Numerical Calculation of Flow Field by Application of Superposition Theory of Partial Differential Equation

Abstract

Based on the superposition theory of partial differential equation (PDE), a new method is introduced here 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. For an instance, by using a software in computational fluid dynamics (CFD), a linear seeping problem in porous media is solved by numerical simulation as well as solutions' superposition of two simpler problems deriving from the proto-problem, and thus the application feasibility of superposition theory in numerical simulation of flow field is verified. More importantly, the application of the new method in CFD can decrease the number of necessary numerical examination greatly.