High-precision difference method for simulating transport diffusion problem

Abstract

The invention relates to a numerical simulation method in the engineering field such as environment, water conservancy and the like and discloses a high-precision difference method with strong universality for series typical model equations suitable for solving problems of flow and heat-mass transfer of various fluids, in particular the problem of transport diffusion. Aiming at the defects that conventional limited difference format of the prior water environment simulation only has low one-order or two-order precision, while the prior multi-step differential equal-high precision method generally relates to a lot of grid points, has over complex construction mode and is most based on quite regular even rectangular meshes, and the like, the invention provides a high-precision difference method under an uneven mesh. The method adopts an indeterminate coefficient method to determine an influence coefficient between a point to be solved and an adjacent point in a difference equation so that the difference format reaches maximum-order precision under the mesh structure. Because the difference format is constructed by adopting an uneven grid system, the density of the mesh distance can be flexibly adjusted according to the size of the variation gradient of physical quantity to be solved, and the simulation precision and efficiency are effectively improved.

Description

technical field [0001] The invention relates to a numerical simulation method in the fields of environment, water conservancy and other engineering fields, and is suitable for high-precision numerical solution of a series of typical model equations of a series of fluid flow and heat and mass transfer problems in a water environment, especially in a non-uniform grid . 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. Numerical simulation method is a common means to study thi...

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Problems solved by technology

[0005] The main purpose of the present invention is to improve the simulation accuracy of the transfer and diffusion problem in the water environment, overcome the defects of the low precision of the conventional numerical method and the inconvenient practical application of the high-precision difference method, and propose a practical fine numerical simulation method for the transfer and diffusion problem

[0006] The present invention aims at the numerical simulation of the transport and diffusion problem in the current water environment. The finite difference scheme often used only has the first-order or second-order accuracy, which cannot meet the requirements of fine simulation of the water environment; while the existing high-precision methods such as multi-step difference are generally There are many grid points involved, or the calculation is more complicated, and based on the current situation of a very regular uniform rectangular grid, a high-precision difference method under a non-uniform grid is proposed

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