porous_medium_exact

porous_medium_exact, a MATLAB code which returns an exact solution u(x,t) of the porous medium equation (PME), related to the diffusion equation, and based on the Barenblatt solution. The partial differential equation (PDE) has the form dudt=Del^2(u^m). This system reduces to a diffusion equation if the exponent m is set to 1.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

porous_medium_exact is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and codes:

porous_medium_exact_test

matlab_exact, a MATLAB code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).

References:

1. Grigory Barenblatt,
   On some unsteady fluid and gas motions in a porous medium,
   Prikladnaya Matematika i Mekhanika (Applied Mathematics and Mechanics,
   Volume 16, Number 1, pages 67-78, 1952.
2. Rouben Rostamian,
   Programming Projects in C for Students of Engineering, Science, and Mathematics,
   SIAM, 2014,
   ISBN: 978-1-611973-49-5

Source Code:

• porous_medium_exact.m, returns an exact solution of the porous medium PDE.
• porous_medium_parameters.m, returns parameters of the porous medium PDE.
• porous_medium_residual.m, returns the residual of the porous medium PDE.