Introduction

In various spheres of activities, we often feel the necessity to find the best or fastest way of solving a relevant problem. Nowadays, computer technologies are applied in solving most problems: in great flow of information processing as well as in scientific research. Complex problems, solution of which is problematic by using only one computer, are solved by several computers connected into a network. Seeking effective usage of computer network for parallel calculations conceptually different software can be applied.

Speaking about parallel calculations, first of all data processing procedures are meant, when several operations of a computer system may be performed at the same time. Parallelism may be achieved if we have: Operation independence of separate calculating machines

Adequacy of calculating system elements:

– applying specialized equipment;

– duplicating calculating machines.

Analyzing organization problems of parallel calculations, the following execution modes of independent program parts should be distinguished:

− Multitask (time distribution mode).

− Parallel execution.

− Distributed calculations.

1.Analyzing of given task.

1.1.Creation of system if equations.

In this course project is needed to calculate net dynamic object, as ventilation net (figure 1.1).

Figure 1.1 – Net dynamic object

Net dynamic object is amount of elements, than are linked by physical nodes, through which air streams are carried out.

Ventilation networks play an important role in addressing security problems in the mines, where they provide air ventilation between objects. The objects are airing and cleaning preparations slaughter and mining works, in which security policies are regulated quantities of air flow and concentration of harmful impurities.

The buildings come airing fresh currents of air and spent the weekend on the surface currents with harmful impurities through the barrel, offset, slope. Objects airing, works that look and look to the air, forming a mine ventilation network, which is a complex simulation: a large number of channels airing and related units, each channel is regarded as a nonlinear system aerofoil; are offset, which is crucial gas-dynamic processes, and adjustable leg locks are nonlinear, dependent on air flow characteristics. Sources of pressure difference, which provide air movement is the fans.

If the basic variable systems change in time and space, the models that describe such processes as systems with distributed parameters and in the form of differential equations in partial derivatives. If major changes in process variables in the space does not occur, models that describe such processes as systems with concentrated parameters.

One of the components of the formal description of a network differential equation of dynamic processes in the branches and nodes. Obtaining equations is the main objective of the theory of network facilities in all the subject areas.

According to given task and 1^st and 2^nd Kirgofs rules were created system of equations by graph, which is represented on figure 1.2:

Figure 1.2. Graph with contours

By 1^st Kirgofs rule amount of equations of equal to (n-1) = 6-1=5, where n – is amount of nodes.

For Node 1: Q1-Q2-Q3-Q4 = 0

For Node 2: Q3+Q7-Q10-Q11 = 0

For Node 4: Q4-Q6-Q7 = 0

For Node 5: Q8+Q5+Q11-Q9 = 0

For Node 6: Q1-Q9-Q10 = 0

By 2^nd Kirgofs rule amount of equations of equal to m-(n-1) = 11-(6-1)=6, where n – is amount of nodes and m is amount of flows.

Contour #1: (K1*dQ1/dt+R1*Q1*Q1) + (K2*dQ2/dt+R2*Q2*Q2) + (K8*dQ8/dt+R8*Q8*Q8) + (K9*dQ9/dt+R9*Q9*Q9)= H1

Contour #2: (K4*dQ4/dt+R1*Q4*Q4) + (K6*dQ6/dt+R6*Q6*Q6) - (K2*dQ2/dt+R2*Q2*Q2) = 0

Contour #3: (K3*dQ3/dt+R3*Q3*Q3) - (K7*dQ7/dt+R7*Q7*Q7) - (K4*dQ4/dt+R4*Q4*Q4)

Contour #4: (K5*dQ5/dt+R5*Q5*Q5) - (K8*dQ8/dt+R8*Q8*Q8) - (K6*dQ6/dt+R6*Q6*Q6)

Contour #5: (K7*dQ7/dt+R7*Q7*Q7) + (K11*dQ11/dt+R11*Q11*Q11) - (K5*dQ5/dt+R5*Q5*Q5)

Contour #6: (K10*dQ10/dt+R10*Q10*Q10) - (K9*dQ9/dt+R9*Q9*Q9) - (K11*dQ11/dt+R11*Q11*Q11)

where:

R1 = 1.35

R2 = 2.53

R3 = 3.34

R4 = 2.87

R5 = 3.35

R6 = 1.52

R7 = 1.36

R8 = 1.25

R9 = 1.53

R10 = 2.13

R11 = 1.34

H1 = 3000

Figure 1.1 is represented as Tree and Antitree graph on figure 1.3:

According to this, threads are enumerated in table 1.1:

Table 1.1. Representation of threads as brunches of tree and antitree

	Threads
	Q1	Q2	Q3	Q4	Q5	Q6	Q7	Q8	Q9	Q10	Q11
Variables	Y4	X1	X2	Y1	Y2	X3	X4	X5	X7	Y3	X6

System of equations was calculated using MatLab system:

X1 = 15.0291

X2 = 14.4717

X3 = 3.4965

X4 = 10.3829

X5 = 23.2863

Y1 = 13.8795

Y2 = 7.2685

Y3 = 20.0939

Y4 = 43.3802

Y5 = 11.2571

Y6 = 4.7607