scholarly journals Analytical solutions for steady state vertical infiltration

2002 ◽  
Vol 38 (8) ◽  
pp. 20-1-20-5 ◽  
Author(s):  
Jianting Zhu ◽  
Binayak P. Mohanty
Keyword(s):  
Steady State ◽  
Analytical Solutions

SEMI-ANALYTICAL SOLUTIONS FOR THE BRUSSELATOR REACTION–DIFFUSION MODEL

2017 ◽  
Vol 59 (2) ◽  
pp. 167-182 ◽  
Author(s):  
H. Y. ALFIFI
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Partial Differential ◽  
Analytical Results ◽  
Transient Solutions ◽  
The Impact

Semi-analytical solutions are derived for the Brusselator system in one- and two-dimensional domains. The Galerkin method is processed to approximate the governing partial differential equations via a system of ordinary differential equations. Both steady-state concentrations and transient solutions are obtained. Semi-analytical results for the stability of the model are presented for the identified critical parameter value at which a Hopf bifurcation occurs. The impact of the diffusion coefficients on the system is also considered. The results show that diffusion acts to stabilize the systems better than the equivalent nondiffusive systems with the increasing critical value of the Hopf bifurcation. Comparison between the semi-analytical and numerical solutions shows an excellent agreement with the steady-state transient solutions and the parameter values at which the Hopf bifurcations occur. Examples of stable and unstable limit cycles are given, and Hopf bifurcation points are shown to confirm the results previously calculated in the Hopf bifurcation map. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with the numerical solutions of partial differential equations.

Dimensionless analytical solutions for steady-state fire smoke spread through high-rise shaft

2017 ◽  
Vol 93 ◽  
pp. 12-20 ◽  
Author(s):  
Dahai Qi ◽  
Liangzhu (Leon) Wang ◽  
Jie Ji ◽  
Man Li
Keyword(s):  
Steady State ◽  
Analytical Solutions ◽  
High Rise ◽  
Smoke Spread ◽  
Fire Smoke

scholarly journals STATIC STRAINING AND LONGITUDINAL OSCILLATIONS OF UNDERGROUND PIPELINE BUILT ON BLOCK FOUNDATION

2021 ◽  
pp. 123-133
Author(s):  
A. B. Struk ◽  
M. I. Vaskovskyi ◽  
I. P. Shatskyi ◽  
M. V. Makoviichuk
Keyword(s):  
Steady State ◽  
Stress State ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Equivalent Stress ◽  
Forced Oscillations ◽  
Underground Pipeline ◽  
Underground Pipelines ◽  
Block Foundation ◽  
Static Tensile

The article considers the issues of forecasting the strength of underground pipelines, which are operated on seismically active sections of the route, composed of relatively rigid mobile blocks. According to the literature, the problems of the influence of the interaction of base faults on the stress state of the pipeline have not been studied to date. The aim of the work is to develop a model for the analysis of abnormal stresses in the underground pipeline on a damaged basis caused by static or time-harmonious mutual movement of its blocks along the axis of the pipe in the presence of several faults. Boundary value problems for differential equations of static tensile-compression and steady-state longitudinal oscillations of a tubular rod with discontinuous right-hand sides are formulated. Based on the analytical solutions of these problems for the cases of antisymmetric and symmetric displacement of the foundation blocks, the distributions of axial displacement and equivalent stress in the pipe, depending on the distance between faults and the frequency of forced oscillations, are investigated.

scholarly journals Benchmark analytical solutions for steady state high frequency broadband sound fields in three rectangular enclosures

2019 ◽  
Vol 145 (4) ◽  
pp. 2601-2612 ◽  
Author(s):  
David Raudales ◽  
Donald B. Bliss ◽  
Krista A. Michalis ◽  
Jerry W. Rouse ◽  
Linda P. Franzoni
Keyword(s):  
Steady State ◽  
Analytical Solutions ◽  
High Frequency ◽  
Sound Fields ◽  
Broadband Sound

scholarly journals Analytical Solutions for Steady-State Multiwell Aquifer Tests in Rectangular Aquifers by Using Double Fourier Transform: A Case Study in the Ordos Plateau, China

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jun-Zhi Wang ◽  
Xu-Sheng Wang ◽  
Qing-Bo Li ◽  
Wei-Feng Wan
Keyword(s):  
Fourier Transform ◽  
Steady State ◽  
Analytical Solutions ◽  
Estimation Method ◽  
Least Square ◽  
Ordos Plateau ◽  
Aquifer Systems ◽  
Aquifer Test ◽  
Double Fourier Transform

Straightforward solutions have long been expected for the analysis of multiwell aquifer tests. In this paper, we derive series analytical solutions of steady-state groundwater flow in a rectangular-shaped aquifer with pumping/injection wells for both confined and unconfined conditions. Double Fourier Transform (DFT) technique is applied to deal with different combinations of impermeable and specified head boundaries on sides. The obtained solutions are compact and concise in mathematics and flexible in terms of well number, well locations, and pumping/injection rates. Hatoucaidang, a groundwater resource field in the Ordos Plateau, Northwestern China, is introduced as a field case study, where a multiwell aquifer test was conducted. One of the analytical solutions derived herein is used to estimate hydraulic conductivities by applying a direct calculation method and a least square estimation method regarding observed versus calculated drawdowns. By comparing with nearby single-well pumping tests, the reliability of the derived analytical solutions is proven. This study facilitates utilizing the multiwell aquifer test to analyze the general behavior of groundwater movement in aquifer systems.

Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator

Open Physics ◽  
2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Erik Sweet ◽  
Kuppalapalle Vajravelu ◽  
Robert Gorder
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Nonlinear Partial Differential Equations ◽  
Coupled System ◽  
Polar Coordinates ◽  
Rotating Flow ◽  
Rotating Sphere

AbstractIn this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.

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