Coupling of the Crank–Nicolson scheme and localized meshless technique for viscoelastic wave model in fluid flow

Nikan, O.; Avazzadeh, Z.

doi:10.1016/j.cam.2021.113695

Cited by 31 publications

(9 citation statements)

References 53 publications

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“…In our initial numerical tests, the external force F(t) is a dead weight W o . Based on the numerical integration with central differencing schemes similar to references [15,16], we have obtained the dynamic responses of these two third-order differential equations with Maxwell and Kelvin viscoelastic models. As depicted in Figures 5 and 6, it is clear that the vibration eventually settles down to an equilibrium position due to the dashpot damping.…”

Section: Resultsmentioning

confidence: 99%

Viscoelastic Representation of the Operation of Sucker Rod Pumps

Wang

Rowlan

Henderson

et al. 2022

Fluids

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The issues of leakage with respect to the clearance between the pump plunger outer surface and the pump barrel inner surface and other operational conditions have been revisited in this paper. Both Poiseuille flow rate due to the pressure difference and Couette flow rate due to the plunger motion have been considered. The purpose of this study is to explore the possibility of representing the entire downhole pump system with a simple viscoelastic model. We have explored both Kelvin and Maxwell viscoelastic models along with the dynamic behaviors of a mass point attached to the viscoelastic model. By using the time-dependent polished rod force measured with a dynamometer as the input to the viscoelastic models, we have obtained the displacement responses, which match closely with the actual measurements in experiments and operations. Further study and experiments have been planned and partially implemented in the McCoy School of Engineering at Midwestern State University, a member of the Texas Tech University System.

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Section: Resultsmentioning

confidence: 99%

Viscoelastic Representation of the Operation of Sucker Rod Pumps

Wang

Rowlan

Henderson

et al. 2022

Fluids

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“…The meshfree RBF method is used in both local and global forms. Some authors have tried localized-RBF-based strategies, such as the localized-RBF-generated FD (RBF-FD) [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] and the RBF partition of unity (RBF-PU) [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 ].…”

Section: Properties Of Rbfsmentioning

confidence: 99%

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Golbabai

Safaei

Molavi-Arabshahi

2022

Entropy

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This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This technique parameterizes solutions with an arbitrary RBF and transforms the two-dimensional variational problem (2DVP) into a constrained optimization problem via arbitrary collocation nodes. The advantage of this method lies in its flexibility in selecting between different RBFs for the interpolation and parameterizing a wide range of arbitrary nodal points. Arbitrary collocation points for the center of the RBFs are applied in order to reduce the constrained variation problem into one of a constrained optimization. The Lagrange multiplier technique is used to transform the optimization problem into an algebraic equation system. Three numerical examples indicate the high efficiency and accuracy of the proposed technique.

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“…Nonetheless, global RBF (GRBF) approximations result in ill-conditioned and full matrices, which makes them unsuitable for large problems. Consequently, local strategies, such as the RBF partition of unity (RBF-PU) [23,[36][37][38][39][40][41] and the RBF-generated finite-difference (RBF-FD) approaches [42][43][44][45], are currently under development.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

et al. 2022

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This paper proposes a local meshless radial basis function (RBF) method to obtain the solution of the two-dimensional time-fractional Sobolev equation. The model is formulated with the Caputo fractional derivative. The method uses the RBF to approximate the spatial operator, and a finite-difference algorithm as the time-stepping approach for the solution in time. The stability of the technique is examined by using the matrix method. Finally, two numerical examples are given to verify the numerical performance and efficiency of the method.

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Coupling of the Crank–Nicolson scheme and localized meshless technique for viscoelastic wave model in fluid flow

Cited by 31 publications

References 53 publications

Viscoelastic Representation of the Operation of Sucker Rod Pumps

Viscoelastic Representation of the Operation of Sucker Rod Pumps

Determination of an Extremal in Two-Dimensional Variational Problems Based on the RBF Collocation Method

Numerical analysis of time-fractional Sobolev equation for fluid-driven processes in impermeable rocks

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