Simulation of the transport of particles in coastal waters using forward and reverse time diffusion

Advances in Water Resources

Volumn 28, Issue 9, 2005, Pages 927-938

  Spivakovskaya, Daria ^a   Heemink, A W ^a   Milstein, G N ^b   Schoenmakers, J G M ^b  

^a Delft University of Technology ^*  (Netherlands)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Advection diffusion equation; Diffusion processes; Particle concentration; Particle models; Stochastic differential equations

Indexed keywords

COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; DIFFUSION; MATHEMATICAL MODELS; MONTE CARLO METHODS; OCEANOGRAPHY;

CALAMITY; COASTAL WATERS; PARTICLE CONCENTRATION; REVERSE-TIME DIFFUSION;

WATER POLLUTION;

NEARSHORE DYNAMICS; SEDIMENT TRANSPORT;

EID: 23444453340     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2005.03.005     Document Type: Article

References (33)

1. V. Bally D. Talay The law of the Euler scheme for stochastic differential equations I: Convergence rate of the distribution function Probab Theory Relat Fields 104 1996 43-60
2. V. Bally D. Talay The law of the Euler scheme for stochastic differential equations I: Convergence rate of the density Monte Carlo Methods Appl 2 1996 93-128
3. 1 view 1985 Wiley New York
4. van den Berg E, Heemink AW, Lin HX, Schoenmakers JGM. Probability density estimation in stochastic environmental models using reverse representations. Stochastic environmental research and risk assessment [to appear] (see also http://ta.twi.tudelft.nl/wagm/users/lin/ Publications/ArticleBHLS.ps).
5. L. Greengard J. Strain The fast Gauss transform SIAM J Sci Stat Comput 12 1 1991 79-94
6. De Jong K. Tidally averaged transport models. Phd. Dissertation. Shaker Publishing BV, Maastricht; 1998.
7. A.W. Heemink Stochastic modeling of dispersion in shallow water Stochast. Hydrol. Hydraul. 4 1990 161-174
8. PE Kloeden E. Platen Numerical solution of stochastic differential equations Series applications of mathematics No. 23 1992 Springer Verlag Berlin
9. G.N. Milstein M.V. Tretyakov Stochastic numerics for mathematical physics 2004 Springer New York
10. G.N. Milstein J.G.M. Schoenmakers Monte Carlo construction of hedging strategies against multi-asset European claims Stochast. Stochast. Rep. 73 1-2 2002 125-157
11. G.N. Milstein J.G.M. Schoenmakers V. Spokoiny Transition density estimation for stochastic differential equations via forward-reverse representations Bernoulli 10 2 2004 281-312
12. B.W. Silverman Density estimation for statistics and data analysis 1986 Chapman and Hall London
13. D.J. Thomson Criteria for the selection of stochastic models of particle trajectories in turbulent flows J Fluid Mech 180 1987 529-556
14. J.G.M Schoenmakers A.W. Heemink K. Ponnambalam P.E. Kloeden Variance reduction for Monte Carlo simulation of stochastic environmental models Appl Mater Model 26 2002 785-795
15. A.M. Jazwinski Stochastic processes and filtering theory 1970 Academic Press New York
16. L. Arnold Stochastic differential equations: Theory and applications 1974 Wiley London
17. B. Oksendal Stochastic differential equations 1985 Springer Berlin
18. Z. Lu D. Zhang On importance sampling Monte Carlo approach to uncertainty analysis for flow and transport in porous media Adv Water Res 26 2003 1177-1188
19. T. Little V. Pant A finite difference method for the valuation of variance swaps J Compuatat Finan 5 1 2001 81-102
20. R.L. Iman W.J. Conover Small sample sensitivity analysis techniques for computer models, with application to risk assessment Comumun Stat, Pt A/ Theory Methods 17 1980 1749-1842
21. R. Caflisch W. Morokoff Quasi-Monte Carlo integration J Comutat Phys 122 1995 218-230
22. M. de Graaf Z. Jager C.B. Vreugdenhil M. Elorche Numerical simulations of tidally cued vertical migrations of flatfish larvae in the North Sea Estuarine Coastal Shelf Sci 59 2 2004 295-305
23. S. Spagnol E. Wolanski E. Deleersnijder R. Brinkman F. McAllister B. Cushman-Roisin E. Hanert An error frequently made in the evaluation of adevctive transport in two-dimensional Lagrangian models of advection-diffusion in coral reef waters Mar Ecol Progr Ser 235 2002 299-302
24. M. Costa J.S. Ferreira Discrete particle distribution model for advection-diffusion transport J Hydraul Eng 126 7 2000 525-532
25. C.F. Scott Particle tracking simulation of pollutant dischrges J Environ Eng 123 9 1997 919-927
26. H.B. Fischer E.J. List R.C.Y. Koh J. Imberger N.H. Brooks Mixing in inland and coastal waters 1979 Academic Press New York
27. S. Zimmermann P. Koumoutsakos W. Kinzelbach Simulation of pollutant transport using a particle method J Comput Phys 173 1 2001 322-347
28. S. Chevalier O. Banton Modeling of heat transfer with the random walk method. Part 1. Application to thermal energy storage in porous aquifers J Hydrol 222 1-4 1999 129-139
29. Y. Yang L.T. Wilson M.E. Makela M.A. Marchetti Accuracy of numerical methods for solving the advection-diffusion equation as applied to spore and insect dispersal Ecol Model 109 1 1998 1-24
30. R.E. Ewing H. Wang A summary of numerical methods for time-dependent advection-dominated partial differential equations J Computat Appl Math 128 1-2 2001 423-445
31. Th.L. van Stijn N. Praagman J. van Eijkeren Positive advection schemes for environmental studies In: C. Taylor editor. Numerical methods in laminar and turbulent slow 1987 Pineridge Press Swansea 1256-1267
32. Uffink GJM. Anaysis of dispersion by the random walk method. Phd. Thesis, Delft University; 1990.
33. E.M. LaBolle G.E. Fogg A.F.B. Tompson Random-walk simulation of transport in heterogeneous porous media: Local mass-conservation problem and implementation methods Water Resour Res 32 3 1996 583-593