Harsh Bhatia , H. Bhatia is with SCI Institute, University of Utah, Salt Lake City, UT, 84112.(email:firstname.lastname@example.org)
The Helmholtz-Hodge decomposition (HHD) describes a flow as the sum of an incompressible, an irrotational, and a harmonic flow, and is a fundamental tool for simulation and analysis. Unfortunately, for bounded domains, the HHD is not uniquely defined, and traditionally, boundary conditions are imposed to obtain a unique solution. However, in general, the boundary conditions used during the simulation may not be known and many simulations use open boundary conditions. In these cases, the flow imposed by traditional boundary conditions may not be compatible with the given data, which leads to sometimes drastic artifacts and distortions in all three components, hence producing unphysical results. Instead, this paper proposes the natural HHD, which is defined by separating the flow into internal and external components. Using a completely data-driven approach, the proposed technique obtains uniqueness without assuming boundary conditions a priori. As a result, it enables a reliable and artifact-free analysis for flows with open boundaries or unknown boundary conditions. Furthermore, our approach computes the HHD on a point-wise basis in contrast to the existing global techniques, and thus supports computing inexpensive local approximations for any subset of the domain. Finally, the technique is easy to implement for a variety of spatial discretizations and interpolated fields in both two and three dimensions.
Harsh Bhatia, Valerio Pascucci, Peer-Timo Bremer, "The Natural Helmholtz-Hodge Decomposition For Open-Boundary Flow Analysis", IEEE Transactions on Visualization & Computer Graphics, , no. 1, pp. 1, PrePrints PrePrints, doi:10.1109/TVCG.2014.2312012