Extrapoltion method on LBM


I’m new on LBM and i’ve some problems in inderstanding the extrapolation method wich is used at many Boundary conditions like curved boundary, open boundary…

I wonder if some one can explain it to me and what’s the difference between extrapolation first and second order ?? such as the exempl of open BC if anyone can help me to write this open BC on the first order accurency please

Thank you