Method, device and equipment for evolving non-linear wave of incompressible fluid model

A compressing fluid, nonlinear technology, applied in the field of obtaining nonlinear waves of nonlinear models, can solve problems such as the inability to provide a solution method, and achieve the effect of rich variety, wide application range and small calculation amount

Pending Publication Date: 2022-04-15
SHAANXI NORMAL UNIV
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

However, symbolic calculation software can only help us solve calculation problems, but cannot provide a solution method
At present, there i

Method used

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  • Method, device and equipment for evolving non-linear wave of incompressible fluid model
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  • Method, device and equipment for evolving non-linear wave of incompressible fluid model

Examples

Experimental program
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Effect test

Embodiment 1

[0074] Taking the incompressible fluid model as an example, the specific steps to visualize the nonlinear wave of the incompressible fluid model based on auxiliary functions are as follows:

[0075] (1) Determine the nonlinear model

[0076] Choose a nonlinear model describing an incompressible fluid:

[0077] u yt + u zt + u st +α(u xxxy + u xxxz + u xxxs )+βu x (u xy + u xz + u xs )+βu xx (u y + u z + u s )=0 (1)

[0078] In the formula, x, y, z, s are space variables, t is a time variable, u is a function of space variables x, y, z, s and time variable t, α, β are arbitrary real constants.

[0079] (2) Potential function transformation

[0080] Introduce the potential function transformation (2) and substitute it into the nonlinear model (1) describing the incompressible fluid

[0081]

[0082] In the formula, f is an auxiliary function about the spatial variables x, y, z, s and the time variable t.

[0083] (3) Construct the bilinear form of the nonlin...

Embodiment 2

[0099] Steps (1)-(4) are the same as those in Embodiment 1, and are omitted here, and start from step (5) directly.

[0100] (5) Obtain the nonlinear wave of the incompressible fluid model and visualize the nonlinear wave

[0101] Substituting the auxiliary function f into the bilinear form (3) and potential function transformation (2) describing the nonlinear model of incompressible fluid, the nonlinear wave of the incompressible fluid model is obtained. Here, the nonlinear wave 2 of the incompressible fluid model is given expression U 2 :

[0102]

[0103] And do the following values ​​to the parameters in this embodiment:

[0104]

[0105] Using the symbolic calculation software Maple to visualize U 2 (Such as Figure 5 shown), it is observed that the nonlinear wave U of the incompressible fluid model obtained here 2 is a periodic wave solution.

Embodiment 3

[0107] Steps (1)-(4) are the same as those in Embodiment 1, and are omitted here, and start from step (5) directly.

[0108] (5) Obtain the nonlinear wave of the incompressible fluid model and visualize the nonlinear wave

[0109] Substituting the auxiliary function f into the bilinear form (3) and potential function transformation (2) describing the nonlinear model of incompressible fluid, the nonlinear wave of the incompressible fluid model is obtained, and the nonlinear wave 3 of the incompressible fluid model is given here expression U 3 :

[0110]

[0111] And do the following values ​​to the parameters in this embodiment:

[0112]

[0113] Using the symbolic calculation software Maple to visualize U 3 (Such as Image 6 shown), it is observed that the nonlinear wave U of the incompressible fluid model obtained here 3 It is an antisymmetric-oscillating breather.

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Abstract

The invention discloses a method, a device and equipment for evolving non-linear waves of an incompressible fluid model. The method comprises the following steps: acquiring a non-linear model for describing an incompressible fluid; according to potential function transformation and the nonlinear model describing the incompressible fluid, a bilinear form of the nonlinear model describing the incompressible fluid is constructed, and the bilinear form comprises an auxiliary function; constructing an auxiliary function in a bilinear form of the nonlinear model describing the incompressible fluid; and obtaining a series of non-linear waves of the incompressible fluid model according to the constructed auxiliary function, potential function transformation and a bilinear form. The invention aims to obtain different types of nonlinear wave solutions of a nonlinear model by using an efficient method with small calculation amount, enrich the types of existing nonlinear waves in the field, apply the method to an incompressible fluid model, and visualize the evolution process of the nonlinear waves of the fluid model.

Description

technical field [0001] The invention belongs to the technical field of obtaining nonlinear waves of nonlinear models in nonlinear science, and in particular relates to a method, device and equipment for evolving nonlinear waves of incompressible fluid models. Background technique [0002] Nonlinear phenomena exist in many disciplines such as physics, mathematics, biology, atmospheric oceanography, etc. The study of the commonality of these nonlinear problems has produced a new science, that is, nonlinear science. The field of nonlinear science is mainly composed of three branches: soliton, chaos and fractal. Among them, soliton theory is known as an important branch of nonlinear science, and it is one of the earliest nonlinear phenomena observed through experiments. It mainly discusses the properties of nonlinear models. From a physical point of view, studying the properties of these nonlinear models can reveal the nature of nonlinear phenomena and the laws of motion of mat...

Claims

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Application Information

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IPC IPC(8): G06F30/28G06F113/08G06F119/14
Inventor 吴宝玉姚若侠
Owner SHAANXI NORMAL UNIV
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