# Different one sided derivative approximation?

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 January 4, 2006, 23:56 Different one sided derivative approximation? #1 zonexo Guest   Posts: n/a In my FVM code, I am trying to approximate the face value of pressure at the boundary wall. Since it is a cell-center code, all pressure values are at the cell's center. For e.g. at the south/bottom wall, dp/dy=0. the simplest approx will be p_s=p(i,j) higher accuracy from Blazark's CFD book gives p_s=(1/8)*(15*p(i,j)-10*p(i,j+1)+3*p(i,j+2)). however, it is also possible to use dp/dy=(1/2h)*(3*p_s-4*p_n+p_nn) where h=delta, p_n=(p(i,j)+p(i,j+1))/2, p_nn=(p(i,j+1)+p(i,j+2))/2 simplifying, p_s=(2/3)*p(i,j)-(1/3)*p(i,j+1)-(1/6)*p(i,j+2) based on the no. of values used, they should be of the same accuracy, but why are their values different? Also, does anyone has similar expression for non-uniform grids? thanks

 January 5, 2006, 00:31 Re: Different one sided derivative approximation? #2 Praveen. C Guest   Posts: n/a They may be of the same order but the error can be different. Remember that the error is of the form Chr and different schemes of the same order can have different values for C. For non-uniforms grids you can fit a polynomial p(y) = ps + p1 y + p2 y2 + ... and also use dp/dy(y=0) = 0 to obtain the value of ps

 January 11, 2006, 04:40 Re: Different one sided derivative approximation? #3 sourabh Guest   Posts: n/a i think there is a mistake in ur simplification, it should come as Ps = (2/3)*Pi,j + (1/2)*Pi,j+1 - (1/6)*Pi,j+2