ALE mesh-smoothing by a simple average?
 

I am solving 2D compressible flow problems. In doing, I need to adjust the fluid mesh in time. There are a number of mesh-smoothing schemes. Among them, I preferred to use the simple averaging scheme due to its simplicity. It is

x_new(i)=1/N*SUM(x_old(k)) over all neighbors. In some literatures, the formula needs to be iterated through few steps. My guess is that the procedure be like the solution method for the laplace equation.

My questions are that

what the convergence criteria for that equation is,

whether it must be iterated through few steps.

,for two-dimensions and whether each dimension is separately

iterated or both dimensions are iterated together. Is there

any good sample code or reference for ALE-mesh-smoothing?

Thanks in advance.

I now have no iteration loop to check the convergence of mesh-smoothing. --- Sample codes ---- DO 100 i=2,nnx-1

DO 100 j=2,nny-1

ip=nnx*(j-1)+i

ie=nnx*(j-1)+(i+1)

iw=nnx*(j-1)+(i-1)

in=nnx*j +i; inw=nnx*j +(i-1); ine=nnx*j +(i+1)

is=nnx*(j-2)+i; isw=nnx*(j-2)+(i-1); ise=nnx*(j-2)+(i+1)

!

temp(ip,1)=(temp(ie,1)+temp(iw,1)+temp(in,1)+temp( inw,1)+temp(ine,1)+&

temp(is,1)+temp(isw,1)+temp(ise,1))/8.d0

temp(ip,2)=(temp(ie,2)+temp(iw,2)+temp(in,2)+temp( inw,2)+temp(ine,2)+&

temp(is,2)+temp(isw,2)+temp(ise,2))/8.d0 100 CONTINUE