Hello I am a Phd student on hydraulic engineering. i want to simulate the bridge hydraulic by shallow water equation considering flooding areas. in solving shallow water equation the computational domain changes and i want to know about modeling of this problem.

Hi,

A simple way is slot-method /porosity method of Tao 1983, which treats the wall/beach as slots. Water can enter the slots first and then swash back and forth.

See references:

1) Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves, P.A.Madsen, O.R.Sorensen, H.A.Schaffer, Coastal Engineerng V32, 1997, pp255-287

2)Boussinesq Modeling of Wave Transfraction, breaking, and Runup,. I: 1D , Andrew B. Kennedy, Qin Chen, J.T. Kirby and R.A. Dalrymple, Journal of Waterway, Port, Coastal, and Ocean Engineering, v126, 2000, pp39-47

It'll be a little hard to tune the code.