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

1. Start
3302
Prefix
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
Exact

Suffix
. 3 1 1 2,1,2,3, 0, iijii ji jjijiiijji i ii vvvvvp vfi tx xxxxxx v x                (1) and by the convection-diffusion equation 3 1 i. ii CC vDC tx     (2) Here the dependence of the viscosity and density on the concentration is expressed by the fo
(check this in PDF content)

2. Start
4914
Prefix
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
Exact

Suffix
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  for thispurpose.
(check this in PDF content)

3. Start
5211
Prefix
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
Exact

Suffix
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.
(check this in PDF content)

4. Start
5564
Prefix
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
Exact

Suffix
. Cohesive soil erosion In order to simulate the process of wetting substance which is cohesive soil, divide it into two parts (see Fig. 1). Figure 1. The initial position and separation scheme of substance Here, number 1 is the part of already soaked substance that behaves like some viscous impurity in the liquid, and number 2 is the part that is consi
(check this in PDF content)