Supercompact multiwavelets for flow field simulation

Abstract A supercompact multiwavelet scheme for computational fluid dynamics is presented. Beam and Warming's supercompact wavelet method is an appropriate wavelet for fluid simulation data in the sense that it can provide compact support. The compactness of the wavelets avoids unnecessary interaction with remotely located data (e.g. across a shock discontinuity or vortex) and significantly reduces computational data processing time. Thresholding for data compression with the supercompact wavelets is applied based on a covariance vector structure of multiwavelets. The extension of this scheme to three dimensions is analyzed. Numerical tests demonstrate that the analytic advantages actually result in large data compression ratios.

[1]  R. F. Warming,et al.  Multiresolution Analysis and Supercompact Multiwavelets , 2000, SIAM J. Sci. Comput..

[2]  G. Strang,et al.  Orthogonal multiwavelets with vanishing moments , 1994 .

[3]  A. Harten.  Multiresolution representation and numerical algorithms: A brief review , 1997 .

[4]  George C. Donovan,et al.  Intertwining multiresolution analyses and the construction of piecewise-polynomial wavelets , 1996 .

[5]  B. Alpert.  A class of bases in L 2 for the sparse representations of integral operators , 1993 .

[6]  A. Harti.  Discrete multi-resolution analysis and generalized wavelets , 1993 .

[7]  J. Dacles-Mariani,et al.  Numerical/experimental study of a wingtip vortex in the near field , 1995 .

[8]  Wim Sweldens,et al.  Lifting scheme: a new philosophy in biorthogonal wavelet constructions , 1995, Optics + Photonics.

[9]  Wim Sweldens,et al.  Building your own wavelets at home , 2000 .

[10]  Stanley Osher,et al.  Fast Wavelet Based Algorithms for Linear Evolution Equations , 1994, SIAM J. Sci. Comput..

[11]  Margot Gerritsen,et al.  Designing an efficient solution strategy for fluid flows. 1. A stable high order finite difference scheme and sharp shock resolution for the Euler equations , 1996 .

[12]  O. Vasilyev,et al.  A Dynamically Adaptive Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain , 1996 .

[13]  L. Jameson,et al.  Wavelet-based Numerical Methods , 1998 .

[14]  N. Rott,et al.  On the viscous core of a line vortex II , 1958 .

[15]  D. Hardin,et al.  Fractal Functions and Wavelet Expansions Based on Several Scaling Functions , 1994 .

[16]  Gilbert Strang,et al.  Wavelets and Dilation Equations: A Brief Introduction , 1989, SIAM Rev..

[17]  Stuart E. Rogers,et al.  Steady and unsteady solutions of the incompressible Navier-Stokes equations , 1991 .

[18]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .