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Random Field Simulation and Applications

In: Monte Carlo and Quasi-Monte Carlo Methods 2006

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  • Karl Sabelfeld

    (Weierstrass Institute for Applied Analysis and Stochastics
    Russian Acad. Sci., Institute of Computational Mathematics and Mathem. Geophysics)

Abstract

Summary In this paper I present some new approaches to the random field simulation, and show in four different examples how this simulation technique works. The first example deals with a transport in turbulent flows, where the Lagrangian trajectories are described by a stochastic differential equation whose drift term involves the Eulerian velocity as a random field with a given spectral tensor. Studies of the second example concern with the flows in porous medium governed by the Darcy equation with random hydraulic conductivity. Elasticity system of elliptic Lamé equations with random loads is considered in the third example. Finally, in the fourth example we solve a nonlinear Smoluchowski equation which is used to model the process of crystal growth.

Suggested Citation

  • Karl Sabelfeld, 2008. "Random Field Simulation and Applications," Springer Books, in: Alexander Keller & Stefan Heinrich & Harald Niederreiter (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 143-165, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74496-2_7
    DOI: 10.1007/978-3-540-74496-2_7
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