Wyniki wyszukiwania - BazTech

1

Zastosowanie metody Monte Carlo do modelowania migracji zanieczyszczeń do ujęć wód gruntowych

Maciejewski S., Zaradny H.

Biuletyn Państwowego Instytutu Geologicznego

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2008

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nr 431, Hydrogeologia

121-126

PL

Prognozowanie dopływu zanieczyszczeń do ujęć wody podziemnej, zbiorników wody i cieków ma duże znaczenie praktyczne, dlatego ciągle poszukuje się efektywnych sposobów matematycznego modelowania tego typu zagadnień. Jednym ze sposobów modelowania jest zastosowanie metody Monte Carlo do rozwiązywania równań różniczkowych, w tym przypadku równania dyspersji hydrodynamicznej. Metoda ta ma wiele zalet: jest nieskomplikowana, nie generuje dyspersji numerycznej związanej z członem konwekcyjnym w równaniu transportu, pozwala w prosty sposób oszacować ładunek zanieczyszczeń docierających do studni, cieków itp., ponadto nie jest czuła na błędy związane z przybliżonym (np. numerycznym) rozwiązaniem równania transportu wody. W pracy przedstawiono zastosowanie metody Monte Carlo do rozwiązania nieustalonego zagadnienia przepływu zanieczyszczeń w obszarze z ustalonym polem prędkości wody gruntowej. Do wyznaczenia pola ciśnień hydrodynamicznych w obszarze ruchu zastosowano metodę elementów skończonych.

EN

Prediction of contaminant inflow to groundwater intakes and water reservoirs is a very important problem from the practical point of view. Development of efficient modelling methods for such problems is still a subject of intense research. A possible approach is to use the Monte Carlo method fto solve partial differential equations (hydrodynamic dispersion equation). This method has significant advantages: it is uncomplicated, it does not generate numerical dispersion connected with convection term, and it allows for a simple estimation of the contaminant load entering wells, streams etc. Moreover, the Monte Carlo method is not sensitive to the errors related to the approximate (numerical) solution of the equation describing groundwater flow. In this paper the application of the Monte Carlo method to solve unsteady contaminant transport in a steady groundwater velocity field is presented. The groundwater pressure heads and velocities are computed using the finite element method.

2

Application of the Moving Average Method of Simplifying Simulation of Random Fields

Maciejewski S., Gorczewska-Langner W.

Archives of Hydro-Engineering and Environmental Mechanics

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2006

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Vol. 53, nr 2

126-136

EN

A method of simulating random fields using a moving average is proposed in this paper. Random fields were simulated for different sizes of sub-field and different numbers of cycles of calculations of the moving average. For the fields obtained the covariance function was analyzed. In order to estimate the efficiency of the proposed simulation method of random field based on the method of diagonal covariance matrix was performed. It is shown that two of the simulation methods presented are able to generate a multidimensional random variable with required correlation function. However, the method of diagonal covariance matrix has some limitations caused by the size of the simulated random field, which result from the necessity of converting a relatively large matrix. Using the proposed simulation method it is possible to simulate, in a comparatively quick and simple manner, a random field with a large number of nodes on PC-s. The presented method can be useful in the stochastic analysis of transport phenomena in soil.

3

Simulation of density dependent transport in groundwater

Maciejewski S., Zaradny H.

Archives of Hydro-Engineering and Environmental Mechanics

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2003

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Vol. 50, nr 3

207-218

EN

A mathematical model of water flow and transport of chemical substances is presented in the paper. This model takes into account the influence of variable density and viscosity of water caused by variable solute concentration in soil. A solution of the problem of water flow and solute transport was sought using numerical methods. A finite elements method for solution of water flow equation and Monte-Carlo method to simulate solute transport were applied. Advantages of the presented model are illustrated on the example of water flow and salt transport in two dimensional ground profile in the region of Puck Bay. The geology of this profile is taken from Jankowska et al (1994). Obtained results from the proposed model are qualitatively conformable with observations in situ.