Implementation of high-order particle-tracking schemes in a water column model

Ocean Modelling

Volumn 36, Issue 1-2, 2011, Pages 80-89

  Gräwe, Ulf ^a  

^a LEIBNIZ INSTITUTE FOR BALTIC SEA RESEARCH   (Germany)

Author keywords

GOTM; Lagrangian particles; Random walk; Stochastic processes; Water column

Indexed keywords

GOTM; LAGRANGIAN PARTICLES; RANDOM WALK; STOCHASTIC PROCESS; WATER COLUMN;

ADVECTION; ASTATINE; DIFFERENTIATION (CALCULUS); DIFFUSION; LAGRANGE MULTIPLIERS; MEASUREMENT THEORY; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; RANDOM PROCESSES; STOCHASTIC SYSTEMS;

ELEMENTARY PARTICLE SOURCES;

ACCURACY ASSESSMENT; ALGORITHM; COMPUTER SIMULATION; DIFFUSIVITY; EFFICIENCY MEASUREMENT; NUMERICAL MODEL; PARTICLE MOTION; RANDOM WALK METHOD; SEDIMENT TRANSPORT; STOCHASTICITY; TRACKING; VELOCITY PROFILE; WATER COLUMN;

EID: 78649949401     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2010.10.002     Document Type: Article

References (55)

1. Addison P., Qu B., Nisbet A., Pender G. A non-Fickian, particle-tracking diffusion model based on fractional Brownian motion. International Journal for Numerical Methods in Fluids 1997, 25(12):1373-1384.
2. Arnold L. Stochastic Differential Equations: Theory and Applications 1974, Wiley, London.
3. Brickman D., Smith P.C. Lagrangian stochastic modeling in coastal oceanography. Journal of Atmospheric and Oceanic Technology 2001, 19(1):83-99.
4. Burchard H., Bolding K., Kühn W., Meister A., Neumann T., Umlauf L. Description of a flexible and extendable physical-biogeochemical model system for the water column. Journal of Marine Systems 2006, 61(3-4):180-211.
5. Burchard H., Petersen O., Rippeth T.P. Comparing the performance of the k-ε{lunate} and the Mellor-Yamada two-equation turbulence models. Journal of Geophysical Research 1998, 103:10543-10554.
6. Burchard H., Rennau H. Comparative quantification of physically and numerically induced mixing in ocean models. Ocean Modelling 2008, 20(3):293-311.
7. Cencini M., Bec J., Biferale L., Boffetta G., Celani A., Lanotte A.S., Musacchio S., Toschi F. Dynamics and statistics of heavy particles in turbulent flows. Journal of Turbulence 2006, 7:N36+.
8. Charles W.M., Heemink A., van den Berg E. Coloured noise for dispersion of contaminants in shallow waters. Applied Mathematical Modelling 2009, 33(2):1158-1172.
9. Charles W.M., van den Berg E., Lin H.X., Heemink A. Adaptive stochastic numerical scheme in parallel random walk models for transport problems in shallow water. Mathematical and Computer Modelling 2009, 50(7-8):1177-1187.
10. Charles W.M., van den Berg E., Lin H.X., Heemink A., Verlaan M. Parallel and distributed simulation of sediment dynamics in shallow water using particle decomposition approach. Journal of Parallel and Distributed Computing 2008, 68(6):717-728.
11. Chung T.J. Computational Fluid Dynamics 2002, Cambridge University Press, Cambridge.
12. Deleersnijder E., Beckers J.-M., Delhez E.J.M. The residence time of settling in the surface mixed layer. Environmental Fluid Mechanics 2006, 6:25-42.
13. Delhez E.J.M., Deleersnijder E. The boundary layer of the residence time field. Ocean Dynamics 2006, 56(2):139-150.
14. Fuller A.T. Horner versus Holdred: an episode in the history of root computation. Historia Mathematica 1999, 26(1):29-51.
15. Gómez-Mourelo P. From individual-based models to partial differential equations: an application to the upstream movement of elvers. Ecological Modelling 2005, 188(1):93-111.
16. Gräwe U., Wolff J.-O. Suspended particulate matter dynamics in a particle framework. Environmental Fluid Mechanics 2009, 10(1):21-39.
17. Heemink A. Stochastic modelling of dispersion in shallow water. Stochastic Hydrology and Hydraulics 1990, 4(2):161-174.
18. Hunter J.R., Craig P., Phillips H.E. On the use of random walk models with spatially variable diffusivity. Journal of Computational Physics 1993, 106:366-376.
19. Isern-Fontanet J., García-Ladona E., Font J., García-Olivares A. Non-Gaussian velocity probability density functions: an altimetric perspective of the mediterranean sea. Journal of Physical Oceanography 2006, 36(11):2153-2164.
20. Jones M.C. Simple boundary correction for kernel density estimation. Statistics and Computing 1993, 3(3):135-146.
21. Kloeden P., Platen E. Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability) 1999, Springer, Berlin, Heidelberg, New York. third ed.
22. Komori Y., Taketomo M. Stable ROW-type weak scheme for stochastic differential equations. Monte Carlo Methods and Applications 1995, 1(4):279-300.
23. Krestenitis Y.N., Kombiadou K.D., Savvidis Y.G. Modelling the cohesive sediment transport in the marine environment: the case of Thermaikos Gulf. Ocean Science 2007, 3(1):91-104.
24. LaBolle E.M., Quastel J., Fogg G.E., Gravner J. Diffusion processes in composite porous media and their numerical integration by random walks: generalized stochastic differential equations with discontinuous coefficients. Water Resources Research 2000, 36(3):651-662.
25. Lalescu C., Teaca B., Carati D. Implementation of high order spline interpolations for tracking test particles in discretized fields. Journal of Computational Physics 2010, 229(17):5862-5869.
26. L'Ecuyer P. Efficient and portable combined random number generators. CACM: Communications of the ACM 1988, 31.
27. L'Ecuyer P. Random numbers for simulation. Communications of the ACM 1990, 33.
28. L'Ecuyer P. Testing random number generators. Proceedings of the 1992 Winter Simulation Conference 1992, 305-313. IEEE Press.
29. L'Ecuyer P. Maximally equidistributed combined Tausworthe generators. Mathematics of Computation 1996, 65(213):203-213.
30. Lekien F., Coulliette C., Mariano A.J., Ryan E.H., Shay L.K., Haller G., Marsden J.E. Pollution release tied to invariant manifolds: a case study for the coast of Florida. Physica D: Nonlinear Phenomena 2005, 210(1-2):1-20.
31. Maier-Reimer E., Sünderman J. On tracer methods in computational hydrodynamics. Engineering Applications of Computational Hydraulics 1982, 1:198-217.
32. Marsaglia G. Xorshift RNGs. Journal of Statistical Software 2003, 8(14):1-6.
33. Marsaglia G., Tsang W.W. The Ziggurat method for generating random variables. Journal of Statistical Software 2000, 5(8):1-7.
34. Marsaglia G., Tsang W.W. Some difficult-to-pass tests of randomness. Journal of Statistical Software 2002, 7(3):1-9.
35. Marsaglia, G., Zaman, A., 1987. Toward a Universal Random Number Generator. Technical Report FSU-SCRI-87-50, Florida State University.
36. Matsumoto M., Nishimura T. Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation 1998, 8(1):3-30.
37. Milstein G.N. A method of second-order accuracy integration of stochastic differential equations. Theory of Probability and its Applications 1979, 23(2):396-401.
38. Munro I., Borodin A. Efficient evaluation of polynomial forms. Journal of Computer and System Sciences 1972, 6(6):625-638.
39. Nagai T., Yamazaki H., Kamykowski D. A Lagrangian photoresponse model coupled with 2nd-order turbulence closure. Marine Ecology Progress Series 2003, 265:17-30.
40. North E., Hood R., Chao S.-Y., Sanford L. Using a random displacement model to simulate turbulent particle motion in a baroclinic frontal zone: a new implementation scheme and model performance tests. Journal of Marine Systems 2006, 60(3-4):365-380.
41. Proehl J.A., Lynch D.R., McGillicuddy D.J., Ledwell J.R. Modeling turbulent dispersion on the North Flank of Georges Bank using Lagrangian Particle Methods. Continental Shelf Research 2005, 25(7-8):875-900.
42. Rippeth T.P., Fisher N.R., Simpson J.H. The cycle of turbulent dissipation in the presence of tidal straining. Journal of Physical Oceanography 2001, 31(8):2458-2471.
43. Rolinski S., Umgiesser G. Modelling short-term dynamics of suspended particulate matter in Venice Lagoon, Italy. Estuarine, Coastal and Shelf Science 2005, 63(4):561-576.
44. Sharma A., Lall U., Tarboton D.G. Kernel bandwidth selection for a first order nonparametric streamflow simulation model. Stochastic Hydrology and Hydraulics 1998, 12(1):33-52.
45. Silverman B.W. Density Estimation for Statistics and Data Analysis. Monographs on Statistics and Applied Probability 1986, Chapman and Hall/CRC. first ed.
46. Simpson J.H., Burchard H., Fisher N.R., Rippeth T.P. The semi-diurnal cycle of dissipation in a ROFI: model-measurement comparisons. Continental Shelf Research 2002, 22(11-13):1615-1628.
47. Spagnol S., Wolanski E., Deleersnijder E., Brinkman R., McAllister F., Cushman-Roisin B., Hanert E. An error frequently made in the evaluation of advective transport in two-dimensional Lagrangian models of advection-diffusion in coral reef waters. Marine Ecology Progress Series 2002, 235:299-302.
48. Spivakovskaya D., Heemink A., Deleersnijder E. Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases. Ocean Dynamics 2007, 57(3):189-203.
49. Spivakovskaya D., Heemink A.W., Deleersnijder E. The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity. Ocean Science 2007, 3(4):525-535.
50. Stijnen J.W., Heemink A., Lin H.X. An efficient 3D particle transport model for use in stratified flow. International Journal for Numerical Methods in Fluids 2006, 51(3):331-350.
51. Visser A.W. Using random walk models to simulate the vertical distribution of particles in a turbulent water column. Marine Ecology Progress Series 1997, 158:275-281.
52. Visser A.W. Lagrangian modelling of plankton motion: from deceptively simple random walks to Fokker-Planck and back again. Journal of Marine Systems 2008, 70(3-4):287-299.
53. Warner J.C., Sherwood C.R., Arango H.G., Signell R.P. Performance of four turbulence closure models implemented using a generic length scale method. Ocean Modelling 2005, 8(1-2):81-113.
54. Woods J. The Lagrangian Ensemble metamodel for simulating plankton ecosystems. Progress in Oceanography 2005, 67(1-2):84-159.
55. Woods J., Barkmann W. Simulating plankton ecosystems by the Lagrangian ensemble method. Philosophical Transactions: Biological Sciences 1994, 343(1303):27-31.