Multidimensional supercompact wavelets for fluid dynamics

Abstract

Highly compact wavelets called supercompact multiwavelets are extended to higher dimensions for the purpose of numetical fluid solution data compression. Due to the compact nature of the wavelets, the proposed multiresolution approach with the supercompact wavelets offers numerous benefits such as high data compression. Supercompact wavelets are well suitable for gas flow in which some local complex features are embedded in an overall smooth solution. Supercompact wavelets provide advantages in that they allow higher-order accurate representation with compact support and therefore avoid unnecessary interaction with remotely located data across singularities such as shocks and vortices. The numerical implementation is relatively easy and less expensive than the comparable interpolator multiresolution scheme. A practical demonstration of multidimensional supercompact wavelets is presented. Several numerical tests demonstrate large data compression ratios for the outputs of flow field simulation.