Initial And Boundary Conditions
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2021 ◽  
Vol 3 (2) ◽  
pp. 18-28
N. Rashkevich ◽  
А. Pastukhova ◽  
V. Konoval ◽  
V. Slovinskyi ◽  

The authors analyze the fire and explosion hazards of solid waste disposal facilities, taking into account current trends in the introduction of biogas (methane) collection and utilization systems. Methane is considered an alternative energy source for power plants. The authors determined the initial and limiting conditions of the mathematical apparatus of the method of combating fire and explosion hazards of solid waste disposal facilities based on the results of analysis and synthesis of factors of occurrence and spread of man-caused danger, existing mathematical models, and methods of counteracting man-caused danger. This is the basis for the further development of appropriate emergency response techniques. During the analysis, the authors found that humidity, the temperature of the landfill (household waste), the presence of sufficient oxygen at some point in time initiate the formation of explosive concentrations of methane in the array and contribute to the spread of hazards in landfills or dumps. The specific weight of the organic component, the value of the density of the array, the height of the landfill affect the process of counteracting the danger, namely the prevention of dangerous events and prevention of emergency from the object to the highest level of distribution (local level), primarily in the first group priorities, such as the number of victims and injured civilians and specialists of the units of the State Emergency Service of Ukraine. The team of authors has defined a system of equations of connection of the existence of the mathematical device taking into account initial and boundary conditions. A system of communication equations is determined taking into account the initial and boundary conditions of the mathematical apparatus, which allows to further develop a control algorithm for emergency response related to fire and explosion hazardous landfills close to settlements.

2021 ◽  
Vol 57 (1) ◽  
pp. 129-134
R. G. ASHRIT ◽  

lkj & bl v/;;u esa 29 vDrwcj] 1999 dks mM+hlk ds rV ij vk, egkpØokr ds izfr:i.k ds fy, ,u- lh- ,- [email protected] ,l- ;w-  ,e- ,e- 5 eslksLdsy fun’kZ ¼xzsy bR;kfn 1995½ dk mi;ksx fd;k x;k gsA bl fun’kZ esa pØokr dh izkjafHkd voLFkk vkSj mldh ifjlhekvksa dh voLFkkvksa ds :i  esa jk"Vªh; e/;&vof/k ekSle iwokZuqeku dsUnz Vh- 80 ds izpkyukRed fo’ys"k.kksa dk iz;ksx fd;k x;k gS vkSj rwQku dh vof/k esa 3 fnu rd dk iwokZuqeku rS;kj djus ds fy, bl fun’kZ dks 72 ?kaVs dh vof/k ds fy, lekdfyr fd;k x;k gSA bl v/;;u dk mn~ns’; pØokr ds ekxZ ij dfYir Hkzfey ds izHkko dk ewY;kadu djuk vkSj pØokr dh rhozrk dk iwokZuqeku yxkuk gSA In this study NCAR/PSU MM5 mesoscale model (Grell et al. 1995) is used to simulate the super cyclone that struck the Orissa coast on 29th October 1999. The model makes use of the operational NCMRWF T 80 analysis as initial and boundary conditions and is integrated up to 72 hr for producing 3-day forecast of the storm. The aim of this study is to assess the impact of bogus vortex on track and intensity prediction. 

2021 ◽  
Vol 1 ◽  
pp. 75-76
Karsten Reiter ◽  
Steffen Ahlers ◽  
Sophia Morawietz ◽  
Luisa Röckel ◽  
Tobias Hergert ◽  

Abstract. Assessment of the stability of deep geological repositories is a key task in the site selection process for high-level radioactive waste. Geomechanical stability is affected by endogenous and exogenous processes as well as by geotechnical operations. Stability prediction requires both an estimate of future stress changes as well as the initial, i.e. current stress state. However, data records on the current stress state in the upper crust are incomplete, sparse and spatially unevenly distributed. Therefore, geomechanical-numerical models are the only way to estimate the full stress tensor at locations where stress observations are not available. The main components of such a 3-D geomechanical model are the distribution of the elastic rock properties and rock density as well as stress data for the model calibration. The aim is to find the optimal initial and boundary conditions that result in a best-fit with respect to available stress data within the model volume. For this reason, the first open access database for stress magnitude data has been developed as an extension of the existing database on stress orientation data ( The new database contains 568 data records from Germany and surrounding areas, but only 15 % of these data records are of acceptable quality. Thus, only one reliable set of stress magnitude data is available for an area of 100×100 km2. Based on existing compilations of the crustal structure in and around Germany, data were merged into one model with the aim of estimating the 3-D stress state in Germany. Geomechanical models for stress estimation in Germany were created with varying geometrical and mechanical resolution. While the first model consists of four mechanical units and 1.3 million finite elements, the subsequent model consists of 12 units and 3.6 million finite elements. The results of the best-fit model with respect to the stress data reveal that there are regional differences when calculating the fracture potential, i.e. the distance to failure of intact rock as well as different values of slip tendency, which provides a measure of the reactivation potential of pre-existing faults. The observed variability of the modelled stress field can be used as a first-order assessment. Since model uncertainties are still high, the absolute values are not yet reliable. However, the model can be used to derive consistent initial and boundary conditions for models on a regional scale. Furthermore, it makes it possible to investigate the influence of the large-scale crustal structure on the overall stress pattern. The modelling workflow is set-up in a way that new information and higher resolution if needed can be implemented when more data are provided. This will improve the reliability of both, the model prediction on the large scale as well as the initial and boundary conditions for high-resolution regional models for selected areas during the site selection process.

2021 ◽  
Vol 2090 (1) ◽  
pp. 012069
Aarne Pohjonen

Abstract For constructing physical science based models in irregular numerical grids, an easy-to-implement method for solving partial differential equations has been developed and its accuracy has been evaluated by comparison to analytical solutions that are available for simple initial and boundary conditions. The method is based on approximating the local average gradients of a field by fitting equation of plane to the field quantities at neighbouring grid positions and then calculating an estimate for the local average gradient from the plane equations. The results, comparison to analytical solutions, and accuracy are presented for 2-dimensional cases.

2021 ◽  
pp. 121
S.S. Kritskaia

We solve one boundary problem of fourth order with initial conditions, that appears, for example, when one solves the problem about lateral oscillations of elastic-viscous-relaxating rod of variable profile with variable momentum of inertia with freely supported ends.

Nur Fatihah Mod Omar ◽  
Husna Izzati Osman ◽  
Ahmad Qushairi Mohamad ◽  
Rahimah Jusoh ◽  
Zulkhibri Ismail

The effects of radiation and magnetohydrodynamic on unsteady Casson fluid through an accelerated plate is analysed. The problem is formulated in the form of Partial Differential Equations (PDE) with imposed initial and boundary conditions. The Partial Differential Equations are transformed into dimensionless form by introducing suitable non-dimensional variables. Laplace transform method is used to derive the exact solutions for temperature and velocity profiles, fulfilling all initial and boundary conditions. The effects of parameters are depicted and illustrated graphically for radiation, Casson fluid and time, as well as Magnetohydrodynamics (MHD). It is found that the thermal radiation rises due to an increase in temperature. Besides, the increasing of Casson fluid and MHD parameter has decreasing effect on velocity. Finally, the influence of time will increase the velocity of the fluid.

Brittany N. Carson-Marquis ◽  
Jianglong Zhang ◽  
Peng Xian ◽  
Jeffrey S. Reid ◽  
Jared Marquis

AbstractWhen unaccounted for in numerical weather prediction (NWP) models, heavy aerosol events can cause significant unrealized biases in forecasted meteorological parameters such as surface temperature. To improve near-surface forecasting accuracies during heavy aerosol loadings, we demonstrate the feasibility of incorporating aerosol fields from a global chemical transport model as initial and boundary conditions into a higher resolution NWP model with aerosol-meteorological coupling. This concept is tested for a major biomass burning smoke event over the Northern Great Plains region of the United States that occurred during summer of 2015. Aerosol analyses from the global Navy Aerosol Analysis and Prediction System (NAAPS) are used as initial and boundary conditions for Weather Research and Forecasting with Chemistry (WRF-Chem) simulations. Through incorporating more realistic aerosol direct effects into the WRF-Chem simulations, errors in WRF-Chem simulated surface downward shortwave radiative fluxes and near-surface temperature are reduced compared with surface-based observations. This study confirms the ability to decrease biases induced by the aerosol direct effect for regional NWP forecasts during high-impact aerosol episodes through the incorporation of analyses and forecasts from a global aerosol transport model.

2020 ◽  
pp. 39-47
Roman Gudak

Roman Gudak, Serghii Iline, Alexandr Soshinskiy FORMATION INITIAL AND BOUNDARY CONDITIONS PROBLEM SOLVING EMERGENCY PREVENTION OF NATURAL ORIGIN, CAUSED BY HYDROLOGICAL AND METEOROLOGICAL PHENOMENA IN CERTAIN REGIONS OF THE HIGHLANDS Based on a comprehensive analysis of natural and climatic features of the Carpathian region of Ukraine, the initial and boundary conditions for solving the problem of prevention of natural emergencies caused by hydrological and meteorological phenomena in a particular region of the mountain area through the use of rescue helicopters. It is determined that the main feature of the soils of the Carpathian Mountains is their relative looseness and water saturation. With the appearance of additional volumes of aquatic environment, which under the influence of gravity, create significant hydraulic gradients that lead to landslides, mudslides, landslides and races of rivers and streams. Emergencies of a natural nature, which are caused by hydrological and meteorological phenomena, in the mountains have five characteristics. This is the inevitability and sudden onset of a catastrophic event, which can cover a long area, accompanied by great destruction and changes in terrain. Features of emergency management in a particular region of mountainous areas include detailed study of the area and monitoring of local information, geo-information modeling of disasters and early preparation of action plans, constant training of rescuers and preparation for the use of new rescue tools - helicopters. As a result, they form a system of initial and boundary conditions for solving the problem of natural disaster prevention in a particular region of the mountain area, namely: initial conditions for solving the problem - a set of conditions that ensure the fulfillment of orders for delivery to the disaster area and evacuation; boundary conditions - are determined by the maximum load of helicopters, weather conditions, flight time and length of routes, the structure of the graph of the flight task plan and the condition of mandatory return of helicopters to base points. Key words: emergency, mountainous region, helicopter, warning task, initial and boundary conditions

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