Conformal Mapping

Panos

Hi, I want to solve a mapping problem. I must to map the coordinates system from curvelinear system (physical domain) to cartesian system (computational domain) and solve my problem in cartesian,(conformal mapping).If I want to map a stationary boundary conditions (x,y,z to xi,etha,zeta),there is not problem. But if I want to map a moving boundary problem , I have problem to find the relations between two domains. In this case we have moving nodes in the domain, then we must to map (x,y,z,t) to (xi,etha,zeta,taw). In this case we must to find dxi/dt ,detha/dt , dzta/dt ,dt/dxi ,dt/detha ,dt/dzta . Of course we have x=x(t), y=y(t), z=z(t) in xyz domain. I wil be very pleased if anybody to tell me what is this values or how can I to find this values . Thanks