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3301
 Prefix

Mathematical model
We consider the motion of the twocomponent incompressible viscous fluid, its viscosity and density depending on the concentration of the components. Then the
model of the fluid is described by the nonstationary
NavierStokes equations
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[2]
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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 convectiondiffusion equation
3
1
i.
ii
CC
vDC
tx
(2)
(),
C
(3)
21 1
21 1
(),
C
where 123,,v
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 Start

4913
 Prefix

The time step for the NavierStokes 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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[1]
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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
predictorcorrector scheme with approximation of the
convective terms against the flow [4] for thispurpose.
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 Start

5210
 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
predictorcorrector scheme with approximation of the
convective terms against the flow
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[4]
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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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 Start

5563
 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
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[3]
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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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