# The 4 reference contexts in paper H. Miloshevich, Y. Zaharov N., N. Kontrec, A. Zimin I., I. Nudner S., V. Ragulin V., Х. Милошевич, Ю. Захаров Н., Н. Контрец, А. Зимин И., И. Нуднер С., В. Рагулин В. (2016) “ОБ ОДНОЙ МОДЕЛИ РАЗМЫВА СВЯЗНОГО ГРУНТА И ДВИЖЕНИЯ ПОВЕРХНОСТНЫХ ВОЛН // MODEL OF COHESIVE SOIL EROSION AND SURFACE WAVE MOTION” / spz:neicon:vestnik-k:y:2015:i:2:p:35-40

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Mathematical model We consider the motion of the two-component incompressible viscous fluid, its viscosity and density depending on the concentration of the components. Then the model of the fluid is described by the non-stationary Navier-Stokes equations
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.  1 vvvvvp iijii 2,1,2,3, 0,            (1) ji jjijiiijji i ii vfi tx xxxxxx v x    3 1 and by the convection-diffusion equation 3 1 i. ii CC vDC tx     (2) (), C        (3) 21 1 21 1 (), C where 123,,v
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The time step for the Navier-Stokes equations (1) is done in the first stage, based on the known velocity and concentration distribution (and hence the density and viscosity). The scheme of splitting on physical factors
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is used for this purpose. The time step for the convectiondiffusion equation (2) is done in the second stage, using the values obtained for the velocity components. We use a predictor-corrector scheme with approximation of the convective terms against the flow [4] for thispurpose.
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The time step for the convectiondiffusion equation (2) is done in the second stage, using the values obtained for the velocity components. We use a predictor-corrector scheme with approximation of the convective terms against the flow
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for thispurpose. The values of density and viscosity in the space are recalculated according to (3) in the third stage. Then the transition to the first stage of the next iteration of the algorithm follows.
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Then the transition to the first stage of the next iteration of the algorithm follows. It is worth noting that the system of equations (1) – (3) is solved numerically by the grid method on the staggered grid
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. Cohesive soil erosion In order to simulate the process of wetting substance which is cohesive soil, divide it into two parts (see Fig. 1). region 2 computational when the concentration at some location of the boundary layer becomes smaller a predetermined value *C.
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