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Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases

Bibliographic reference Spivakovskaya, Darya ; Heemink, Arnold W. ; Deleersnijder, Eric. Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases. In: Ocean Dynamics : theoretical, computational oceanography and monitoring, Vol. 57, no. 3, p. 189-203 (2007)
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  1. Arnold L (1974) Stochastic differential equations. Wiley, New York
  2. Beckers JM, Burchard H, Campin JM, Deleersnijder E, Mathieu PP (1998) Another reason why simple discretizations of rotated diffusion operators cause problems in ocean models: comments on “Isoneutral diffusion in a z-coordinate ocean model”. J Phys Oceanogr 28:1552–1559
  3. Beckers JM, Burchard H, Deleersnijder E, Mathieu PP (2000) Numerical discretization of rotated diffusion operators in ocean models. Mon Weather Rev 128:2711–2733
  4. Bolin B, Rodhe H (1973) A note on concepts of age distribution and transit time in natural reservoirs. Tellus 25:58–62
  5. Burchard H (2002) Applied turbulence modelling in marine waters. Lecture notes in earth sciences, vol 100. Springer, Berlin Heidelberg New York
  6. Celia MA, Russell TF, Herrera I, Ewing RE (1990) An Eulerian–Lagrangian localized adjoint method for an advection-diffusion equation. Adv Water Resour 13(4):187–206
  7. Cox MD (1987) Isopycnal diffusion in a z-coordinate model. Ocean Model 74:1–5
  8. Deleersnijder E, Camin JM, Delhez EJM (2001) The concept of age in marine modelling. I. Theory and preliminary model results. J Mar Syst 28:229–267
  9. Deleersnijder E, Beckers JM, Delhez EJM (2006a) The residence time of settling in the surface mixed layer. Environ Fluid Mech 6(1):25–42
  10. Deleersnijder E, Beckers JM, Delhez EJM (2006b) On the behaviour of the residence time at bottom of the mixed layer. Environ Fluid Mech 6:541–547
  11. Delhez EJM, Heemink AW, Deleersnijder E (2004) Residence time in a semi-enclosed domain from the solution of an adjoint problem. Estuar Coast Shelf Sci 61:691–702
  12. de Haan P (1999) On the use of density kernels for concentration estimations within particles and puff dispersion models. Atmos Environ 33:2007–2021
  13. Dimou KN, Adams EE (1993) A random-walk, particles tracking models for well-mixed estuaries and coastal waters. Estuar Coast Shelf Sci 37:99–110
  14. Jazwinski AW (1970) Stochastic differential processes and filtering theory. Academic, New York
  15. Jones MC (1993) Simple boundary correction for kernel density estimation. Stat Comput 3:135–146
  16. Heemink AW (1990) Stochastic modeling of dispersion in shallow water. Stoch Hydrol Hydraul 4:161–174
  17. Kinzelbach Wolfgang, The Random Walk Method in Pollutant Transport Simulation, Groundwater Flow and Quality Modelling (1988) ISBN:9789401078016 p.227-245, 10.1007/978-94-009-2889-3_15
  18. Kloeden Peter E., Platen Eckhard, Numerical Solution of Stochastic Differential Equations, ISBN:9783642081071, 10.1007/978-3-662-12616-5
  19. Konikow LF, Bredehoeft JD (1978) Computer model of two-dimensional solute transport and dispersion in ground water. Techniques of water-resources investigations of the US Geological Survey, chapter C2, book 7, US Government Printing Office, Washington DC
  20. LaBolle EM, Fogg GE, Tompson AFB (1996) Random-walk simulation of transport in heterogeneous porous media: local mass-conservation problem and implementation methods. Water Resour Res 32(3):583–593
  21. Mathieu PP, Deleersnijder E (1998) What is wrong with isopycnal diffusion in world ocean models? Appl Math Model 22:367–378
  22. Mathieu PP, Deleersnijder E, Beckers JM (1999) Accuracy and stability of the discretised isopycnal-mixing equation. Appl Math Lett 12:81–88
  23. Milstein Grigori N., Tretyakov Michael V., Stochastic Numerics for Mathematical Physics, ISBN:9783642059308, 10.1007/978-3-662-10063-9
  24. MÜLLER HANS-GEORG, Smooth optimum kernel estimators near endpoints, 10.1093/biomet/78.3.521
  25. Proehl JA, Lynch DE, McGillicuddy Jr DJ, Ledwell JR (2005) Modelling turbulent dispersion of the North Flank of Georges Bank using Lagrangian methods. Cont Shelf Res 25:875–900
  26. Øksendal Bernt, Stochastic Differential Equations, ISBN:9783540152927, 10.1007/978-3-662-13050-6
  27. Redi MH (1982) Oceanic isopycnal mixing by coordinate rotation. J Phys Oceanogr 12:1154–1158
  28. Riddle AM (1998) The specification of mixing in random walk models for dispersion in the sea. Cont Shelf Res 18:441–456
  29. Sawford B (2001) Turbulent relative dispersion. Annu Rev Fluid Mech 33:289–317
  30. Schoenmakers JGM, Heemink AW (1997) Fast valuation of financial derivatives. J Comput Financ 1:47–62
  31. Silverman B. W., Density Estimation for Statistics and Data Analysis, ISBN:9780412246203, 10.1007/978-1-4899-3324-9
  32. Spivakovskaya D, Heemink AW, Milstein GN, Schoenmakers JGM (2005) Simulation of the transport of particles in coastal waters using forward and reverse time diffusion. Adv Water Resour 28:927–938
  33. Stijnen JW (2002) Numerical methods for stochastic environmental models. Ph.D. dissertation, Delft University of Technology, The Netherlands
  34. Sun NZ (1999) A finite cell method for simulating the mass transport process in porous media. Water Resour Res 35(12):3649–3662
  35. Talay D, Tubaro L (1991) Expansion of the global error for numerical schemes solving stochastic differential equations. Stoch Anal Appl 8(4):485–509
  36. Thomson DJ (1987) Criteria for the selection of stochastic models of particles trajectories in turbulent flow. J Fluid Mech 180:529–556
  37. Uffink Gerard J. M., Modeling of Solute Transport with the Random Walk Method, Groundwater Flow and Quality Modelling (1988) ISBN:9789401078016 p.247-265, 10.1007/978-94-009-2889-3_16
  38. Umlauf L, Burchard H (2005) Second order turbulence closure models for geophysical boundary layers. A review of recent work. Cont Shelf Res 25:795–827
  39. van Stijn ThL, Praagman N, van Eijkeren J (1987) Positive advection schemes for environmental studies. In: Taylor C et al. (eds) Numerical methods in laminar and turbulent flow. Pineridge, Swansea, pp 1256–1267
  40. Wand M. P., Jones M. C., Kernel Smoothing, ISBN:9780412552700, 10.1007/978-1-4899-4493-1
  41. Yang Y, Wilson LT, Makela ME, Marchetti MA (1998) Accuracy of numerical methods for solving the advection-diffusion equation as applied to spore and insect dispersal. Ecol Model 109:1–24
  42. Yeh GT (1990) A Lagrangian–Eulerian method with zoomable hidden fine-mesh approach to solving advection-dispersion equations. Water Resour Res 26(6):1133–1144
  43. Zhang R, Huang K, van Geruchten MT (1993) An efficient Eulerian–Lagrangian method for solving solute transport problems in steady and transient flow fields. Water Resour Res 28(12):4131–4138
  44. Zheng C, Bennett GD (2002) Applied contaminant transport modeling. Wiley, New York
  45. Zheng C, Wang PP (1999) MT3DMS: a modular three-dimensional multispecies transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems; documentation and user’s guide, contract report SERDP-99-1. US Army engineer research and development center, Vicksburg, MS
  46. Zimmermann S, Koumoutsakos P, Kinzelbach W (2001) Simulation of pollutant transport using a particle method. J Comput Phys 173(1):322–347