Would anyone know of references that give detailed explanations on concepts such as moving grids and nested grids in models?



Shyy W, Udaykumar HS, Rao MM, Smith RW. Computational Fluid Dynamics with Moving Boundaries. Taylor& 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.

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    $\begingroup$ Can you please comment which flavor of POM uses moving grids? The original variants by Mellor, Blumberg, Oey, etc., do not. $\endgroup$ Apr 28 '15 at 4:33
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    $\begingroup$ Moving grids are quite common in atmospheric applications (e.g., WRF), but in ocean applications adaptive meshes are only now being applied. An example that I like is Hofmeister et al., 2010 (dx.doi.org/10.1016/j.ocemod.2009.12.003). $\endgroup$
    – arkaia
    Apr 28 '15 at 16:46
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    $\begingroup$ @milancurcic It seems my notes are wrong. I was looking at old notes from my Ocean Modeling course and it was described as employing a moving grid. Looking at the original paper it clearly does not. The link by @@aretxabaleta shows an implementation of an adaptive/moving grid concept in POM which I will go ahead and include in the answer. $\endgroup$ Apr 28 '15 at 17:40

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