Solution of a Two-Dimensional, Steady-State Watershed Flow System Part I. Description of Mathematical Model

1972 ◽  
Vol 15 (3) ◽  
pp. 0457-0463 ◽  
Author(s):  
Roland W. Jeppson and David L. Schreiber
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Flow System ◽  
Two Dimensional ◽  
System Part

Solution of a Two-Dimensional, Steady-State Watershed Flow System Part It Evaluation by Field Data

1972 ◽  
Vol 15 (3) ◽  
pp. 0464-0470 ◽  
Author(s):  
D. L. Schreiber ◽  
R. W. Jeppson ◽  
G. R. Stephenson ◽  
C. W. Johnson ◽  
C. M. Cox ◽  
...  
Keyword(s):  
Steady State ◽  
Field Data ◽  
Flow System ◽  
Two Dimensional ◽  
System Part

Modeling of Groundwater Flow and Contaminant Transport in Two-Dimensional Geometries in an Unconfined Aquifer

2014 ◽  
Vol 1010-1012 ◽  
pp. 1023-1027
Author(s):  
Fouad Dimane ◽  
Issam Hanafi ◽  
Abdelouahad El Himri ◽  
Khadija Haboubi ◽  
Francisco Mata Cabrera ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Steady State ◽  
Groundwater Flow ◽  
Contaminant Transport ◽  
Cross Section ◽  
Flow System ◽  
Unconfined Aquifer ◽  
Two Dimensional ◽  
Groundwater Flow System ◽  
Subsurface Fluid

Models of groundwater flow are widely used for a variety of purposes ranging from water supply studies to designing contaminant cleanup. In general, groundwater flow system can be divided into steady-state and transient. In the present work, we investigate the usefulness of finite element method in modelling of steady-state subsurface fluid flow and transient solute transport along a vertical cross section in an unconfined aquifer. Details are explained on numerical approximations leading to different numerical results. Extensions for pollutant transport are mentioned.

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State

Study on Grinding Force in Two-Dimensional Ultrasonic Grinding Nano-Ceramics

2010 ◽  
Vol 42 ◽  
pp. 204-208 ◽  
Author(s):  
Xiang Dong Li ◽  
Quan Cai Wang
Keyword(s):  
Mathematical Model ◽  
Ultrasonic Vibration ◽  
Contact Time ◽  
Reaction Force ◽  
Grinding Force ◽  
Two Dimensional ◽  
Indentation Fracture ◽  
Ultrasonic Grinding ◽  
The Impact ◽  
Ultrasonic Vibration Assisted Grinding

In this paper, the characteristic of grinding force in two-dimensional ultrasonic vibration assisted grinding nano-ceramic was studied by experiment based on indentation fracture mechanics, and mathematical model of grinding force was established. The study shows that grinding force mainly result from the impact of the grains on the workpiece in ultrasonic grinding, and the pulse power is much larger than normal grinding force. The ultrasonic vibration frequency is so high and the contact time of grains with the workpiece is so short that the pulse force will be balanced by reaction force from workpiece. In grinding workpiece was loaded by the periodical stress field, which accelerates the fatigue fracture.

Numerical study of electric field effects on the deformation of two-dimensional liquid drops in simple shear flow at arbitrary Reynolds number

2009 ◽  
Vol 626 ◽  
pp. 367-393 ◽  
Author(s):  
STEFAN MÄHLMANN ◽  
DEMETRIOS T. PAPAGEORGIOU
Keyword(s):  
Steady State ◽  
Shear Flow ◽  
Electric Field ◽  
Electric Fields ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Liquid Drops

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

2009 ◽  
Vol 30 (4) ◽  
pp. 455-462
Author(s):  
Gai-ping Zhao ◽  
Er-yun Chen ◽  
Jie Wu ◽  
Shi-xiong Xu ◽  
M. W. Collins ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Discrete Mathematical Model
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