The Laguerre spectral method as applied to
numerical solution of a two−dimensional linear
dynamic seismic problem for porous media

Imomnazarov, Kholmatzhon Kh.; Jian-gang, Tang; Mikhailov, A.A.

doi:10.1515/comp-2016-0018

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…In [20], a linear initial boundary value problem of the dynamics of fluid-saturated porous media, described by three elastic parameters in a reversible hydrodynamic approximation, is solved numerically. The issue of computational model adequacy remains open.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Development of an algorithm for calculating stable solutions of the Saint-Venant equation using an upwind implicit difference scheme

Aloev

Akbarova

Baishemirov

2021

EEJET

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The problem of numerical determination of Lyapunov-stable (exponential stability) solutions of the Saint-Venant equations system has remained open until now. The authors of this paper previously proposed an implicit upwind difference splitting scheme, but its practical applicability was not indicated there. In this paper, the problem is solved successfully, namely, an algorithm for calculating Lyapunov-stable solutions of the Saint-Venant equations system is developed and implemented using an upwind implicit difference splitting scheme on the example of the Big Almaty Canal (hereinafter BAC). As a result of the proposed algorithm application, it was established that: 1) we were able to perform a computational calculation of the numerical determination problem of the water level and velocity on a part of the BAC (10,000 meters) located in the Almaty region; 2) the numerical values of the water level height and horizontal velocity are consistent with the actual measurements of the parameters of the water flow in the BAC; 3) the proposed computational algorithm is stable; 4) the numerical stationary solution of the system of Saint-Venant equations on the example of the BAC is Lyapunov-stable (exponentially stable); 5) the obtained results (according to the BAC) show the efficiency of the developed algorithm based on an implicit upwind difference scheme according to the calculated time. Since we managed to increase the values of the difference grid time step up to 0.8 for calculating the numerical solution according to the proposed implicit scheme.

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Development of an algorithm for calculating stable solutions of the Saint-Venant equation using an upwind implicit difference scheme

Aloev

Akbarova

Baishemirov

2021

EEJET

Self Cite

View full text Add to dashboard Cite

show abstract

“…The problems of the numerical solution and its stability have not been studied. A linear initial-boundary value problem of the dynamics of fluid-saturated porous media, described by three elastic parameters in a reversible hydrodynamic approximation, is solved numerically in [15]. The issue of the computational model adequacy remains open.…”

Section: Introductionmentioning

confidence: 99%

Stability of the Numerical Solution for the Mixed Problem of the Saint-Venant Equations

Aloev

Abdullah

JURAEV

et al. 2021

JMSI

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This article is devoted to the construction and study of the exponential stability of an explicit upwind difference scheme for a mixed problem for the linear system of the Saint Venant equation. For the numerical solution of the mixed problem for the linear system of the Saint Venant equation, an explicit upwind difference scheme is constructed. For a numerical solution, a discrete Lyapunov function is constructed and an a priori estimate for it is obtained. On the basis of the discrete Lyapunov function, the exponential stability of the numerical solution of the initial-boundary-value difference problem of the mixed problem for the linear system of the Saint Venantequation is proved. A theorem on the exponential stability of the numerical solution of the initial-boundary-value difference problem is proved. The behavior of the discrete Lyapunov function is numerically investigated depending on the algebraic condition of exponential stability of the numerical solution of the mixed problem. The results of the theorem on the exponential stability of the numerical solution are confirmed by a specific example of an open channel flow problem.

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“…It is particularly important due to the complexity, both forexperimental and theoretical study, of the internal structure of porous medium.While a wide application of computer simulations based on realistic mathematical models drives further research in that direction [1]- [11]. The latest advances in such mathematical modelling and simulations help to develop many other areas of research, including earth and material sciences, mechanics, biotechnology and medicine,the theory of energy and filtration theory.Frenkel-Biottype theories [12], [13] areoften used for studying dynamic processes in porous media.…”

Section: Introductionmentioning

confidence: 99%

Computer Simulation and Visualization of the Dynamic Poroelasticity Problem Solutions

2020

IJATCSE

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In this paper, we numerically computed the analytical solution of the initial-boundary poroelasticity problem. We applied parallel computation for inverse Laplace transformation and consecutive computation forinverse Fourier transformation to obtainthe two-dimensional timedependent solution. Visualization of the dynamic solution functions is presented for the fixed time values and confirms that the boundary conditions are satisfied at zero and in infinity.

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The Laguerre spectral method as applied to numerical solution of a two−dimensional linear dynamic seismic problem for porous media

Cited by 6 publications

References 9 publications

Development of an algorithm for calculating stable solutions of the Saint-Venant equation using an upwind implicit difference scheme

Development of an algorithm for calculating stable solutions of the Saint-Venant equation using an upwind implicit difference scheme

Stability of the Numerical Solution for the Mixed Problem of the Saint-Venant Equations

Computer Simulation and Visualization of the Dynamic Poroelasticity Problem Solutions

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