Analytical Construction of Uniformly Convergent Method for Convection Diffusion Problem

In this paper, we study the uniformly convergent method on equidistant meshes for the convection-diffusion problem of type; where the formal adjoint operator of L. Lu=-εu''+bu'+c u=f(x), u(0)=0, u(1)=0 At the end of the this paper we will generate the scheme; -e^(ρ_i )/(e^(ρ_i )+1) U_(i-1)+U_i-1/(e^(ρ_i )+1) U_(i+1)=(f_i-c_i U_i ) h/b ((e^(ρ_i )-1)/(e^(ρ_i )+1))

Development of the flow part of reactive type HPC of K-325-23,5 series steam turbine based on the use of modern computer technologies

The results of gas-dynamic design of a new flow part of a reactive type high-pressure cylinder (HPC) of the K-300 series condensing steam turbine are presented. The turbine was developed using a comprehensive methodology implemented in the IPMFlow software package. The methodology includes gas-dynamic calculations of various levels of complexity, as well as methods for analytical construction of the spatial shape of the blade rows based on a limited number of parameterized values. The real thermodynamic properties of water and steam were taken into account in 3D calculations of turbulent flows. At the final stage, 3D end-to-end calculations of the HPC, which consists of 18 stages, were carried out. The technology of parallel computing was applied in the said calculations. It is shown that a significant increase in efficiency and power has been achieved in the developed HPC due to the use of reactive type stages with modern smooth blade profiles and monotonic meridional contours.

Material point physical model rationale while studying kinematic characteristics of a motor vehicle in case of oblique collision with side cable barriers

Introduction. A review of the application of theoretical mechanics methods for the development of algorithms of approximate analytical simulation of a motor vehicle (MV) movement in case of oblique collision with side cable barriers is performed. The representation of the MV as a material point in this type of collision is validated. The study objective is to demonstrate the application of a physical model of a material point to describe the motor vehicle dynamics in the event of its oblique collision with side cable barrier.Materials and Methods. A new physical model that describes the opposition to the motor vehicle movement from the side of a cable barrier in an oblique collision is proposed. New methods of approximate analytical construction of the MV movements during an oblique collision with the side cable barriers are presented. The analytical calculation results are verified by the data of the finite element (FE) simulation of the collision according to the data of field tests. The FE simulation was carried out using a multi-purpose finite element complex LS-Dyna.Results. New analytical algorithms have been developed for the MV movement in case of an oblique collision with side cable barriers, as well as a new physical model describing the opposition to the MV movement from the side of cable barriers. The application of a physical model of a material point to study the motor vehicle dynamics during an oblique collision with side cable barriers is established scientifically, including the comparative analysis of the kinematic results of the virtual test with kinematic calculations obtained on the basis of algorithms for analytical construction of the MV movements.Discussion and Conclusions. The analysis of the kinematic results of the virtual test in comparison with the analytical kinematic calculations has shown that the representation of a motor vehicle as a material point in case of an oblique collision with side cable barriers is reasonable since the MV movement is close to translational motion. The results obtained can be used in the development and analysis of the correctness of the FE modeling of a side collision of a motor vehicle with cable barriers.

Analytical construction of the projectile motion trajectory in midair

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. An analytic approach is mainly applied for the investigation. Equations of the projectile motion are solved analytically for an arbitrarily large period of time. The constructed analytical solutions are universal, that is, they can be used for any initial conditions of throwing. As a limit case of motion, the vertical asymptote formula is obtained. The value of the vertical asymptote is calculated directly from the initial conditions of motion. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball, a tennis ball, and a shuttlecock of badminton are presented as examples.

Analytical Construction of Linear Loop Response with Delay Covered by Feedback

Disclosed is a method of obtaining an analytical description of a response of a linear chain with a lag covered by feedback. The process is considered at consecutive intervals. Their duration is equal to the time of net lag. The possibility of obtaining an analytical description of the process is achieved by solving the linear differential equation of the open circuit, and not the differential-difference equation of the closed circuit. An example of analytical construction of the response of the simplest chain with a delay covered by negative feedback is given, and its digital modeling is carried out. The coincidence of the results of the calculation and digital modeling of the circuit confirmed the correctness of the proposed method of analytical response construction.