Time change method for dynamic data reconstruction of anomalous diffusion problems

A technology of anomalous diffusion and dynamic data, applied in the field of dynamic data reconstruction time transformation, which can solve the problems of unstable process and unreliable results.

Inactive Publication Date: 2016-12-07
HOHAI UNIV
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  • Abstract
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Problems solved by technology

[0006] Purpose of the invention: The purpose of the present invention is to provide a dynamic data reconstruction time transformation method for anomalous diffusion problems in view of the shortcomings of the existing anomalous diffusion concentration reconstruction technolo

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  • Time change method for dynamic data reconstruction of anomalous diffusion problems
  • Time change method for dynamic data reconstruction of anomalous diffusion problems
  • Time change method for dynamic data reconstruction of anomalous diffusion problems

Examples

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Example

[0081] Example: Example 1: Consider the following fractal convection and diffusion problem:

[0082] ∂ γ u ( x , t ) ∂ t γ ( x , t ) = - A ∂ u ( x , t ) ∂ x + D ∂ 2 u ( x , t ) ∂ x 2 + f ( x , t ) , x A [ 0 , 10 ] , t A [ 0 , 1 ] , 0 γ ≤ 2 u ( 0 , t ) = e t γ u ( 10 , t ) = 121 · e t γ u ( x , 0 ) = e · ( 1 + x ) 2

[0083] The analytical solution of this problem is:

[0084] u ( x , y , t ) = e t γ · ( 1 + x ) 2

[0085] Among them, the diffusion coefficient D=0.5, and the convection coefficient A=1.

[0086] In order to verify the effectiveness of the method, we choose the time step and space step to be Δt = 0.005 and Δ...

Example Embodiment

[0087] Embodiment 2: Consider the point source problem of the following fractal convection diffusion equation:

[0088] ∂ u ( x , t ) ∂ t γ = - A ∂ u ( x , t ) ∂ x + D ∂ 2 u ( x , t ) ∂ x 2 , x A [ 0 , 15 ] , t > 0 , 0 γ ≤ 2 ∂ u ( 0 , t ) ∂ x = ∂ u ( 10 , t ) ∂ x = 0 , u ( x , 0 ) = 1 x = 10 0 e l s e

[0089] Among them, the diffusion coefficient D=0.5, the convection coefficient A=0, and the fractal order γ=0.5.

[0090] In order to verify the effectiveness of the method, we select the number of time points and the number of space points as nt=300 and nx=600, respectively, and the spatial items are discrete in C-N format. according to figure 2 Arrange the time nodes as shown, Figure 4 The compariso...

Example Embodiment

[0091] Embodiment 3: Consider the point source problem of the following fractional convection-diffusion equation:

[0092] ∂ γ u ( x , t ) ∂ t γ = - A ∂ u ( x , t ) ∂ x + D ∂ 2 u ( x , t ) ∂ x 2 , x A [ 0 , 15 ] , t > 0 , 0 γ ≤ 2 ∂ u ( 0 , t ) ∂ x = ∂ u ( 10 , t ) ∂ x = 0 , u ( x , 0 ) = 1 x = 10 0 e l s e

[0093] Among them, the diffusion coefficient D=0.5, the convection coefficient A=0, and the fractal order γ=0.5.

[0094] In order to verify the effectiveness of the method, we choose the number of time points and the number of space points as nt=200 and nx=100, respectively, and the spatial items are discrete in C-N format. according to figure 2 Arrange the time nodes as shown, Figure 5 The ...

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Abstract

The invention discloses a time change method for dynamic data reconstruction of anomalous diffusion problems. According to the method, fractal derivative and fractional derivative models have the characteristics of spatial and temporal scale changes, so that dynamic data of anomalous diffusion is reconstructed on the basis of intrinsic time change; a characteristic time of a diffusion process is used as a time term scale to respond the interior movement of the diffusion process in a diffusion format, so that the reliability of a calculation result is improved, the calculation error is reduced, the stability of the calculation result is improved, the calculation efficiency is improved, a calculated amount and a memory space do not need to be added, the calculation is simple, rapid and easy to implement, the problem of result oscillation in the initial stage can be effectively solved, an accurate stable numerical value result can be obtained, solute arrival times and speeds in a relocation diffusion process of solutes can be reflected more really, and reliable guidance can be provided for engineering application; and the method can be used for simulating the processes of migration, in soil, of pollutants, petroleum seepage, underground water transportation, and relocation diffusion of moisture such as turbulent flows and the solutes, provide scientific instructions for scientifically preventing and treating environment pollution, and has important theoretical and engineering meanings.

Description

technical field [0001] The invention relates to the problem of anomalous diffusion of fluid, in particular to a dynamic data reconstruction time transformation method for the problem of anomalous diffusion. Background technique [0002] In many engineering fields such as environment, water conservancy, chemical industry, and energy, the transfer and diffusion of basic parameters such as momentum, heat, and mass of fluids in the flow process have attracted much attention. The fundamental solution to all kinds of fluid flow and heat and mass transfer problems must be based on the scientific grasp of the laws of transport and diffusion in the fluid environment, so as to understand the changes of the fluid or the substances contained in it with time and space. With the improvement of the level of human cognition of the world, the phenomenon of abnormal diffusion is becoming more and more common and attracting attention. [0003] The diffusion and migration of water in complex m...

Claims

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Application Information

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IPC IPC(8): G06F17/12
CPCG06F17/12
Inventor 孙洪广刘肖廷
Owner HOHAI UNIV
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