Summary: Water And Air Flow Numerical Techniques

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• Lec: Introduction + FD

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• What do environment flow models have in common

  1. The models involve flow in space
  2. The models involve flow in time
  3. most are modeled using some form of the advection-diffusion equation

• There's various types of flow models, what is ours called?

  Environmental flow models

• How do we describe environmental flow models?

  In terms of balance equations, where balance equations are defined as fluxes

• Name 3 techniques that can be used to solve environmental flow models? Describe their characteristics

  
  

  • Finite differences (solving equations on a spatial grid at the node)
  • Finite volumes (budgeting flow in control volumes; representative area attached to node)
  • Finite elements (budgeting flow in control volumes with more accuracy)

• How do internal and external fluxes differ?

  Internal: advection & diffusion within the system
  External: Spatial (2D) eg precipitation, line (1D) or point (locally) eg exit at water reservoir

• What is implied in finite volumes and why?

  Conservation of mass, as representative areas are attached to the node and the edges of this volume are budgetted

• What is the difference between state variables and parameters?

  State variable (s): change over time and describe state of system at certain time & space. 
  Parameters: given and fixed

• What do the terms of the advection/diffusion equation mean?

  1) change of state over time
  2) u: advection: transport with mean velocity
  3) D: diffusion: spread of molecules/turbulence

• What is an ODE as explained by Chiel?

  An equation that tells you how the state variable changes over time, as a function of the state variable itself and the time.

• Which form of ODE will we use in WANT, where s is the state variable?

  Ds/dt = f (t,s)