Abstract
This chapter deals with moving grids and the time-dependent co-ordinate systems. It also shows the transformation of both the continuity and momentum equations of continuum mechanics to a general time-dependent curvilinear co-ordinate system. The numerical solution of time-dependent, also known as transient, evolution, or unsteady transport equations, may require time-dependent moving grids in physical space. The problem includes fixed boundaries in physical space, with internal grid-nodes moving in response to the flow developed and moving boundaries. The grid point velocity vector W plays an important role, and both the cartesian and the contravariant components of W will be required at the grid nodes at any instant. With a differential model of grid generation, a partial differential equation will have to be solved at each time-step to obtain the new grid.
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