This paper presents a supercompact multi-wavelet scheme and its application to fluid simulation data. The supercompact wavelet method is an appropriate wavelet for fluid simulation data in the sense that it can provide compact support and avoid unnecessary interaction with remotely located data (e.g. across a shock discontinuity or vortices). thresholding for data compression is applied based on a covariance vector structure of multi-wavelets. The extension of this scheme to three dimensions is analyzed. The numerical tests demonstrate that it can allow various analytic advantages as well as large data compression ratios in actual practice.