Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 14, No 1, (2003), 107p-116p
The actual transport of the air pollutants is due to the wind.
This normally called “advection of the air pollutants”. Diffusion and deposition are other two major physical processes, which take place during the transport of pollutants in the atmosphere.
In this paper we study two classes of grid-free Monte Carlo (MC) algorithms for solving an elliptic boundary value problem, where the partial differential equation contains advection, diffusion and deposition parts. The grid-free MC approach to solve the above equation uses a local integral representation and leads to a stochastic process called a random “Walk on balls” (WOB).
In the first class of algorithms, the choice of a transition density function in the Markov chain depends on the radius of the maximal ball, lying inside the domain, in which the problem is defined, and on the parameters of the differential operator. While the choice of a transition density function in
the second class of algorithms does not depend on the deposition part of the problem.
The computational complexity of both classes of grid-free MC algorithms was investigated using varied numerical tests on a PowerPC (G4 w/AltiVec) 450 MHz running YDL 2.0.