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Abstract The Protvino accelerator facility located in the Moscow region, Russia, is in a good position to offer a rich experimental research program in the field of neutrino physics. Of particular interest is the possibility to direct a neutrino beam from Protvino towards the KM3NeT/ORCA detector, which is currently under construction in the Mediterranean Sea 40 km offshore Toulon, France. This proposal is known as P2O. Thanks to its baseline of 2595 km, this experiment would yield an unparalleled sensitivity to matter effects in the Earth, allowing for the determination of the neutrino mass ordering with a high level of certainty after only a few years of running at a modest beam intensity of $$\approx ~90~\hbox {kW}$$ ≈90kW . With a prolonged exposure ($$\approx 1500\hbox { kW}\,\,\hbox {year}$$ ≈1500kWyear ), a $$2\sigma $$ 2σ sensitivity to the leptonic CP-violating Dirac phase can be achieved. A second stage of the experiment, comprising a further intensity upgrade of the accelerator complex and a densified version of the ORCA detector (Super-ORCA), would allow for up to a $$6\sigma $$ 6σ sensitivity to CP violation and a $$10^\circ {-}17^\circ $$ 10∘-17∘ resolution on the CP phase after 10 years of running with a 450 kW beam, competitive with other planned experiments. The initial composition and energy spectrum of the neutrino beam would need to be monitored by a near detector, to be constructed several hundred meters downstream from the proton beam target. The same neutrino beam and near detector set-up would also allow for neutrino-nucleus cross section measurements to be performed. A short-baseline sterile neutrino search experiment would also be possible.

The problem of the accuracy improving is considered for vortex method. The general Galerkin-type approach is considered for the numerical solution of the boundary integral equation. It is shown that the airfoil surface line representation as a polygon consisting of rectilinear panels can lead to incorrect behavior of the numerical solution of the boundary integral equation with respect to unknown vortex sheet intensity, especially in case of considerably different lengths of the neighboring panels. However, in this case, the exact analytical formulae are derived for the coefficients of the linear algebraic system, which approximate the integral equation. The approach is developed which makes it possible to take into account explicitly the curvature of the airfoil surface line. The approximate analytical formulae are derived for the coefficients of the linear system, which are expressed through the integrals of the fractions, which denominators can be equal to zero. Numerical example is considered for the elliptic airfoil in the incident flow at its essentially non-uniform discretization. The suggested algorithm has acceptable numerical complexity, however it permits to obtain rather good numerical results.

The main computational complexity of vortex methods is concentrated in the calculation of the convective and diffusive velocities of all vortex elements. The analogue of the Barnes - Hut algorithm is considered as one of the most efficient ways to acceleration of the velocities computation in vortex element method. This method is based on the tree (hierarchical structure of regions) construction. When calculating the convective velocities this algorithm makes it possible to take into account the influence of vortex elements, which are located far enough from each other, approximately by using Taylor approximation of expression for convective velocity. The influence of vortex elements, which are close to each other is calculated directly using Biot -Savart law. There are two parameters of algorithm that affect the computational complexity of the algorithm and the problem solving accuracy: is the maximum tree level, is the parameter, which determines the radius of a near-field zone. When calculating diffusive velocities the influence of the vortex elements to each other decays exponentially with increasing distance between them. Therefore, constructed algorithm of diffusive velocities calculation allows finding vortex elements from near-field zone using tree structure and calculating diffusive velocities using only vortex elements from this zone. The estimations of computational complexity, which depends on algorithm parameters and number of vortex elements, are obtained for the algorithms for convective and diffusive velocities calculation. Also estimations for the errors of the vortex elements velocities computation, which depend on the algorithm parameters, are constructed. These estimates allow in practice to choice the optimal parameters of the whole algorithm and achieve the maximum possible acceleration of the computations for the given maximum error level.

The paper considers two-dimensional problem of numerical flow simulation around an airfoil. The flow is assumed to be incompressible, so a meshless lagrangian vortex element method (VEM) can be used to simulate the flow. The aim of this research is to investigate the accuracy of the numerical schemes of VEM, which use different approaches to satisfy boundary conditions on the surface of airfoil in case of simulation of the flow around airfoils with angle point.When constructing a numerical scheme, airfoil is replaced by polygon, which consists of panels. The airfoil is assumed to be rigid and immovable. The numerical schemes are based on two mathematically equivalent approaches to the boundary conditions satisfaction. The first (\classical") approach implies the equality to zero of the normal component of the flow velocity on the airfoil surface. It leads to the singular integral equation with Hilbert-type kernel, and the principal value of the corresponding integral should be understood in Cauchy sense. This equation should be solved numerically, but the mentioned features impose strong restrictions on discretization of airfoil, in particular, lengths of neighboring panels should not differ significantly. In the second case, the limit value of the tangential component of flow velocity from the airfoil side equates to zero. This approach leads to an integral equation of the second kind, which kernel is bounded in case of a smooth airfoil. This approach is free from limitations of the previous way. The numerical schemes based on the first and the second approaches are called NVEM and TVEM, correspondingly.When solving engineering problems the airfoil sometimes should be split into panels with significantly different lengths. In order to investigate the accuracy of the mentioned NVEM and TVEM schemes the model problem of the flow simulation around the airfoil with angle point is considered. The asymptotic behavior of the solution, which is singular near the angle point, is known. Different algorithms of splitting airfoil into panels are used, and it is analyzed how it influences on the accuracy of the numerical schemes.

The article offered for consideration provides a survey of methods to study a tracked vehicle movement over unpaved grounds and obstacles using various software systems. The relevant issue is to optimize chassis elements of a caterpillar at the design stage. The challenges, engineers face using different methods to study the tracked vehicle elements, are given. Advantages of using simulation to study a state of the various components of the loaded chassis are described. Beside, an important and relevant issue is brought up i.e. modeling a vehicle movement in real time.While writing an article, different modeling methods for an interaction between a tracked vehicle chassis and an underlying subgrade used both in domestic and in foreign practice have been analysed. The applied analytical assumptions in creating these models and their basic elements are described. The way to specify an interaction between the track and road wheels of a caterpillar, crawler belt specification, and interaction between its elements have been analysed in detail as well. Special attention was also paid to the various ways of specifying the subgrade both in planar models and in models enabling us to study all chassis elements of a caterpillar as a whole.In addition to the classical simulation of tracked vehicle movement used to analyse Ride qualities of tracked vehicle and loaded state of various chassis elements, is offered a model used to simulate a movement coil in real time.The article presents advantages and disadvantages of different models of movement in terms of engineering analysis of caterpillar elements. A task to develop a simulation model of caterpillar movement is set. Requirements for a model in case of its use in engineering analysis of chassis elements of a caterpillar are defined. A problem of a lack of the single technique to conduct engineering analysis of tracked vehicle chassis is noted.