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Granular computing acceleration solving method of non-linear convective diffusion equation

A convective diffusion, nonlinear technology, applied in the field of granular computing and fluid mechanics, can solve problems such as low efficiency

Inactive Publication Date: 2016-01-06
CHONGQING INST OF GREEN & INTELLIGENT TECH CHINESE ACADEMY OF SCI
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Problems solved by technology

[0003] In view of this, the purpose of the present invention is to solve the problem of low efficiency in solving the nonlinear convection-diffusion equation, and propose a granular computing accelerated solution method for the nonlinear convection-diffusion equation, and quickly reconstruct the solution by switching between granularity levels, so as to reduce computational complexity Degree, the purpose of improving the solution speed

Method used

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  • Granular computing acceleration solving method of non-linear convective diffusion equation
  • Granular computing acceleration solving method of non-linear convective diffusion equation
  • Granular computing acceleration solving method of non-linear convective diffusion equation

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[0092] c · u t + b · ▿ u - ▿ · ( α ▿ u ) = f ( u ) , i n Ω × ( 0 , T ] , ...

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Abstract

The invention relates to a granular computing acceleration solving method of a non-linear convective diffusion equation, and belongs to the technical field of granular computing and hydromechanics. The method comprises the following steps: firstly, the non-linear convective diffusion equation is solved on a granular layer with coarse granularity to obtain a convergent solution, the granular layer is switched, a one-order Taylor expansion is applied to carry out linearization on an equation set on a fine-granularity layer to further lower computing complexity, so that solving speed is quickened on the basis of a situation that the equation keeps stability and accuracy, and efficiency is improved. From practical demands, the method combines the advantages of multi-granularity, a complex nonlinear problem is firstly solved on an aspect of coarse granularity, the granular layers are switched through the quick reconstruction of a solution between the granular layers, the solution on the fine-granularity layer can be reckoned from the solution on a coarse-granularity layer, the non-linear equation set is artfully linearized, problem complexity is effectively lowered, and efficiency is improved.

Description

technical field [0001] The invention belongs to the technical field of granular computing and fluid mechanics, and relates to a granular computing accelerated solution method for a nonlinear convection-diffusion equation. Background technique [0002] Regarding the problem of convection and diffusion, there are currently three main solutions in engineering applications: finite element method, finite difference method, and finite volume method. In the case of convection dominance, the convection-diffusionequation appears hyperbolic equation properties. At this time, the problem of numerical oscillation and numerical dispersion will appear when solving the equation with the finite element method and finite difference method. JimDouglas, Jr.andThomasF.Russell aimed at this kind of Situation is the first to propose feature correction technology, combined with general methods such as finite element method and finite difference method, there are characteristic finite element metho...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/11
Inventor 王国胤田亚兰徐计尚明生张学睿
Owner CHONGQING INST OF GREEN & INTELLIGENT TECH CHINESE ACADEMY OF SCI
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