Numerical Modeling of First and Second Order SLD Effects on 3D Geometries

2016 ◽  
Author(s):  
David R. Bilodeau ◽  
Wagdi G. Habashi ◽  
Guido S. Baruzzi ◽  
Marco Fossati
Keyword(s):  
Numerical Modeling ◽  
Second Order

scholarly journals Numerical Modeling of Self-Consistent Dynamics of Shallow and Ground Waters

2021 ◽  
pp. 45-62
Author(s):  
Sergey Khrapov
Keyword(s):  
Numerical Modeling ◽  
Numerical Solution ◽  
Software Package ◽  
Simulation Software ◽  
Second Order ◽  
Order Of Accuracy ◽  
Ground Waters ◽  
Spatially Inhomogeneous ◽  
Tvd Method ◽  
Joint Dynamics

A mathematical and numerical model of the joint dynamics of shallow and ground waters has been built, which takes into account the nonlinear dynamics of a liquid, water absorption from the surface into the ground, filtration currents in the ground, and water seepage from the ground back to the surface. The dynamics of shallow waters is described by the Saint-Venant equations, taking into account the spatially inhomogeneous distributions of the terrain, the coefficients of bottom friction and infiltration, as well as non-stationary sources and flows of water. For the numerical integration of Saint-Venant’s equations, the well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented as a software package “EcoGIS-Simulation” for high-performance computing on supercomputers with graphic coprocessors (GPU). The dynamics of groundwater is described by the nonlinear Bussensk equation, generalized to the case of a spatially inhomogeneous distribution of the parameters of the porous medium and the surface of the aquiclude (the boundary between water-permeable and low-permeable soils). The numerical solution of this equation is built on the basis of a finite-difference scheme of the second order of accuracy, the CUDA algorithm of which is integrated into the calculation module of the “EcoGIS-Simulation” software package and is consistent with the main stages of the CSPH-TVD method. The relative deviation of the numerical solution from the exact solution of the nonlinear Boussinesq equation does not exceed 10−4–10−5. The paper compares the results of numerical modeling of the dynamics of groundwater with analytical solutions of the linearized Bussensk equation used as calculation formulas in the methods for predicting the level of groundwater in the vicinity of water bodies. It is shown that the error of these methods is several percent even for the simplest case of a plane-parallel flow of groundwater with a constant backwater. Based on the results obtained, it was concluded that the proposed method for numerical modeling of the joint dynamics of surface and ground waters can be more versatile and efficient (it has significantly better accuracy and productivity) in comparison with the existing methods for calculating flooding zones, especially for hydrodynamic flows with complex geometry and nonlinear interaction of counter fluid flows arising during seasonal floods during flooding of vast land areas.

Numerical modeling of the mixing flow of second-order fluids with helical ribbon impellers

1999 ◽  
Vol 180 (3-4) ◽  
pp. 267-280 ◽  
Author(s):  
F. Bertrand ◽  
P.A. Tanguy ◽  
E. Brito de la Fuente ◽  
P. Carreau
Keyword(s):  
Numerical Modeling ◽  
Second Order ◽  
Helical Ribbon ◽  
Second Order Fluids

3D cell-centered Lagrangian second order scheme for the numerical modeling of hyperelasticity system

2020 ◽  
Vol 207 ◽  
pp. 104523
Author(s):  
Jérôme Breil ◽  
Gabriel Georges ◽  
Pierre-Henri Maire
Keyword(s):  
Numerical Modeling ◽  
Second Order ◽  
Order Scheme

scholarly journals NUMERICAL MODELING OF KINETICS OF HEAVY METAL SORPTION FROM POLLUTED WATER

2006 ◽  
Vol 14 (1) ◽  
pp. 10-15 ◽  
Author(s):  
Dainius Paliulis
Keyword(s):  
Heavy Metal ◽  
Experimental Investigation ◽  
Numerical Modeling ◽  
Computer Program ◽  
Negative Influence ◽  
Second Order ◽  
Polluted Water ◽  
Sorption Method ◽  
Pseudo Second Order ◽  
Wastewater Pollutants

Water protection is one of the most important priorities of environmental protection. It is necessary to reduce pollution of wastewater in order to reduce pollution of drinking‐water and water pools. One of the most dangerous wastewater pollutants are heavy metals (HM). They have a negative influence on people and aquatic water systems. The paper analyses possibilities of the sorption method application for heavy metal elimination from waste‐water. Experimental investigation of HM sorption from water and numerical modeling usage possibilities for prognosis of the HM sorption kinetic process was carried out as well as experimental study of HM elimination efficiency dependence on sorption time of HM from wastewater, when using sorbents. Two pseudo kinetic models, i e the pseudo first‐ and second‐order models, were developed on the basis of experimental investigation. These models were applied in numerical modeling in the computer program PHOENICS. The results of the computer program PHOENICS and those of experimental investigation describing HM sorption from water were compared. After comparing the two pseudo models, it is determined that the pseudo second‐order model suits better for HM sorpti.

Two-Dimensional Numerical Analyses of Acoustophoresis Phenomena in Microfluidic Channel With Microparticle-Suspended, Viscous, Moving Fluid Medium

2012 ◽  
Author(s):  
Zhongzheng Liu ◽  
Arum Han ◽  
Yong-Joe Kim
Keyword(s):  
Numerical Modeling ◽  
Boundary Conditions ◽  
Second Order ◽  
Viscous Drag ◽  
Acoustic Excitation ◽  
Governing Equations ◽  
Fluid Medium ◽  
Modeling Procedure ◽  
High Efficient ◽  
Moving Fluid

Microfluidic, acoustophoretic separation of cells and microparticles has gained significant interest since it can offer a high-throughput, high-efficient, label-free, continuous separation. However, the designs of state-of-the-art, acoustophoretic separation devices have been mainly derived from a simplistic, one-dimensional (1-D), analytical acoustic model in a “static” fluid medium. Therefore, it is not possible to consider the effects of 2-D or 3-D geometries, “moving” fluid media, and viscous boundary layers that can significantly influence cell/microparticle motions in reality. Here, a 2-D numerical modeling procedure for analyzing the acoustophoretic microparticle motion in microfluidic channels is presented to address the aforementioned deficiencies. Here, the mass and momentum conservation equations and the state equation are decomposed into zeroth-, first-, and second-order governing equations by using a perturbation method. Then, zeroth-, first-, and second-order acoustic pressures are calculated by applying a sixth-order finite difference method to the decomposed governing equations with appropriate boundary conditions under an acoustic excitation. In particular, non-reflective boundary conditions are derived for the first- and second-order governing equations and applied at the ends of a microchannel. The acoustophoretic force calculated by integrating the acoustic pressure over the surface of a rigid microparticle along with viscous drag force is then applied to the Newton’s equation of motion to analyze the acoustophoretic motion of the microparticle. By comparing numerical and 1-D analytical microparticle motions, the proposed numerical modeling procedure is validated for a 1-D plane-wave-like excitation case. It is also shown that numerically-predicted microparticle behavior is quite different from that of the 1-D analytical model for a 2-D acoustic excitation case in a realistic microchannel. Additionally, the effects of the microparticle’s size and density on its acoustophoretic motions are studied.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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