References for moving and nested grids in models
Book:

Shyy W, Udaykumar HS, Rao MM, Smith RW. Computational Fluid Dynamics with Moving Boundaries. Taylor&amp; Francis: London, 1996.

Some relevant papers:

Jin C, Xu K. A unified moving grid gas-kinetic method in Eulerian space for viscous flow comnputation. Journal of Computational Physics 2007; 222:155–175.

Hirt CW, Amsden AA, Cook JL. An arbitrary Lagrangian–Eulerian computing method for all flow speeds. Journal of Computational Physics 1997; 135:203–216.

Piggott M, Pain C, Gorman G, Power P, Goddard A. h, r, and hr adaptivity with applications in numerical ocean modeling. Ocean Modelling 2005; 10:95–113

HuangWZ, Ren Y, Russell RD.Moving mesh methods based on moving mesh partial differential equations. Journal of Computational Physics 1994; 113:279–290.

Miller K, Miller RN. Moving finite element. SIAM Journal of Numerical Analysis 1981; 18:1019–1032.

Dorfi EA, Drury LO. Simple adaptive grids for 1-D initial value problems. Journal of Computational Physics 1987; 69:175–195.

Tang T. Moving mesh methods for computational fluid dynamics. Contemporary Mathematics 2005; 383:141–174.

Tang H, Tang T. Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. SIAM Journal of Numerical Analysis 2003; 41(2):487–515.

Tang H, Tang T. Multi-dimensional moving mesh method for shock computations. Contemporary Mathematics 2003; 330:169–183.



Adaptive grid concepts have been applied to the Princeton Ocean Model (POM).

Original Paper for POM:

Blumberg, A. F. and G. L. Mellor, A description of a three-dimensional coastal ocean circulation model. Three-Dimensional Coastal ocean Models, edited by N. Heaps, 208 pp., American Geophysical Union., 1987

With adaptive mesh:

Hofmeister, Richard, Hans Burchard, and Jean-Marie Beckers. "Non-uniform adaptive vertical grids for 3D numerical ocean models." Ocean Modelling 33.1 (2010): 70-86.