Handling boundaries

• Boundaries \(x=0\), \(x=N_x-1\), \(y=0\), \(y=N_y-1\) need special care

• - For density
• • Assume value \(C^0\) continuity on the boundary
  • • Row/Column \(f_{x,0}=f_{x,1}\), \(f_{0,y}=f_{1,y}\) etc.

• - For velocity: \(f=(f^x,f^y)\)
• • Assume reflexion on walls
  • • Row: \(f_{x,0}=(f^x_{x,1},-f^y_{x,1})\)
    • Column: \(f_{0,y}=(-f^x_{1,y},f^y_{1,y})\)

• - In all cases: Average value for corners
• • \(f_{0,0}=(f_{1,0}+f_{0,1})/2\), etc.