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October 25, 2013, 10:08 |
Basic Numerics Question
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#1 |
Senior Member
Philipp
Join Date: Jun 2011
Location: Germany
Posts: 1,297
Rep Power: 26 |
Dear All,
I have some basic numerics question regarding 1st and 2nd order upwind scheme for the convective term for the 1d convection-diffusion equation: u*rho*Phi' - Gamma* Phi'' = 0 When using the 1st order upwind scheme, one can see, that the first derivative in your differential equation is substituted by the first derivative minus dx/2 * second derivative. Ok, so that means you will introduce some additional diffusion (namely u*rho*dx/2) into your equation, because diffusion has exact the same appearance. When using the 2nd order upwind (or linear upwind scheme), the second derivative will cancel out in the error. That means there is no additional term that has exactly the same appearance as the diffusion. So why do I read in every book that 2nd order upwind is also diffusive (but less then the 1st order)? Why is there additional diffusion at all?
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