Well-balanced compressible cut-cell simulation of atmospheric flow

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 367, Issue 1907, 2009, Pages 4559-4575

  Klein, R ^a   Bates, K R ^b   Nikiforakis, N ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Atmospheric; Conservative; Cut cell; Dimensional splitting; Numerical methods; Well balancing

Indexed keywords

BUBBLES (IN FLUIDS); GRAVITATION; NUMBER THEORY; NUMERICAL ANALYSIS; NUMERICAL METHODS;

APPROXIMATION SCHEME; ATMOSPHERIC FLOWS; BOUNDARY CELL; BUOYANT BUBBLES; CELL SIMULATION; CONSERVATIVE; CUT CELL; DIMENSIONAL SPLITTING; GRAVITATIONAL SOURCE; NUMERICAL SOLUTION; POTENTIAL STABILITY; REGULAR GRIDS; STABLE SIMULATION; TEST PROBLEM; TIME STEP; TOPOGRAPHIC GRADIENTS; WAVE GENERATION;

ATMOSPHERIC MOVEMENTS;

EID: 73249151558     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2009.0174     Document Type: Article

References (35)

1. Adcroft, A., Hill, C. &Marshall, J. 1997 Representation of topography by shaved cells in a height coordinate ocean model. Mon. Weather Rev. 125, 2293-2315. (doi:10.1175/1520-0493(1997)125<2293:ROTBSC>2.0.CO;2)
2. Aftosmis, M., Berger, M. J. & Melton, J. 1998 Robust and efficient Cartesian mesh generation for component based geometry. AIAA J. 36, 952-960. (doi:10.2514/2.464)
3. Almgren, A. S., Bell, J. B., Colella, P. &Marthaler, T. 1997 A Cartesian grid projection method for the incompressible Euler equations in complex geometries. SIAM J. Sci. Comput. 18, 1289-1309.(doi:10.1137/ S1064827594273730)
4. Artebrant, R. &Schroll, H. J. 2006 Limiter-free third order logarithmic reconstruction. SIAM J. Sci. Comput. 28, 359-381. (doi:10.1137/040620187)
5. Barad, M. F. 2006 An adaptive Cartesian grid projection method for environmental flows. PhD thesis, University of California.
6. Botta, N., Klein, R., Langenberg, S. &Luetzenkirchen, S. 2004 Well balanced finite volume methods for nearly hydrostatic flows. J. Comput. Phys. 196, 539-565. (doi:10.1016/j.jcp.2003.11.008) (Pubitemid 38613256)
7. Causon, D. M., Ingram, D. M., Mingham, C. G., Yang, G. &Pearson, R. V. 2000 Calculation of shallow water flows using a Cartesian cut cell approach. Adv. Water Resour. 23, 545-562. (doi:10.1016/S0309-1708(99 00036-6)
8. Clarke, D., Salas, M. &Hassan, H. 1986 Euler calculations for multielement airfoils using Cartesian grids. AIAA J. 24, 353-358. (doi:10.2514/3.9273)
9. Colella, P., Graves, D. T., Keen, B. J. &Modiano, D. 2006 A Cartesian grid embedded boundary method for hyperbolic conservation laws. J. Comput. Phys. 211, 347-366. (doi:10.1016/j.jcp.2005.05.026) (Pubitemid 41363989)
10. Durran, D. R. 1986 Another look at downslope windstorms. Part I: The development of analogs to supercritical flow in an infinitely deep, continuously stratified fluid. J. Atmos. Sci. 43, 2527-2543.(doi:10.1175/1520-0469(1986) 043<2527:ALADWP>2.0.CO;2)
11. Egger, J. 1974 Numerical experiments on lee cyclogenesis. Mon. Weather Rev. 102, 847-860. (doi:10.1175/1520-0493(1974)102<0847:NEOLC>2.0.CO;2)
12. Einfeldt, B. 1988 On Godunov-type methods for gas dynamics. SIAMJ. Numer. Anal. 25, 294-318.(doi:10.1137/0725021)
13. Gal-Chen, T. &Somerville, R. C. J. 1975 On the use of a coordinate transformation for the solution of the Navier-Stokes equations. J. Comput. Phys. 17, 209-228. (doi:10.1016/0021-9991(75)90037-6)
14. Gallus, W. A. &Klemp, J. B. 2000 Behavior of flow over step orography. Mon. Weather Rev. 128, 1153-1164. (doi:10.1175/1520-0493(2000) 128<1153:BOFOSO>2.0.CO;2)
15. Gatti-Bono, C. &Colella, P. 2006 An anelastic allspeed projection method for gravitationally stratified flows. J. Comput. Phys. 216, 589-615. (doi:10.1016/j.jcp.2005.12.017) (Pubitemid 43792902)
16. Greenberg, J. M. &Le Roux, A. Y. 1996 A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM Numer. Anal. 33, 1-16. (doi:10.1137/0733001)
17. Helzel, C., Berger, M. &Leveque, R. 2005 High-resolution rotated grid method for conservation laws with embedded geometries. SIAM J. Sci. Comput. 26, 785-809. (doi:10.1137/S106482750343028X)
18. Janjic, Z. I. 1989 On the pressure gradient force error in ρ-coordinate spectral models. Mon. Weather Review 117, 2285-2292. (doi:10.1175/1520-0493(1989)117<2285:OTPGFE>2.0.CO;2)
19. Janjic, Z. I. 1989 On the pressure gradient force error in ́-coordinate spectral models. Mon. Weather Review 117, 2285-2292. (doi:10.1175/1520-0493(1989)117<2285:OTPGFE>2.0.CO;2)
20. Klein, R. 2009 Asymptotics, structure, and integration of sound-proof atmospheric flow equations. Theor. Comput. Fluid Dyn. 23, 161-195. (doi:10.1007/s00162-009-0104-y)
21. LeVeque, R. J. 1998 Balancing source terms and flux gradients in high-resolution Godunov methods. J. Comput. Phys. 146, 346-365. (doi:10.1006/jcph.1998.6058) (Pubitemid 128347128)
22. LeVeque, R. &Shyue, K. 1996 Two dimensional front tracking based on high resolution wave propagation methods. J. Comput. Phys. 123, 354-368. (doi:10.1006/jcph.1996.0029) (Pubitemid 126161923)
23. Mesinger, F., Janjí, Z. I., Nîkoví, S., Gavrilov, D. &Deaven, D. G. 1988 The step-mountain coordinate: model description and performance for cases of alpine lee cyclogenesis and for a case of an Appalachian redevelopment. Mon. Weather Rev. 116, 1493-1518. (doi:10.1175/1520-0493(1988)116<1493:TSMCMD>2.0.CO;2)
24. Murman, S., Aftosmis, J. &Berger, M. 2003 Implicit approaches for moving boundaries in a 3 D Cartesian method. Technical Report, American Institute of Aeronautics and Astronautics, Reston, VA.
25. Oevermann, M., Scharfenberg, C. &Klein, R. 2009 A sharp interface finite volume method for elliptic equations on Cartesian grids. J. Comput. Phys. 228, 5184-5206. (doi:10.1016/j.jcp.2009.04.018)
26. Pember, R. B., Bell, J. B., Colella, P., Crutchfield, W. Y. &Welcome, M. L. 1995 An adaptive Cartesian grid method for unsteady compressible flow in irregular regions. J. Comput. Phys. 120, 278-304. (doi:10.1006/jcph.1995.1165)
27. Purvis, J. W. &Burkhalter, J. E. 1979 Prediction of critical Mach number for store configurations. AIAA J. 17, 1170-1177. (doi:10.2514/3.7617)
28. Quirk, J. 1994 An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies. Comput. Fluids 23, 125-142. (doi:10.1016/0045-7930(94)90031-0)
29. Rosatti, G., Cesari, D. &Bonaventura, L. 2005 Semi-implicit, semi-Lagrangian modelling for environmental problems on staggered Cartesian grids with cut cells. J. Comput. Phys. 204, 353-377. (doi:10.1016/j.jcp.2004.10. 013) (Pubitemid 40305790)
30. Simmons, A. J. &Burridge, D. M. 1981 An energy and angular-momentum conserving vertical finite-difference scheme and hybrid vertical coordinates. Mon. Weather Rev. 109, 758-766. (doi:10.1175/1520-0493(1981)109<0758: AEAAMC>2.0.CO;2)
31. Steppeler, J., Bitzer, H.-W., Minotte, M. &Bonaventura, L. 2002 Nonhydrostatic atmospheric modeling using a z-coordinate representation. Mon. Weather Rev. 130, 2143-2149. (doi:10.1175/1520-0493(2002)130<2143: NAMUAZ>2.0.CO;2)
32. Sundqvist, H. 1976 On vertical interpolation and truncation in connection with use of sigma system models. Atmosphere 14, 37-52.
33. Webster, S., Thuburn, J., Hoskins, B. &Rodwell, M. 1999 Further development of a hybrid-isentropic GCM. Q. J. R. Meteorol. Soc. 125, 2305-2331. (doi:10.1002/qj.49712555817)
34. Yamazaki, H. &Satomura, T. 2008 Vertically combined shaved cell method in a z-coordinate nonhydrostatic atmospheric model. Atmos. Sci. Lett. 9, 171-175. (doi:10.1002/asl.187)
35. Zhu, Z., Thuburn, J., Hoskins, B. J. &Haynes, P. H. 1992 A vertical finite-difference scheme based on a hybrid ́-⊖-p coordinate. Mon. Weather Rev. 120, 851-862. (doi:10.1175/1520-0493(1992)120<0851:AVFDSB>2. 0.CO;2)