary cement job are to provide support for the casing and to provide hydraulic isolation between zones. A poor cement job may cause many issues during the well production. Therefore, cement bond evaluation is very important in well completion. The Sector Bond log (SBL) has been widely used for cement bond evaluation for years. The SBL tool has eight pairs of directional transmitter-receivers, which are equally distributed in azimuth and used for identifying channels and channel azimuths. To better understand SBL, using a parallel 3D finite difference algorithm, we numerically simulated acoustic responses of the SBL under a variety of cement bond scenarios and investigated the sensitivity of the integral amplitudes to channel size and its azimuth. We further developed a new approach to image potential channels in cement annulus using the integral amplitudes. The comparisons between conventional SBL images and the reprocessed ones using the new approach showed significant improvement on both synthetic and field data.

A New Singularity Treatment Approach for Journal-Bearing Mixed Lubrication Modeled by the Finite Difference Method With a Herringbone Mesh

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Yanfeng Han ◽  
Shangwu Xiong ◽  
Jiaxu Wang ◽  
Q. Jane Wang
Keyword(s):  
Finite Difference ◽  
Journal Bearing ◽  
Hydrodynamic Lubrication ◽  
Computational Time ◽  
Maximum Pressure ◽  
Computational Accuracy ◽  
Pressure Derivative ◽  
New Approach ◽  
Rectangular Mesh ◽  
Difference Form

Steady-state mixed hydrodynamic lubrication of rigid journal bearing is investigated by using a finite difference form of the Patir–Cheng average Reynolds equation under the Reynolds boundary condition. Two sets of discretization meshes, i.e., the rectangular and nonorthogonal herringbone meshes, are considered. A virtual-mesh approach is suggested to resolve the problem due to the singularities of pressure derivatives at the turning point of the herringbone mesh. The effectiveness of the new approach is examined by comparing the predicted load with that found in the literature for a smooth-surface case solved in the conventional rectangular mesh. The effects of the skewness angles of symmetric and asymmetric herringbone meshes on the predicted parameters, such as load, friction coefficient, attitude angle, and maximum pressure, are investigated for smooth, rough, and herringbone-grooved bearing surfaces. It is found that the new approach helps to improve the computational accuracy significantly, as demonstrated by comparing the results with and without the treatment of the pressure derivative discontinuity although the latter costs slightly less computational time.

scholarly journals Automated Linearization of Nonlinear Coupled Differential and Algebraic Equations

1994 ◽  
Vol 116 (2) ◽  
pp. 429-436 ◽  
Author(s):  
J. D. Trom ◽  
M. J. Vanderploeg
Keyword(s):  
Finite Difference ◽  
Dynamic Systems ◽  
Large Scale ◽  
Algebraic Equations ◽  
New Approach ◽  
Large Scale Systems ◽  
Equation Formulation ◽  
Relative Coordinate ◽  
Equilibrium Configurations ◽  
Multibody Dynamic

This paper presents a new approach for linearization of large multibody dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute linearizations for large-scale systems that were previously impossible.

scholarly journals New approach to construct freeform surface by numerically differential formulation

2013 ◽  
Vol 53 (3) ◽  
pp. 031307 ◽  
Author(s):  
Yu-Lin Tsai ◽  
Ming-Chen Chiang ◽  
Ray Chang ◽  
Chung-Hao Tien ◽  
Chin-Tien Wu
Keyword(s):  
Freeform Surface ◽  
New Approach ◽  
Differential Formulation

scholarly journals Automated Linearization of Nonlinear Coupled Differential and Algebraic Equations

1991 ◽  
Author(s):  
Martin J. Vanderploeg ◽  
Jeff D. Trom
Keyword(s):  
Finite Difference ◽  
Dynamic Systems ◽  
Large Scale ◽  
Algebraic Equations ◽  
New Approach ◽  
Large Scale Systems ◽  
Equation Formulation ◽  
Equilibrium Configurations ◽  
Multi Body ◽  
Body Dynamic

Abstract This paper presents a new approach for linearization of large multi-body dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute linearizations for large-scale systems that were previously impossible.

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