Divergence-Free Wavelet Frames

Divergence-free Wavelet Bases on the Hypercube

Abstract. Given a biorthogonal pair of multi-resolution analyses on the interval, by integration or differentiation, we build a new biorthogonal pair of multiresolution analyses. Using both pairs, isotropic or, as we focus on, anisotropic divergence-free wavelet bases on the hypercube are constructed. Our construction generalizes the one from [Rev. Mat. Iberoamericana, 8 (1992), pp. 221–237] by...

Divergence-Free Wavelet Analysis of Turbulent Flows

In this paper we study the application of divergence-free wavelet bases for the analysis of incompressible turbulent flows and perform several experiments. In particular, we analyze various nominally incompressible fields and study the influence of compressible perturbations due to experimental and computational errors. In addition, we investigate the multiscale structure of modes obtained from...

Divergence - Free Wavelet Analysis of Turbulentflowscem

The three-dimensional Fueter equation and divergence-free frames

This paper extends hyperkähler Floer theory with flat target manifolds from the case where the source is a 3-sphere or 3-torus, equipped with a standard frame, to the case where the source is a general closed orientable 3-manifold, equipped with a regular divergence-free frame. Regular divergence-free frames are characterized by the nonexistence of nonconstant solutions to the unperturbed linea...

Divergence-free Wavelet Projection Method for Incompressible Viscous Flow

We present a new wavelet numerical scheme for the discretization of Navier-Stokes equations with physical boundary conditions. The temporal discretization of the method is inspired from the projection method. Helmholtz-Hodge decomposition using divergence-free and curl-free wavelet bases satisfying physical boundary conditions allows to define the projection operator. This avoids the use of Poi...