hydrodynamic models
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Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 254
Author(s):  
María S. Bruzón ◽  
Rafael de la Rosa ◽  
María L. Gandarias ◽  
Rita Tracinà

A family of third-order partial differential equations (PDEs) is analyzed. This family broadens out well-known PDEs such as the Korteweg-de Vries equation, the Gardner equation, and the Burgers equation, which model many real-world phenomena. Furthermore, several macroscopic models for semiconductors considering quantum effects—for example, models for the transmission of electrical lines and quantum hydrodynamic models—are governed by third-order PDEs of this family. For this family, all point symmetries have been derived. These symmetries are used to determine group-invariant solutions from three-dimensional solvable subgroups of the complete symmetry group, which allow us to reduce the given PDE to a first-order nonlinear ordinary differential equation (ODE). Finally, exact solutions are obtained by solving the first-order nonlinear ODEs or by taking into account the Type-II hidden symmetries that appear in the reduced second-order ODEs.


2022 ◽  
Vol 17 ◽  
pp. 29-33
Author(s):  
Asad Salem

The stability of a two-phase interface is a crucial occurrence that involves the design of many engineering applications. It correlates the spatial and droplet size-distributions of many fluid spraying applications and has a great effect on the estimations of the critical heat flux of systems that involves phase change or evaporation. However, the existing hydrodynamic models are only able to predict the stability of a plane fluid sheet, surrounded by an infinite pool of liquid. The case of a thin sheet of liquid surrounding a vapor sheet and enclosed between two walls has not been studied yet. The present paper solves this problem using a linearized stability analysis. Velocity potentials satisfying these conditions are introduced and a complete analysis is presented.


2021 ◽  
Vol 21 (3) ◽  
pp. 117-122
Author(s):  
Aleksey Yu. Vishnyakov

The initial data when creating both geological and hydrodynamic reservoir models can lead to errors in the modeling results and the subsequent distortion of the economic assessment and prospects of an oil or gas field. In order to improve the predictive reliability of reservoir hydrodynamic models, a core material study for the Tula object of four fields at the Babkinskaya anticline was carried out. The ratio analysis of porosity (Kp), rock density () and permeability (Kperm) for sandstones and aleurolites was carried out. Using a statistical core sampling based on porosity, density and permeability parameters, a separation by sedimentation processes was carried out for all considered lithological differences. For aleurolite and sandstone, we could talk about the differentiation of characteristics in the process of reservoir properties formation. The values of the parameters Kp, and Kperm, determined from laboratory core studies, were combined into a single statistical sample for the possibility of developing a methodology that would be aimed at describing Kperm using the integrated laboratory studies, namely by adding rock to the analysis. As a result of statistical analysis, it was found that permeability in intervals with low reservoir properties was controlled with the same significance degree by both porosity and rock density for all lithological differences. At the same time, the presence of highly permeable reservoirs for sandstones and their practically absence for aleurolites were noted. For all lithological differences, relationships were established between the permeability coefficient not only with porosity, but also with rock density. The methodology for constructing statistical models for calculating permeability from the values of porosity and rock density was implemented separately for the fields of the eastern and western parts of the Babkinskaya anticline. The described approach to taking into account the influence of rock density on permeability made it possible to determine the differentiated influence of lithotypes on the filtration characteristics of the reservoir. When modeling a reservoir, it is necessary to move from linearity to nonlinearity and take into account that the problem of permeability distribution in the reservoir being solved is somewhat more complicated: in different areas, sometimes the permeability is not controlled by porosity in principle, but somewhere only this parameter prevails. The methodical approach was recommended for 3D modeling. Revealing the relationships between the parameters was most important when developing a methodology for tuning the model in the interwell space. The development of a reliable estimate of permeability for the vast majority of wells will significantly improve the efficiency of hydrodynamic modeling. At the same time, it is necessary to comprehensively take into account the identified relationships between the petrophysical characteristics of production layers. The use of the approach to the analysis of petrophysical characteristics will allow obtaining a more reliable and less subjective hydrodynamic model of the formation.


Author(s):  
H Jafaryeganeh ◽  
C Guedes Soares

A panel cutting technique is developed for automatic modification of an initial mesh of a ship hull used for hydrodynamic computations leading to improved meshes for the prediction of wave induced vertical load effects. The technique can provide a model with divided panels in any defined position regardless of the initial discretization of the body. The applications of the provided technique include panel distinction and division in predetermined positions, generation of finer mesh based on the initial coarser model of meshes and improvement of vertical load prediction in predetermined positions. The method is applied for case studies of a barge, shuttle tanker and frigate to depict various applications. Finally, the hydrostatic and hydrodynamic vertical shear forces are calculated for two models of initial and modified panels of well-known frigate 5415. The results are compared for the sections alongside the ship and accuracy of load integration is shown for predetermined sections.


Author(s):  
V. V. Veremenyuk ◽  
V. V. Ivashechkin ◽  
O. V. Nemeravets

153 reservoirs have been created in the Republic of Belarus. During the period of passing catastrophic floods and high waters along the river, there is a risk of overflowing reservoirs, overflow of water masses through the crest of an earthen dam and flooding of significantly large areas. The destruction of the dam is accompanied by the formation of a breach and the outflow through it of an unsteady flow of water in the form of a breakthrough wave into the downstream. A breakthrough wave and catastrophic flooding of the area are the main destructive factors of hydrodynamic accidents. Calculations to determine parameters of the wave and to assess the possible consequences of flooding are necessary when drawing up operational-and-tactical plans for the prevention and elimination of emergencies in case of accidents at retaining structures, determining the probable damage from flooding of the territory in the downstream of a hydraulic structure as a result of the passage of a breakthrough wave. It is necessary to assess the flooding zone and the hydrodynamic parameters of the flow, viz. the maximum values of the depth and velocity of the flow in the zone of catastrophic flooding, the time from the beginning of the accident to the arrival of a breakthrough wave at the particular point of the terrain, the duration of flooding, the boundaries of the zone of catastrophic flooding, the hydrographic flow rate in the section of the eroded dam and the graph of the fall headwater level. The degree of reliability of predictive calculations is determined by the accuracy of the two applied mathematical models, viz.: 1) erosion of the dam; 2) the movement of the breakout wave. The analysis of the applied mathematical models shows that in all cases the hydrodynamic models based on the oneand two-dimensional equations of Boussinesq – Saint-Venant are used to calculate the movement of the breakthrough wave. Wave parameters, i. e. wave height and speed of its propagation, completely depend on the hydrograph of the discharge in the section of the eroded dam, which, in its turn, is determined by the dynamics of its erosion. The aim of the work is to develop a methodology for calculating the flooding of the downstream as a result of the destruction of a soil dam.


2021 ◽  
Vol 9 (12) ◽  
pp. 1347
Author(s):  
Jessie Louisor ◽  
Jérémy Rohmer ◽  
Thomas Bulteau ◽  
Faïza Boulahya ◽  
Rodrigo Pedreros ◽  
...  

As low-lying coastal areas can be impacted by flooding caused by dynamic components that are dependent on each other (wind, waves, water levels—tide, atmospheric surge, currents), the analysis of the return period of a single component is not representative of the return period of the total water level at the coast. It is important to assess a joint return period of all the components. Based on a semiparametric multivariate extreme value analysis, we determined the joint probabilities that significant wave heights (Hs), wind intensity at 10 m above the ground (U), and still water level (SWL) exceeded jointly imposed thresholds all along the Corsica Island coasts (Mediterranean Sea). We also considered the covariate peak direction (Dp), the peak period (Tp), and the wind direction (Du). Here, we focus on providing extreme scenarios to populate coastal hydrodynamic models, SWAN and SWASH-2DH, in order to compute the 100-year total water level (100y-TWL) all along the coasts. We show how the proposed multivariate extreme value analysis can help to more accurately define low-lying zones potentially exposed to coastal flooding, especially in Corsica where a unique value of 2 m was taken into account in previous studies. The computed 100y-TWL values are between 1 m along the eastern coasts and a maximum of 1.8 m on the western coast. The calculated values are also below the 2.4 m threshold recommended when considering the sea level rise (SLR). This highlights the added value of performing a full integration of extreme offshore conditions, together with their dependence on hydrodynamic simulations for screening out the coastal areas potentially exposed to flooding.


2021 ◽  
Vol 922 (2) ◽  
pp. 176
Author(s):  
A. W. Hindle ◽  
P. J. Bushby ◽  
T. M. Rogers

Abstract Magnetically driven hotspot variations (which are tied to atmospheric wind variations) in hot Jupiters are studied using nonlinear numerical simulations of a shallow-water magnetohydrodynamic (SWMHD) system and a linear analysis of equatorial SWMHD waves. In hydrodynamic models, mid-to-high-latitude geostrophic circulations are known to cause a net west-to-east equatorial thermal energy transfer, which drives hotspot offsets eastward. We find that a strong toroidal magnetic field can obstruct these energy transporting circulations. This results in winds aligning with the magnetic field and generates westward Lorentz force accelerations in hotspot regions, ultimately causing westward hotspot offsets. In the subsequent linear analysis we find that this reversal mechanism has an equatorial wave analogy in terms of the planetary-scale equatorial magneto-Rossby waves. We compare our findings to three-dimensional MHD simulations, both quantitatively and qualitatively, identifying the link between the mechanics of magnetically driven hotspot and wind reversals. We use the developed theory to identify physically motivated reversal criteria, which can be used to place constraints on the magnetic fields of ultra-hot Jupiters with observed westward hotspots.


2021 ◽  
Author(s):  
Denys Grytsai ◽  
Petro Shtefura ◽  
Vadym Dodukh

Abstract A methodology has been developed that, in conditions of limited geological and production data, ensures the integration of petrophysical, geological, and hydrodynamic models as components of a permanent 3D model, establishing physical relationships between parameters that describe the entire system. In the proposed method, the modelling is based on the results of the interpretation of continuous shale volume and porosity curves. Based on the analysis of core data, the multi-vector physical correlations with other parameters are made. To distinguish the reservoirs and non-reservoirs, the cut-off values of shale volume are defined; to exclude tight reservoirs with no filtration, the cut-off values of porosity are set. Using the Winland R35 method the radius of the pore throat is computed, allowing dividing the reservoirs into classes. For each class of reservoirs, the permeability vs porosity dependence is determined, and the Wright-Woody-Johnson method allows deriving equations for the bound water content. A system of configured workflows has been developed and allows automating re-modelling and simplifying its history matching. This technique was successfully applied to several 3D models of gas condensate fields, which, with a significant drilling level on the areas and a long development history, are characterized by limited geological and production data. Workflows System together with the proposed approach allowed simplifying the history matching process by splitting it into several stages. At each stage, depending on the type of input data, various parameters were matched (production, reservoir and wellhead pressures, etc.). Due to cross-functional correlation of all components, the model has significantly reduced the uncertainty parameters and allowed a detailed history matching of the development history for the entire well stock. The results obtained were tested by several geological and technological measures, including drilling new wells, and showed high convergence with the forecast indicators. The proposed approach to modelling and history matching in conditions of limited geological and production data allows: – ensuring integration and correlation of petrophysical, geological, and hydrodynamic models as components of a permanent 3D model; – automating and simplifying the modelling, history matching, and updating a model; – improving the quality of parameters’ matching results.


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