2ª aula. Evolution Equation . The Finite Volume Method . . Objective of the lecture. The Students “ mise à zero” as francophone say. To show that the conservation principle can be written on: Words (is a concept) Integral equation form, Differential form (can have analytical solution),
TheFinite Volume Method.
The rate of accumulation is “minus” the divergence of the fluxes + (Souces-Sinks)
The Finite (Control) Volume :
1) isolates a portion of the space,
2) systematises budgets’ computation across its faces,
3) Computes the rate of accumulation,
4) Permits the computation of a property rate of change.
In 1D case properties can change along one direction only.
And assuming that the volume is a parallelepiped that doesn’t change in time:
That is the 1D advection-diffusion equation for one property. In a 3D case, for a generic property “k” one would get:
That represents the conservation principle in one point