
 Start

3302
 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
 Exact

[2]
 Suffix

.
3
1
1
2,1,2,3,
0,
iijii
ji
jjijiiijji
i
ii
vvvvvp
vfi
tx xxxxxx
v
x
(1)
and by the convectiondiffusion 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)

 Start

4914
 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
 Exact

[1]
 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
predictorcorrector scheme with approximation of the
convective terms against the flow [4] for thispurpose.
 (check this in PDF content)

 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
predictorcorrector scheme with approximation of the
convective terms against the flow
 Exact

[4]
 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)

 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

[3]
 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)