[ANPDEstudent]

Hi all,
Does anyone know of a good source/method for solving the following problem?
u_t + d/dx( f(u) ) = 0 on [0,h(t)]

I'm looking for proper techniques to treat the moving boundary under a variety of value/derivative conditions at the boundaries. I haven't found much in my literature searches.

I have tried adapting a LxF method with MUSCL interpolants from Nessyahu and Tadmor. Non-oscillatory Central Differencing for Hyperbolic Conservation Laws. J. of Comp. Phys. 1990.
I have had little success.

Thanks!