<p><strong>Book:</strong></p>

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

<p><strong>Some relevant papers:</strong></p>

<p>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.</p>

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

<p>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</p>

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

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

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

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

<p>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.</p>

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

<hr>

<p>Adaptive grid concepts have been applied to the <a href="http://www.ccpo.odu.edu/POMWEB/">Princeton Ocean Model (POM)</a>.</p>

<p><strong>Original Paper for POM:</strong></p>

<p><a href="http://www.stevens-tech.edu/ses/ceoe/fileadmin/ceoe/pdf/alan_publications/AFB032.pdf">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</a></p>

<p><strong>With adaptive mesh:</strong></p>

<p><a href="http://www.sciencedirect.com/science/article/pii/S1463500309002248">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.</a></p>

CC BY-SA 3.0
2015-04-28T04:33:50.160Z
Can you please comment which flavor of POM uses moving grids? The original variants by Mellor, Blumberg, Oey, etc., do not.
milancurcic
CC BY-SA 3.0
2015-04-28T16:46:14.257Z
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 (http://dx.doi.org/10.1016/j.ocemod.2009.12.003).
arkaia
CC BY-SA 3.0
2015-04-28T17:40:18.357Z
@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.
Isopycnal Oscillation
CC BY-SA 3.0
2015-04-27T23:34:39.067Z
2015-04-28T17:44:29.937Z
2015-04-28T17:44:29.937Z
Isopycnal Oscillation
<p>Would anyone know of references that give detailed explanations on concepts such as moving grids and nested grids in models?</p>

CC BY-SA 3.0
2015-04-24T10:12:54.447Z
This is probably answerable as a request for a reference to a review article or textbook, but if you want a good answer here you may need to be much more specific.
Semidiurnal Simon
CC BY-SA 3.0
2015-04-27T23:06:17.197Z
http://www2.mmm.ucar.edu/wrf/users/hurricanes/moving_nest.html
f.thorpe
CC BY-SA 3.0
2015-04-27T23:35:26.897Z
Did you try http://scicomp.stackexchange.com/?
Isopycnal Oscillation
CC BY-SA 3.0
2015-04-29T03:17:39.577Z
@SimonW I agree. I just recently heard about nonstationary grids used in models, so I was just looking for something to read up on. I also found that the H*WRF documentation (http://www.emc.ncep.noaa.gov/HWRF/HWRFScientificDocumentation2013.pdf) contains a brief discussion on this as well.
user4624937
CC BY-SA 3.0
2015-04-29T03:18:14.450Z
@IsopycnalOscillation no I was not aware of that site! Thanks for pointing that out.
user4624937
<models><reference-request>
References for moving and nested grids in models
user4624937
# References for moving and nested grids in models

(Asked by: username_0 on 2015-04-23)

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

**Tags:** models, reference-request

> **Comments:**
> **username_1**: This is probably answerable as a request for a reference to a review article or textbook, but if you want a good answer here you may need to be much more specific.  
> **username_2**: http://www2.mmm.ucar.edu/wrf/users/hurricanes/moving_nest.html  
> **username_3**: Did you try http://scicomp.stackexchange.com/?  
> **username_0**: @SimonW I agree. I just recently heard about nonstationary grids used in models, so I was just looking for something to read up on. I also found that the H*WRF documentation (http://www.emc.ncep.noaa.gov/HWRF/HWRFScientificDocumentation2013.pdf) contains a brief discussion on this as well.  
> **username_0**: @username_3 no I was not aware of that site! Thanks for pointing that out.  

---

## 1 answers

### Answer by username_3 on 2015-04-27. Score: 9 | Accepted answer

**Book:**

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)](http://www.ccpo.odu.edu/POMWEB/).

**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](http://www.stevens-tech.edu/ses/ceoe/fileadmin/ceoe/pdf/alan_publications/AFB032.pdf)

**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.](http://www.sciencedirect.com/science/article/pii/S1463500309002248)

> **Comments:**
> **username_4**: Can you please comment which flavor of POM uses moving grids? The original variants by Mellor, Blumberg, Oey, etc., do not.  
> **username_5**: 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 (http://dx.doi.org/10.1016/j.ocemod.2009.12.003).  
> **username_3**: @username_4 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.  

---

