|Article title||MATHEMATICAL MODELING OF GEOFILTRATION IN SOILS WITH FRACTAL STRUCTURE ON MULTIPROCESSOR COMPUTER SYSTEMS|
|Section||SECTION III. THE USE OF SUPERCOMPUTER TECHNOLOGIES|
|Month, Year||12, 2014 @en|
|Abstract||When modeling the geofiltration in soils it is necessary to consider the fractal structure of the soil. The complex geometry of the pores and capillaries provides this structure. Anomalous diffusion describes the fractal diffusion mathematically, which is described by equations in partial fractional derivatives. This paper describes the construction of mathematical models based on equations of Buckingham-Richards, in which the differentiation operator time was replaced by the private fractional derivative Riemann-Louiville. For the continuous model was obtained the discrete analogue using the integro-interpolation method. In the numerical solution of problems of this type is to process large amounts of data, hence there is the need to use in the calculations the super computer To solve this problem was developed parallel implementation of the modified alternating triangular method, which allowed to increase several times the speed of the program complex (PC). High performance PC needed for rapid simulation results. For example, this will allow the rise of the groundwater table in real time, and thus to minimize damage from flooding.|
|Keywords||Gelfiltration; anomalous diffusion; supercomputers; numerical method; the modified alternating triangular method; fractional derivatives; fractal patterns.|
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