Question: Find the second-order accurate finite difference approximation of the first derivative of the velocity component (u) in the x-direction using the Taylor series expansion. (Note: i and j are in the x and y-direction respectively).
Options
A : frac{u_{i,j+1}-u_{i,j-1}}{Delta x}u i,j+1 ?u i,j?1 ?x
B : frac{u_{i+1,j}-u_{i-1,j}}{Delta x}
C : frac{u_{i+1,j}-u_{i-1,j}}{2Delta x}
D : frac{u_{i,j+1}-u_{i,j-1}}{2Delta x}
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