B6a - advection equation
- advection equation arises when momentum, energy or mass is transported in space
- the simplest form is passive advection of a scalar, when the scalar is constant along the line of the velocity field
- analytical solutions are difficult to find
- starting with a 1D case:
- if
constant, plane wave solutions can be found - the general solution is a travelling wave:
- the flow lines are characteristic of the flow
- the change of variables,
, turns the PDE into an ODE