I have a 2D (x,y) scalar advection problem that describes net blowing snow ($q$) transport at a point. This takes the form$$q = A - F*\nabla\cdot(q {\bf \hat u}),$$where A ($kg\cdot m^{-2}\cdot s^{-1}$) is a spatially variable scalar source term, $F$ is fetch (m) and $\hat u$ unit normal parallel to to the wind direction (unitless); $\hat u$ is spatially variable. Initial conditions are [ I believe] $q(x,y)=0$ (no blowing snow, develop steady state) and 0 flux boundary condition. This equation is from the literature, but feels a bit wonky so I'm trying to piece it together.I would like to solve this via an upwind-scheme -- blowing snow transport moves down wind and should only transport snow to cells downwind.Further, I would like to solve this on a unstructured triangular mesh.My hang up (and it's likely a dumb one):do I discretize this via FVM and then, for each edge, apply an unwind scheme? Ah the moment I'd like to keep it simple (can move to a better upwind method later), and just find the 'upwind' triangle (via dot-product signs at the edge?) and compute the difference with the current cell. Will that work? If not what is the best way to piece this together? I appreciate any help, I feel like this is a silly question, but I can't quite wrap my head around the order in which to do this.
Simple steady-state advection problem: do I need FVM with upwind scheme?
finite volume;advection