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Finite Difference solution to nonlinear diffusion equation 1.0

  Date Added: July 11, 2013  |  Visits: 288

Finite Difference solution to nonlinear diffusion equation

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Solves nonlinear diffusion equation which can be linearised as shown for the general nonlinear diffusion equation in Richtmyer & Morton [1]. The approach is to linearise the pde and apply a Crank-Nicolson implicit finite difference scheme to solve the equation numerically.Matlab run command--------------------------type:IsoFreeSurfaceSolversolves the pde:-------------------frac{partial h}{partial t}=frac{1}{12}frac{partial^2 h^4}{partial x^2}The pde has the application to isothermal viscous fluid flow spreading on a horizonatal substrate under gravity - Huppert [2]. Note that PDE has been nondimensionlised.Initial conditions: t=0: h = (1 - x^2)_{+} + 10^-6 (has prewetting film) The spatial domain is discretised taking account of symmetry at x = 0: frac{partial h}{partial x} = 0 and is also used to close the free surface model at the end of the discretised domain (x = xend) - assumes fluid won't reach this boundary.The pde can be solved analytically using similarity equations as discussed by Barenblatt [3]; used below to validate numerical solution.References--------------[1] "Difference Methods for initial value problems," R. D. Richtmyer and K. W. Morton, John Wiley and Sons, 1967.[2] "The Propagation of two-dimensional and axisymmetric visous gravity currents over a rigid horizontal surface," H. E. Huppert, Journal of Fluid Mechanics, 1982.[3] "On some unsteady motions of a liquid or gas in a porous medium, Russian journal Prikladnaya Matematika i Mekhanika, 1952.

Requirements: No special requirements
Platforms: Matlab
Keyword: Barenblatt Initial Numerical Problemsquot Quotdifference References Solution Validate
Users rating: 0/10

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