Lec: FV1
10 important questions on Lec: FV1
"Between nodes, linear interpolation is done to approach the solution". Does this statement belong to FD or FV?
What is the main difference between FD and FV?
For FV, the same domain but the nodes are in the middle of cells or volumes. Each cell is called a control volume.
For volumes: only one value can be assigned to the volume: you can put the node in the middle of the CV or the faces can be drawn exactly in between two nodes.
What are the advantages of XXXX
Advantage of the CV faces centered (right): makes fluxes between nodes more accurate. Straightforward interpolation when the face over which flux occurs is exactly in the middle.
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Write down the math formulation of the flux q in FV
- sign for D:
- sign for -dq/dx:
flux related to advection: if u and s are positive, it will go to the right
D as process goes in the opposite direction of the gradient, as gradient always points in the direction of the largest increase, but D goes in direction of lowest concentration. This is what the minus sign indicates
What is the recipe for Finite Volumes?
- Write down advection diffusion eq in flux form
- Add directions/dimensions
- Integrate over volume
- Check your units
How does FV work in voronoi cells?
How are Voronoi cells made up?
- Put nodes at places of interest: eg close to river, high concentrations
- Start at nodes and blow 'balloons' until one balloon hits another and a border is formed. Interface is in the middle between two nodes and is perpendicular to the line between two nodes.
- Calculate fluxes over the faces
What is the consequence of a large interface between two control volumes if the gradient is high?
Why is FV also called budgetting?
- For every face: how much flux is going over which face
- Size of area of contributing face determines the magnitude of contribution
Do you need initial conditions for a steady state model?
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