Hybrid three-dimensional supercompact multiwavelets for computational fluid dynamics

Abstract

Supercompact wavelets are extended to hybrid-type applications for practical fluid dynamics data management. Beam and Warming's supercompact multiwavelet method is regarded as one proper tool for representing fluid simulation data because of its compact support. This wavelet compactness significantly reduces storage requirements as well as data processing time, and can prevent unnecessary interaction with closely located data across singularities such as shocks and vortices. For effective domain subdivision, a hybrid method that combines 3-D, 2-D, and 1-D versions of supercompact multiwavelets is developed. The hybrid 3-D type of supercompact multiwavelet shows high data compression ratio in practical fluid simulation data because the mother wavelets are highly effective and encompass subdivision methods. With the present method, efficient data management for datasets of huge size is enabled without losing important features. Several numerical tests substantiate large data compression for flow field simulation.