Write down the Navier-Stokes equation and explain its terms!
Which simplifications are made in CG applications?
inviscid: viscosity = 0
incompressible: compressibility = 0
What are the components of a Helmholtz decomposition?
Name the three steps of the fractional step method!
advection, pressure solving, pressure projection
Can every compressible fluid be made incompressible? If so, is this a unique map?
yes with the map
𝛻^2𝜙 = 𝛻 ⋅ 𝑢
Where are velocities stored in co-located and staggered grids?
Collocated:
cell centers
Staggered:
u velocity on vertical edge
v velocity on horizontal edge
Which derivative connects the Eulerian and Lagrangian perspective on fluid simulation?
Material derivative
Explain the semi-Lagrangian fluid advection!
What are the conceptual steps of a MacCormack advection?
Forward advection, backward advection, error estimation, Back and forth error compensation and correction, MacCormack
Why do we need limiters in the MacCormack advection?
MacCormack advection can produce unbounded new extrema
How do we set up the pressure matrix for the pressure projection step?
5 diagonal sparse matrix
Name and explain the boundary conditions for velocities and pressures!
velocity:
Dirichlet boundary conditions 𝑢_𝑛 = 0
No-slip 𝑢_𝑡 = 0
Free-slip 𝑢_𝑡 = f(a)
pressure:
Neumann boundary conditions 𝜕p/𝜕𝑛 = 0
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