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Stochastic Lagrangian models and algorithms for spatially inhomogeneous Smoluchowski equation

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  • Sabelfeld, Karl
  • Kolodko, Anastasia

Abstract

The following generally unsolved yet problem is studied: construct the solution of a spatially inhomogeneous Smoluchowski equation governing coagulating and diffusing particles in a host gas, on the basis of solutions to homogeneous Smoluchowski equation. In [Math. Comput. Simul. 49 (1999) 57], we solved this problem in the case when there is no diffusion. The non-zero diffusion term drastically complicates the situation. Under some general assumptions we give the interrelations between the homogeneous and inhomogeneous cases. This provides an effective numerical scheme especially when the host gas is incompressible. New Lagrangian scheme leads to a new model governing by a Smoluchowski type equation with an additional effective source. We give a numerical comparison of these two models.

Suggested Citation

  • Sabelfeld, Karl & Kolodko, Anastasia, 2003. "Stochastic Lagrangian models and algorithms for spatially inhomogeneous Smoluchowski equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 115-137.
    • Handle: RePEc:eee:matcom:v:61:y:2003:i:2:p:115-137
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    References listed on IDEAS

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    1. Sabelfeld K.K. & Rogasinsky S.V. & Kolodko A.A. & Levykin A.I., 1996. "Stochastic algorithms for solving Smolouchovsky coagulation equation and applications to aerosol growth simulation," Monte Carlo Methods and Applications, De Gruyter, vol. 2(1), pages 41-88, December.
    2. Kolodko, A. & Sabelfeld, K. & Wagner, W., 1999. "A stochastic method for solving Smoluchowski's coagulation equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(1), pages 57-79.
    3. Sabelfeld K. & Shalimova I., 2001. "Forward and Backward Stochastic Lagrangian Models for turbulent transport and the well-mixed condition," Monte Carlo Methods and Applications, De Gruyter, vol. 7(3-4), pages 369-382, December.
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    Cited by:

    1. Sabelfeld Karl K., 2016. "Splitting and survival probabilities in stochastic random walk methods and applications," Monte Carlo Methods and Applications, De Gruyter, vol. 22(1), pages 55-72, March.
    2. Sabelfeld, Karl K., 2018. "A random walk on spheres based kinetic Monte Carlo method for simulation of the fluctuation-limited bimolecular reactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 46-56.
    3. Sabelfeld K. & Levykin A. & Privalova T., 2007. "A Fast Stratified Sampling Simulation of Coagulation Processes," Monte Carlo Methods and Applications, De Gruyter, vol. 13(1), pages 71-88, April.
    4. Guiaş, Flavius, 2010. "Direct simulation of the infinitesimal dynamics of semi-discrete approximations for convection–diffusion–reaction problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(4), pages 820-836.
    5. Sabelfeld Karl K. & Levykin Alexander I. & Kireeva Anastasiya E., 2015. "Stochastic simulation of fluctuation-induced reaction-diffusion kinetics governed by Smoluchowski equations," Monte Carlo Methods and Applications, De Gruyter, vol. 21(1), pages 33-48, March.

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