From two-dimensional nonlinear diffusion to coupled Haar wavelet shrinkage

2007 ◽  
Vol 18 (2) ◽  
pp. 162-175 ◽  
Author(s):  
Pavel Mrázek ◽  
Joachim Weickert
Keyword(s):  
Nonlinear Diffusion ◽  
Haar Wavelet ◽  
Two Dimensional ◽  
Wavelet Shrinkage

A MULTISCALE WAVELET-INSPIRED SCHEME FOR NONLINEAR DIFFUSION

2006 ◽  
Vol 04 (01) ◽  
pp. 1-21 ◽  
Author(s):  
GERLIND PLONKA ◽  
GABRIELE STEIDL
Keyword(s):  
Nonlinear Diffusion ◽  
Haar Wavelet ◽  
Explicit Scheme ◽  
Wavelet Shrinkage ◽  
Numerical Examples ◽  
Diffusion Filtering ◽  
Signal Value ◽  
The Mean ◽  
Nonlinear Diffusion Filtering

Nonlinear diffusion filtering and wavelet shrinkage are two successfully applied methods for discontinuity preserving denoising of signals and images. Recently, relations between both methods have been established taking into account wavelet shrinkage at one scale. In this paper, we propose a new explicit scheme for nonlinear diffusion which directly incorporates ideas from multiscale Haar wavelet shrinkage. We prove that our scheme permits larger time steps while preserving convergence to the mean signal value. Numerical examples demonstrate the behavior of our scheme for two and three scales.

Grid-Free Vortex Methods for Natural Convection in Two-Dimensional Domains

2012 ◽  
Author(s):  
Issam Lakkis
Keyword(s):  
Natural Convection ◽  
Nonlinear Diffusion ◽  
Reacting Flows ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Vortex Methods ◽  
Free Vortex ◽  
Low Mach Number ◽  
Buoyancy Driven Flows ◽  
Vorticity Generation

Vortex methods for simulating natural convection of an ideal gas in unbounded two-dimensional domains are presented. In particular, the redistribution method for diffusion is extended to enable simulation of nonlinear diffusion of an ideal gas in isobaric conditions encountered in unbounded low-Mach number flows. We also address the problem of handling source terms in grid-free vortex methods and propose a fast, accurate, and physically motivated method for solving the associated inverse problems. Examples include generation of baroclinic vorticity in non-reacting buoyancy driven flows, and in addition, generation of internal energy and species in buoyant reacting flows. Accuracy and speed of the proposed algorithms for nonlinear diffusion and vorticity generation are investigated separately. Simulations of natural convection of a “thermal patch” for Grashof number ranging from to 1562.5 to 25000 are presented.

Sign in / Sign up

Export Citation Format

Share Document