Methods Of Increasing Spectral Resolution Of Imaging Spectrometers Built On The Basis Of Multi–channel Radiation Detectors

The article proposes the methods of object shooting by means of a spectrometer based on a multi-channel radiation detector and further processing of its results allowing spectral resolution of such spectrometers significantly to increase with the same original spatial resolution. The mathematical model of the shooting process is provided. It is determined that restoration of spectral radiance of objects based on the shooting data using the proposed method is a mathematically incorrect inverse task. The Greville method, the method of wavelet transformation, the Tikhonov regularisation method, and the Godunov method were considered as methods for its solution. The results of computational modelling of the considered methods are shown and it is found that restoration of spectral radiance of objects based on the shooting data using the considered methods is possible and relative error of restoration is at a fraction of per cent scale. It is determined that the wavelet transformation method is an optimal method of solution of the incorrect spectral radiance restoration task. It is also shown that the proposed method of imaging spectrometry is applicable both when using matrix radiation detectors with increased number of narrow-band filters and when using widely spread standard three-channel matrix RGB detectors of radiation.

Determination of flood parameters during the fire hazardous liquid spreading after the accident

Пролив пожароопасных жидкостей на свободную поверхность является одним из наиболее опасных сценариев аварии, приводящей к пожару. Для решения задачи по оценке параметров такого пролива было использовано численное интегрирование уравнений сохранения методом Годунова, на примере растекания пожароопасной жидкости по бетонному основанию. Возможности метода численного интегрирования позволяют спрогнозировать размеры пролива на текущий момент времени. Результаты расчета показали, что пролив объемом 245 м в течение 4-5 мин достигает равновесного состояния, после чего площадь зеркала пролива практически не увеличивается. Nowadays, various containers are used for storage and transportation of fire hazardous liquids. It is impossible to eliminate completely the possibility of tank depressurization and the scenarios associated with their destruction should be taken into account when developing technical solutions and organizational measures aimed at minimizing the possible consequences of such accidents. As a result of the flammable liquid spreading a mirror of the flood can form, from which subsequently the evaporation of combustible products occurs, which, when mixed with air, forms explosive mixtures. At a fuel concentration in the cloud above the upper limit of flame propagation, a fire development characterized by a flash fire is possible. If the concentration of vapors in the mixture with air is inside the concentration region of the flame propagation, a deflagration explosion is possible. In both cases, a flood fire can occur characterized by the formation of a high temperature flame. The initial task in predicting such accidents is to determine the surface area of the spilled liquid from which evaporation can occur. To solve this problem it is necessary to solve the hydraulic problem associated with the fluid spreading on a free surface having hydraulic resistance. Similar problems were solved in the practice of building design while determining the parameters of water movement along a dry riverbed. One of the forms of solution is the method of numerical integration of the conservation equations with the Godunov method, which is effective in solving problems of gas dynamics, as well as hydraulic problems. The calculation results showed that this method is applicable to the considered problem of forming a fire hazardous liquid flood on a free surface. Also, the results of the work indicate that a very significant volume of the fire hazardous liquid flood (245 m) reaches quickly enough a quasi-equilibrium state with a flood thickness of 0.03 ч 0.04 m.

A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations

We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation. This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. IP is reduced to an optimization problem, which is solved by the gradient descent method. The quality of the IP solution highly depends on the quantity of IP data and positions of receivers. We introduce a new approach for computing a gradient in the descent method in order to use as much IP data as possible on each iteration of descent.

Efficient approach toward the application of the Godunov method to hydraulic transients

The proposed study investigated the applicability of the finite volume method (FVM) based on the Godunov scheme to transient water hammer with shock front simulation, in which intermediate fluxes were computed using either first-order or second-order Riemann solvers. Finite volume (FV) schemes are known to conserve mass and momentum and produce the efficient and accurate realization of shock waves. The second-order solution of the Godunov scheme requires an efficient slope or a flux limiter for error minimization and time optimization. The study examined a range of limiters and found that the MINMOD limiter is the best for modeling water hammer in terms of computational time and accuracy. The first- and second-order FVMs were compared with the method of characteristics (MOCs) and experimental water hammer measurements available in the literature. Both the FV methods accurately predicted the numerical and experimental results. Parallelization of the second-order FVM reduced the computational time similar to that of first-order. Thus, the study presented a faster and more accurate FVM which is comparable to that of MOC in terms of computational time and precision, therefore it is a good substitute for the MOC. The proposed study also investigated the implementation of a more complex convolution-based unsteady friction model in the FVM to capture real pressure dissipation. The comparison with experimental data proved that the first-order FV scheme with the convolution integral method is highly accurate for computing unsteady friction for sudden valve closures.