Welcome to Tug’s documentation!

Welcome to the documentation of the TUG project, a simulation program for solving transport equations in one- and two-dimensional uniform grids using cell centered finite differences.

Diffusion

TUG can solve diffusion problems with heterogeneous and anisotropic diffusion coefficients. The partial differential equation expressing diffusion reads:

\[\frac{\partial C}{\partial t} = \nabla \cdot \left[ \mathbf{\alpha} \nabla C \right]\]

In 2D, the equation reads:

\[\frac{\partial C}{\partial t} = \frac{\partial}{\partial x}\left[ \alpha_x \frac{\partial C}{\partial x}\right] + \frac{\partial}{\partial y}\left[ \alpha_y \frac{\partial C}{\partial y}\right]\]

Indices and tables