PRESSURE OUTFLOW BOUNDARIES FOR SPH AND COUPLING SPH TO FINITE VOLUME METHODS

摘要

Smoothed Particle Hydrodynamics (SPH) is a method well suited to simulate dynamic flow when moving interfaces or free surfaces are present [1,2]. In contrast, the finite volume (FV) method may be the best choice for (viscous) flow with boundary layers but without interfaces [3]. Hence, it would be beneficial to couple SPH and FV. Since SPH is a Lagrangean approach, linking it to the Eulerian FV method yields a serious algorithmic and software engineering challenge. A first step for coupling is to transfer fluid from the SPH domain to the FV model. This requires development of an outflow algorithm for holes in the boundary of SPH domains against a non-constant pressure field as well as the transfer of flow data from moving SPH outflow openings to a fixed FV inflow surface. Since SPH does not know the concept of faces, numerical algorithms have been developed to evaluate the pressure force acting on the outflow area and to distribute this force over relevant particles. The orifice geometry is updated during the simulation in order to account for wall motion resulting from fluid-structure interaction [4]. Particles inside the reservoir in the proximity of the orifice will get a part of the force. Examples are outflow from a large container into pipes or blood flow from the left ventricle of a human heart into the aorta. The orifice geometry and the computed flux define the fluid flow entering the domain of an independent numerical simulation. When the pressure at the interface computed by the FV method is returned to the SPH outflow a two-way coupling is established. Details of the SPH outflow boundary algorithm and of the data exchange and mapping procedures will be discussed. Special attention has been given to efficient software engineering of mapping and data exchange workflow, focusing on numerical data exchange between highly inhomogeneous data structures of SPH and FVM solvers. Object Oriented concept of an abstract solver data exchange interface is shortly discussed [5], based on the efficient polymorphic interface class hierarchy, specifically designed for the data exchange process. Advantages and implications of abstract objects implementation are also discussed. Some comparisons with traditional procedural software engineering approaches are provided. Some examples will be presented.