A Multigrid Algorithm with Time-Dependent, Locally Refined Grids for Solving the Nonlinear Diffusion Equation on a Nonrectangular Geometry

1991 ◽  
pp. 241-252 ◽  
Author(s):  
W. Joppich
Keyword(s):  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Nonlinear Diffusion Equation ◽  
Time Dependent ◽  
Multigrid Algorithm

scholarly journals Conditionally Integrable Nonlinear Diffusion with Diffusivity 1/u

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 804 ◽  
Author(s):  
Philip Broadbridge ◽  
Joanna M. Goard
Keyword(s):  
Diffusion Equation ◽  
Nonlinear Diffusion ◽  
Meromorphic Functions ◽  
Nonlinear Diffusion Equation ◽  
Direct Application ◽  
Time Dependent ◽  
Flux Boundary Conditions ◽  
General Complex ◽  
Laser Heated ◽  
Special Time

An explicit mapping is given from the space of general complex meromorphic functions to a space of special time-dependent solutions of the 1 + 2-dimensional nonlinear diffusion equation with diffusivity depending on concentration as D = 1 / u. These solutions have constant-flux boundary conditions. Some simple examples are constructed, including that of a line source enclosed by a cylindrical barrier. This has direct application to electron diffusion in a laser-heated plasma.

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