Numerical Solution of Counter-Current Imbibition Phenomenon in Homogeneous Porous Media Using Polynomial Base Differential Quadrature Method with Chebyshev-Gauss-Lobatto Grid Points

2021 ◽  
pp. 195-206
Author(s):  
Amit K. Parikh ◽  
Jishan K. Shaikh
Keyword(s):  
Porous Media ◽  
Numerical Solution ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Homogeneous Porous Media ◽  
Grid Points ◽  
Counter Current

scholarly journals Differential Quadrature Solution of Hyperbolic Telegraph Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
B. Pekmen ◽  
M. Tezer-Sezgin
Keyword(s):  
Numerical Solution ◽  
Good Accuracy ◽  
Differential Quadrature Method ◽  
Telegraph Equation ◽  
Differential Quadrature ◽  
Time Interval ◽  
Quadrature Method ◽  
Time Level ◽  
Time Direction ◽  
Grid Points

Differential quadrature method (DQM) is proposed for the numerical solution of one- and two-space dimensional hyperbolic telegraph equation subject to appropriate initial and boundary conditions. Both polynomial-based differential quadrature (PDQ) and Fourier-based differential quadrature (FDQ) are used in space directions while PDQ is made use of in time direction. Numerical solution is obtained by using Gauss-Chebyshev-Lobatto grid points in space intervals and equally spaced and/or GCL grid points for the time interval. DQM in time direction gives the solution directly at a required time level or steady state without the need of iteration. DQM also has the advantage of giving quite good accuracy with considerably small number of discretization points both in space and time direction.

scholarly journals A Coupled Pseudospectral-Differential Quadrature Method for a Class of Hyperbolic Telegraph Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Fangzong Wang ◽  
Yong Wang
Keyword(s):  
Differential Quadrature Method ◽  
Pseudospectral Method ◽  
Engineering Calculation ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Quadrature Methods ◽  
Telegraph Equations ◽  
Lagrange Interpolation Polynomials ◽  
Grid Points ◽  
Interpolation Polynomials

Pseudospectral methods and differential quadrature methods are two kinds of important meshless methods, both of which have been widely used in scientific and engineering calculation. The Lagrange interpolation polynomials are used as the trial function of the two methods, and the same distribution of grid points is used. This paper points out that the differential quadrature method is a special form of the pseudospectral method. On the basis of the above, a coupled pseudospectral-differential quadrature method (PSDQM) is proposed to solve a class of hyperbolic telegraph equations. Theoretical analysis and numerical tests show that the new method has spectral precision convergence in spatial domain and has A-stability in time domain. And it is suitable for solving multidimensional telegraph equations.

Differential Quadrature Method in Computational Mechanics: A Review

1996 ◽  
Vol 49 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Charles W. Bert ◽  
Moinuddin Malik
Keyword(s):  
Numerical Solution ◽  
Computational Mechanics ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Solution Technique ◽  
General Interest ◽  
Quadrature Method ◽  
Physical Sciences ◽  
Boundary Problems ◽  
Potential Alternative

The differential quadrature method is a numerical solution technique for initial and/or boundary problems. It was developed by the late Richard Bellman and his associates in the early 70s and, since then, the technique has been successfully employed in a variety of problems in engineering and physical sciences. The method has been projected by its proponents as a potential alternative to the conventional numerical solution techniques such as the finite difference and finite element methods. This paper presents a state-of-the-art review of the differential quadrature method, which should be of general interest to the computational mechanics community.

Harmonic Differential Quadrature Method for Surface Location Error Prediction and Machining Parameter Optimization in Milling

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Ye Ding ◽  
XiaoJian Zhang ◽  
Han Ding
Keyword(s):  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Machining Parameters ◽  
Quadrature Method ◽  
Location Error ◽  
Sampling Grid ◽  
Surface Location Error ◽  
Harmonic Differential Quadrature Method ◽  
Surface Location ◽  
Grid Points

This paper presents a semi-analytical numerical method for surface location error (SLE) prediction in milling processes, governed by a time-periodic delay-differential equation (DDE) in state-space form. The time period is discretized as a set of sampling grid points. By using the harmonic differential quadrature method (DQM), the first-order derivative in the DDE is approximated by the linear sums of the state values at all the sampling grid points. On this basis, the DDE is discretized as a set of algebraic equations. A dynamic map can then be constructed to simultaneously determine the stability and the steady-state SLE of the milling process. To obtain optimal machining parameters, an optimization model based on the milling dynamics is formulated and an interior point penalty function method is employed to solve the problem. Experimentally validated examples are utilized to verify the accuracy and efficiency of the proposed approach.

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