偏微分方程叠加原理在流场数值计算中的应用

Application of superposition theory of partial differential equation in numerical calculation of flow field

以偏微分方程叠加原理为基础,阐述了一种求解复杂流场问题的新方法。该方法首先将一个具有复杂边界条件和源项的、难以求解的流场问题拆分为若干具有简单边界条件和源项,从而易于求解流场问题,然后用若干个简单流场问题的解的叠加来描述复杂问题的解。以多孔介质的线性渗流问题为例,应用计算流体力学软件,通过对原问题及经过拆分的简单问题进行数值模拟。将简单问题的数值解叠加并与原问题的数值解进行对比,证明了叠加原理在流场数值模拟中应用的可行性。该方法在计算流体力学中的应用可以极大地降低所需的数值试验次数。

Based on the superposition theory of partial differential equation, a new method is introduced to solve complicated problems of flow field .In this method, a problem of flow field with complex boundary conditions and source items is divided into several problems of flow fields with simple boundary conditions and source items, and then the solution of a complicated problem of flow field can be determined by the solutions＇ superposition of several simple problems of flow fields. Using a CFD software, a linear seeping problem in porous media is solved by numerical simulation and solutions＇ superposition of two simpler problems deriving from the proto-problem. The result verifies the application feasibility of superposition theory in numerical simulation of flow field. The application of the new method in CFD can decrease the number of needed numerical examination.