Solving just simple algebraic equation implicitly
 

Hi foamers, I'm trying to edit the source code of interFoam to implement sediment load.

And to do this, I need to estimate the value of 'x' in below equation :

x/abs(x) + [abs(u-x)]*(u-x) == a

'u' is known vectorfield

and 'x' is unknown vectorfield that I want to find at every cells.

'a' is just a constant.

but I don't have any idea to deal with such an implicit solution on the source code in OpenFOAM.

I'll appreciate any comments about this.

Thanks in advance :)