MATHEMATICAL AND NUMERICAL MODELS OF THE OVERLAND RUNOFF OF RAINFALLS ON THE RIVER SYSTEM’S DRAINAGE SURFACE
V. M. Konyukhov, A. A. Saveliev, M. G. Khramchenkov, A. N. Chekalin, N. E. Galiullina
VANT. Ser.: Mat. Mod. Fiz. Proc 2013. Вып.3. С. 41-54.
The mathematical modeling and numerical simulation issues are considered for the overland runoff of rainfalls on the river system’s drainage surface. A mathematical model includes equations of a 2D kinematic wave, space-and-time variations of the water layer thickness on the drainage surface with regard to rainfalls and water absorption. The paper offers an approximate approach based on the capillary imbibition model to determine the water content in subsaturation area (soil). The specific features of solutions to the problem have been studied. It is shown, in particular, that no overland runoff is generated at initial time of liquid falls because water is completely absorbed by soil. The retarded argument and the overland runoff origination time are calculated from the algebraic equation system. If rainfalls continue after a short period of no falls the retarded argument value should be recalculated. The finite-difference method is used to solve the problem numerically. An algorithmic model has been developed and implemented in the software system that allows the surface water runoff calculations. The paper gives an example of studies for the overland runoff in the Mesha river basin in the Republic of Tatarstan.Keywords: numerical simulation, kinematic wave, overland runoff, drainage surface, subsaturation area, capillary imbibition.
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English
