Fast difference scheme for the reaction-diffusion-advection equation with exact artificial boundary conditions

Li, Can; Wang, Haihong; Yue, Hongyun; Guo, Shenyang

doi:10.1016/j.apnum.2021.12.013

Cited by 8 publications

(4 citation statements)

References 39 publications

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“…Recently, the Lie symmetry analysis has been applied to the nonlinear space-fractional boundary layer equation by Pan et al [6]. Mohammadein et al [7] found a similarity solution for a viscous fluid flow on an infinite vertical plate with a fractional laminar boundary layer by means of fractional power series technique, and, recently, in [8], artificial boundary conditions on an unlimited domain were considered.…”

Section: Introductionmentioning

confidence: 99%

Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution

Jannelli,

Speciale

2024

Mathematics

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In this paper, we present a fractional version of the Sakiadis flow described by a nonlinear two-point fractional boundary value problem on a semi-infinite interval, in terms of the Caputo derivative. We derive the fractional Sakiadis model by substituting, in the classical Prandtl boundary layer equations, the second derivative with a fractional-order derivative by the Caputo operator. By using the Lie symmetry analysis, we reduce the fractional partial differential equations to a fractional ordinary differential equation, and, then, a finite difference method on quasi-uniform grids, with a suitable variation of the classical L1 approximation formula for the Caputo fractional derivative, is proposed. Finally, highly accurate numerical solutions are reported.

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Section: Introductionmentioning

confidence: 99%

Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution

Jannelli,

Speciale

2024

Mathematics

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“…1 To use numerical methods, the challenge of infinite domains should be handled. 2 A direct approach is to establish a relatively large mesh so that the boundaries have no effect on the interest area. However, this scheme demands a high computational capacity resulting in an inefficient computation.…”

Section: Introductionmentioning

confidence: 99%

“…Methods for solving these PDEs in unbounded domains have so far received a great attention 1 . To use numerical methods, the challenge of infinite domains should be handled 2 . A direct approach is to establish a relatively large mesh so that the boundaries have no effect on the interest area.…”

Section: Introductionmentioning

confidence: 99%

A local absorbing boundary condition for 3D seepage and heat transfer in unbounded domains

Liu

Wei

et al. 2023

Num Anal Meth Geomechanics

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For the parabolic problems in an infinite space, previous methods basically focused on the one‐ and two‐dimensional artificial boundary. Here, a high‐order local absorbing boundary condition (ABC) used for the fluid seepage and heat transfer in unbounded one‐ and two‐dimensional domains is extended to the relative three‐dimensional analysis. The local ABCs are first derived for the problem in an isotropic media and then stretched to the case in an orthotropic media. The function including time‐related variables in Laplace‐Fourier space is approximated through the Gauss‐Legendre quadrature formula. By using the inverse Laplace‐Fourier transformation, the local ABCs in Laplace‐Fourier space are inverted into the ones in time space. The numerical examples indicate that the local ABCs can provide satisfactory results with high computational efficiency, especially for the long‐term analysis. Moreover, the relationship among the diffusion coefficient, maximum simulation time and approximation order value is also investigated.

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“…Solving this system of equations is not an easy task to be done analytically. Thus, numerical approaches are often taken for practicality [2], [3].…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Deep Learning Implementation in Operational Condition Forecasting of a Gas Transmission Pipeline Network

Ihsan,

Darmadi,

Uttunggadewa

et al. 2023

Int. J. Adv. Sci. Eng. Inf. Technol.

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Monitoring natural gas transmission in a pipeline network is important to maintain the supply and demand balance in natural gas transactions and distribution. Gas pressure, temperature, flowrate, and gas properties must be monitored during the transmission process. These variables, also known as operational conditions, need to be simulated carefully to understand the dynamics and behavior over time. Commonly used physical equations, such as thermodynamic or hydraulic equations, have limitations in simulating future trends because they need some known boundary conditions to be solved. In that case, data-driven method is needed, especially nowadays when data management is widely implemented. This paper implements a deep Recurrent Neural Network (RNN) to forecast the future behavior of gas pressure as an operational condition in a gas pipeline network receiving platform. Different types of recurrent cells are used, i.e., Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). The model is trained in 8 years of a gas pipeline network operational data. Historical flowrate data in the end-nodes become the forecast input in addition to the past pressure data. The sensitivity of the model and learning parameters is experimented with and analyzed to understand the capacity of the RNN in the given task. Mean absolute error is set as the satisficing metric, whereas the training time is set as optimizing metrics. The obtained best model successfully forecasts the future pressure of one day ahead with only around 2% relative error.

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Fast difference scheme for the reaction-diffusion-advection equation with exact artificial boundary conditions

Cited by 8 publications

References 39 publications

Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution

Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution

A local absorbing boundary condition for 3D seepage and heat transfer in unbounded domains

Performance Analysis of Deep Learning Implementation in Operational Condition Forecasting of a Gas Transmission Pipeline Network

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