Open Repository of Keldysh Institute of Applied Mathematics of RAS
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On the comparison of Boltzmann and Landau collision integrals
No full textAbstract:
The estimate for the difference of the Landau collision integral and the Boltzmann collision integral with delta-kernel is obtained. The estimate holds in a class of smooth and rapidly decreasing at infinity distribution functions. It is proved in the general case of multicomponent gas mixture. Results can be used for theoretical and numerical problems related to the nonlinear Landau-Fokker-Planck kinetic equation.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Taking into account the correct determination of internal energy when construction models of non-ideal liquid mixtures by methods of non-equilibrium thermodynamics
No full textAbstract:
Taking into account of the methods of thermodynamics of irreversible processes using the Onsager principle, a model of a multicomponent medium is constructed, the internal energy of which is free from the kinetic energy of diffusion. The model was developed for non-ideal continuous medium with chemical reactions in the field of conservative external forces. Thermodynamic generalized Stefan–Maxwell relations are derived, which are a system of hydrodynamic equations of a mixture with genuine inertia forces. The proposed phenomenological methodology allowed us to obtain a number of algebraic relations for the transfer coefficients, relating, in particular, thermal diffusion relations with thermal diffusion coefficients and multicomponent diffusion, true and partial heat transfer coefficients, multicomponent and binary diffusion coefficients, which testifies to their universal nature. The results obtained are intended to simulate not only liquid non-ideal solutions, but also gas-dust mixtures with a fine-dispersed component of dust.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Identification of potentially dangerous space objects and conjunctions
No full textAbstract:
There are proposals on the methods of solving and the requirements for software implementation of the tasks of identifying and tracking potentially dangerous space objects and conjunctions present in this paper. The statistics of conjunctions in the GEO, MEO and HEO areas in 2018 are given.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Explicit time integration of the Navier-Stokes equations using the local iteration method
No full textAbstract:
New time integration algorithm LI-M is proposed for the Navier-Stokes equations of compressible heat-conducting flows. This algorithm is based on the splitting procedure by convection and diffusion processes over a time step. The explicit scheme computes solution of convection part and the explicit-iteration Chebyshev scheme computes the diffusion part. The resulting scheme makes it possible to avoid diffusion restriction on time step. The scheme has a predictor-corrector structure and ensures the fulfillment of conservation laws. The explicit nature of the calculations ensures the efficiency of the use of the scheme in various parallel technologies.Note:
Research direction:Mathematical problems and theory of numerical method
Determination of the Sun position onboard the spacecraft by photoelectric solar sensor
No full textAbstract:
The preprint deals with the development of a mathematical model of the solar sensor on the basis of photoelectric elements to the spacecraft attitude motion to construct and maintain a constant solar orientation (CSO).
A mathematical model that allows to form the output of the sensor in the form of analog currents (or voltages) depending on the Sun position relative to the sensor is developed, as well as algorithms that restore the Sun position by magnitude of output currents of photoelectric cells in the instrument coordinate system.
A statistical analysis was carried out to estimate the performance of spacecraft control algorithms at construction and maintenance of the CSO mode together with a mathematical model of the sensor and algorithms for restoring the position of the Sun for different initial spacecraft orientation relative to the Sun.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Ensuring the entropy stability of the discontinuous Galerkin method in gas-dynamics problems
No full textAbstract:
A new variational principle for deriving the discontinuous Galerkin method modified equations is proposed for solving one-dimensional equations of ideal gas dynamics, based, in particular, on the implementation of a discrete analogue of entropic inequality. А special entropic tilt limiter has been developed in connection with the proposed principle, which ensures non-negative entropy production in each finite element. Numerical calculations of some model problems have been carried out in order to evaluate the efficiency of the method.Note:
Research direction:Mathematical problems and theory of numerical method
To the theory of linear response for quantum nonextensive system on dynamic external disturbance
No full textAbstract:
In the framework of quantum statistical mechanics, based on the parametric nonadditive entropy of Tsallis, related to the density matrix, a dynamic theory of linear response of nonextensive quasi-equilibrium many-body systems to an external time-dependent perturbation is developed. In this paper, for the nonextensive quantum system proposed a modification of the Kubo theory developed in the framework of classical quantum mechanics. The construction of the microscopic theory of the linear reaction was carried out on the basis of the generalized canonical type of the density matrix, obtained by maximizing the Tsallis quantum entropy by averaging the observed values over the escort distribution. The generalized expressions for the admittance and the response function are presented, which describe the linear dependence of the system (with a time independent Hamiltonian) on a weak external mechanical action. The symmetry property for the relaxation function under time reversal and the Onsager reciprocity relation for generalized susceptibility are discussed. It is shown that these properties known in classical quantum statistics also remain valid for anomalous systems.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Bistability analysis of virus infection models with delayed arguments
No full textAbstract:
Mathematical models with time delays are widely used to analyze the mechanisms of the immune response to viral infections and predict various therapeutic effects. Using the LCMV infection model as an example, this work describes an original computational technology for searching the bistable regimes of such models. This technology includes numerical methods for finding all
possible steady states at fixed values of parameters, for tracing these states along the parameters and for analyzing their stability.Note:
Research direction:Mathematical modelling in actual problems of science and technic
Research of vibrations of structure elements of the space station on video information
No full textAbstract:
Video information about vibrations of elements of ISS structure allows to establish quantitative characteristics of these vibrations. Such characteristics are found as a result of processing of time series obtained by digitizing of video film shots. Digital data are vertical and horizontal coordinates, expressed in pixels, of some points on a station structure element in a shot. Processing of the time series allows evaluating the real time dependence of the coordinates. This dependence in common has an oscillation character and can be presented by the sum of eventual number of simple harmonics, their amplitudes and frequencies being determined by means of spectral analysis.Note:
Research direction:Theoretical and applied problems of mechanic
On the conservativity of the Particles-on-Demand method for solution of the Discrete Boltzmann Equation
No full textAbstract:
It is well known that the standard Lattice-Boltzmann method (LBM) is applicable in the range of small flow velocities and under the isothermal conditions.
The novel Particle-on-demand method [1] allows to numerically solve the discrete Boltzmann equation for high Mach numbers.
We validate its capabilities with our implementation on the problems with shock waves.
In comparison with the standard Lattice Boltzmann Method, the collision step is simple, but the streaming step is implicit, non-conservative and excessively computationally heavy.
We propose a way that in specific cases improves the method by making the streaming step explicit and conservative.
The results are validated by examining the total mass, momentum and energy change in the problem of shock formation due to the sound wave distortion.
The scheme also performs well in both 1D and 3D test Sod problems.Note:
Research direction:Programming, parallel computing, multimedi