|
[Sponsors] |
July 7, 2007, 23:26 |
Abt. L1norm and L2norm in CFD
|
#1 |
Guest
Posts: n/a
|
I am testing the convergence property of an approach. The initial conditions are likely to a real case(e.g. 10GPa in left and 100MPa in right for the one-dimensional Riemann problem). Due to inherent numerical diffusion across shock front, the shock front is shifted a little bit, 3~4 grids.
Thus, the relative errors may be large. My question is how to apply the L1norm and L2norm in the CFD when the numerical diffusion arises. L1norm was implemented by DO i=1,nx rL1norm=rL1norm+ABS( u0(0,i,1)-ua0(i,1) ) END DO L2norm was DO i=1,nx rL2norm=rL2norm+((ue(0,i,1)-u0(i,1))*(ue(0,i,1)-u0(i,1))) END DO rL2norm=SQRT(rL2norm)/nx In case of L1norm, the error values are pretty high compared with other papers mentioning the L1norm is about 10^-3 order. In my case, L1norm was about 10^3(e.g. 127000...). In the CFD, is there any other definition of L1norm compared with the vector norm? |
|
July 9, 2007, 02:39 |
Re: Abt. L1norm and L2norm in CFD
|
#2 |
Guest
Posts: n/a
|
Dear Jinwon,
The norm of error can be defined in numerous ways. Specifically, a suitable error norm that works for both regular and irregular grids is to use the following area(or volume) weighted norm, implemented as : norm = 0.0 totvol = 0.0 DO i=1,nx norm = norm +(abs(ue(0,i,1)-u0(i,1)))*volume(i) totvol = totvol + volume(i) END DO norm = norm/totvol It is easy to see that for regular grids where the cell volumes are identical this reduces to \sigma(abs(error(i))/nx, which is the discrete L1 norm of error. Hope this helps, Regards, Ganesh |
|
July 9, 2009, 08:14 |
|
#3 |
Member
Nishant Kumar
Join Date: Jun 2009
Posts: 32
Rep Power: 16 |
Hi Jinwon,
Were you able to solve Riemann problem for the real case? reply me at babuu.nishu@gmail.com |
|
|
|