# Abt. L1norm and L2norm in CFD

 User Name Remember Me Password
 Register Blogs Members List Search Today's Posts Mark Forums Read

 July 7, 2007, 23:26 Abt. L1norm and L2norm in CFD #1 jinwon 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 ganesh 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: 10 Hi Jinwon, Were you able to solve Riemann problem for the real case? reply me at babuu.nishu@gmail.com

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

All times are GMT -4. The time now is 09:33.

 Contact Us - CFD Online - Privacy Statement - Top