Wavelets, turbulence, and boundary value problems for partial differential equations

John E. Weiss

doi:10.1117/12.205447

6 April 1995 Wavelets, turbulence, and boundary value problems for partial differential equations

John E. Weiss

Proceedings Volume 2491, Wavelet Applications II; (1995) https://doi.org/10.1117/12.205447
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

In this paper the qualitative properties of an inviscid, incompressible two-dimensional fluid are examined by numerical methods based on the compactly supported wavelets (the wavelet- Galerkin method). In particular, we examine the behavior of the spatial gradients of the vorticity. The growth of these gradients is related to the transfer of enstrophy (integral of squared vorticity) to the small-scales of the fluid motion. Implicit time differencing and wavelet-Galerkin space discretization allow a direct investigation of the long time behavior of the inviscid fluid. The effects of hyperviscosity on the long time limit are examined. To solve boundary problems we developed a new numerical method for the solution of partial differential equations in nonseparable domains. The method uses a wavelet-Galerkin solver with a nontrivial adaptation of the standard capacitance matrix method. The numerical solutions exhibit spectral convergence with regard to the order of the compactly supported, Daubechies wavelet basis. Furthermore, the rate of convergence is found to be independent of the geometry. We solve the Helmholtz equation since, for the indefinite case, the solutions have qualitative properties that well illustrate the applications of our method.

Citation Download Citation

John E. Weiss "Wavelets, turbulence, and boundary value problems for partial differential equations", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); https://doi.org/10.1117/12.205447

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available