The Level Set Equation in Porous Domains
In a porous domain, the equation that determines the evolution of the interface is
(5-5)
Here upore is the pore velocity. Instead using the Darcy velocity u=upore/εp, multiplying the equation with the porosity εp, and rescaling γ such that it again can be set proportional to the maximum magnitude of the velocity field u, the equation can be rewritten as:
(5-6)
This is the nonconservative form of the level set equation that is solved in the Porous Medium feature.
To obtain exact numerical conservation of the integral of εpϕ, switch to the conservative form
(5-7)
The conservative form can be derived from the nonconservative form if it is assumed that the velocity field u satisfies the following continuity equation:
(5-8)