基于叠加原理的气体浓度场数值计算方法

以线性偏微分方程叠加原理为基础,介绍了一种数值计算具有复杂边界条件和源项的气体浓度场的新方法.忽略浓度场对速度场的影响,则已知速度场的组分输运方程为线性对流扩散方程,可以应用线性叠加原理.首先将具有复杂边界条件和源项的浓度场问题分解为若干具有简单边界条件和源项的浓度场问题,然后对每个简单浓度场问题做一次数值模拟,获得其数值解,最后通过叠加这些简单浓度场的数值解,就可以求出复杂浓度场问题的解.该方法的应用可以达到减少数值试验数量、节约计算时间的目的.

Numerical Solutions of a Gas Concentration Field Based on the Superposition Theory of Partial Differential Equations

A new method of numerically calculating a gas concentration field is proposed. It is based on the superposition theory of partial differential equations and included complex bounda-ry conditions and sources. The transportation equations of a given velocity field are linear con-vective and diffusive ones if the impact of the gas-concentration field on the velocity is ignored. This is true where a linear superposition theory exists. The concentration field with complex boundary conditions and sources was first divided into several different concentration field problems having simple boundary conditions and sources. A numerical simulation was carried out on each simple problem to obtain a solution. Finally, the solutions of these simple prob-lems were linked to provide a solution of the complete problem. This new method can reduce the number of simulations required and thus saves much time.