HyPAM [Zhang and Liu 2009 J. Comput. Phys. In press, doi:10.1016/j.jcp.2008.10.029] is a new hybrid continuum-particle framework developed by Qinghai Zhang. HyPAM addresses three major issues associated with numerical simulations of complex free-surface flows, viz. interface tracking, fragmentation and large physical jumps. HyPAM consists of three parts: (1) the Polygonal Area Mapping (PAM) method for interface tracking; (2) a new graph-based single-phase decomposition algorithm that decomposes a phase into a continuum zone, a buffer zone and a particle zone; (3) a 'passive-response' assumption, in which the air phase is assumed to respond passively to the continuum part of the water phase.
The PAM method [Zhang and Liu 2008 J. Comput. Phys. 227(8):4063-4088] represents material areas explicitly as piecewise polygons, traces characteristic points on polygon boundaries along pathlines and calculates new material areas inside interface cells via polygon-clippings in a discrete manner. PAM has very little spatial numerical diffusion and tracks the interface singularities naturally and accurately. In addition to its high accuracy, PAM can be directly used on either a structured rectangular mesh or an unstructured mesh without any modifications. The results from a set of widely used benchmark tests, e.g. the vortex test and deformation test, show that the PAM method is superior to existing volume-of-fluid (VOF) methods. In fact, it can be rigorously proven that VOF methods are not consistent while the PAM method is [Zhang and Liu 2008 SIAM J Numer. Anal., submitted].
For the illustration and validation of HyPAM, A number of examples, including water droplet impact, solitary wave propagation, and dam-break problems, are simulated. The hybrid feature of HyPAM can be clearly observed in a more detailed examination on spilling breakers in a dam-break test. It is shown that HyPAM is more accurate and versatile than Cobras. One major contribution of this work is the single-phase decomposition algorithm, useful for many other hybrid formulations.
Future improvements of HyPAM include the following:
- incorporation of irregular solid boundaries into HyPAM; (work in progress)
- generalization of the PAM method to 3-D dimensions and for tracking interface of more than 2 materials;
- increasing the accuracy of Navier-Stokes solver to fourth-order accuracy; (work in progress)
- enlarging the application range of HyPAM by utilizing the Adaptive Mesh Refinement (AMR) technique.
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