CFD Online Discussion Forums (https://www.cfd-online.com/Forums/)
-   Main CFD Forum (https://www.cfd-online.com/Forums/main/)
-   -   4th order discretization of 2nd order difference (https://www.cfd-online.com/Forums/main/12963-4th-order-discretization-2nd-order-difference.html)

 dusky.He February 11, 2007 04:01

4th order discretization of 2nd order difference

Does anyone can tell me the form of 4th-order discretization of 2-order difference in cylindrical coordinate.

In Cartesian coordinate, it is (-F(i-2)+16F(i-1)-30F(i)+16F(i+1)-F(i+2))/(12*dx)

 Harish February 12, 2007 01:36

Re: 4th order discretization of 2nd order differen

If you have mathematica/maple/maxima you can find the coefficients using it.Also look for the paper on compact scheme by sanjeev lele ( JCP 1992),it should give you the required finite difference discretization.

 Chandra February 14, 2007 05:16

Re: 4th order discretization of 2nd order differen

discretization is independent of co-ordinate system [d2u/dx2 or d2u/dr2 are same]. If, whatever u have wrote, is correct in Cartesian co-ordinate, it is correct in Cylindrical co-ordinate as well. So, enjoy!! you already have what r u looking for :)

What changes with change in co-ordinate system is terms itself, not the way it is discretized.

hope it helps.

 qunwuhe February 14, 2007 09:00

Re: 4th order discretization of 2nd order differen

You are right, but I want to discretize the Lapace of Phi in cylindrical coordinate. So the divergence of a gradient in cylindrical is different from the one in Cartetian coordinate.

 All times are GMT -4. The time now is 21:34.