A note on the performance of the multiply-upstream semi-Lagrangian advection schemes for one-dimensional nonlinear momentum conservation equation

1995 ◽  
Vol 55 (1-2) ◽  
pp. 1-16 ◽  
Author(s):  
Z. I. Janjić
Keyword(s):  
Momentum Conservation ◽  
Conservation Equation ◽  
One Dimensional ◽  
Advection Schemes ◽  
Lagrangian Advection ◽  
Momentum Conservation Equation

Effects of Non-Linearity of the Momentum Conservation Equation During Electrokinetic Transport in Nano and Microchannels

2010 ◽  
Author(s):  
Subir Bhattacharjee ◽  
Noor Al Quddus
Keyword(s):  
Porous Media ◽  
Electric Fields ◽  
Stokes Equations ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Small Scale ◽  
Electrokinetic Transport ◽  
Electrokinetic Flow ◽  
Non Linear ◽  
Momentum Conservation Equation

Electrokinetic transport phenomena, such as electroosmosis, streaming potential, electrophoresis, and sedimentation potential, are central to many micro- and nano-channel flows. During continuum modeling of such phenomena, incorporation of the electrical body force term can make the fluid momentum conservation equation highly non-linear. This non-linearity is often ignored in small-scale electrokinetic flow modeling because of our implicit reliance on the linearity of the Stokes equations for low Reynolds number flows. In this paper, ramifications of this non-linear Stokes equation in electrokinetic flows will be described with examples of our recent studies on pressure driven flows through porous media for electrokinetic power generation, electroosmotic flow of charged entities in nanochannels, and flow of DNA through self-assembled porous media under pulsed electric fields.

The coordinated motion planning of a dual-arm space robot for target capturing

Robotica ◽  
2011 ◽  
Vol 30 (5) ◽  
pp. 755-771 ◽  
Author(s):  
Wenfu Xu ◽  
Yu Liu ◽  
Yangsheng Xu
Keyword(s):  
Center Of Mass ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Space Robot ◽  
Coordinated Motion ◽  
First Case ◽  
Solution Equation ◽  
Target Capturing ◽  
Dual Arm ◽  
Momentum Conservation Equation

SUMMARYIn this paper, autonomous motion control approaches to generate the coordinated motion of a dual-arm space robot for target capturing are presented. Two typical cases are studied: (a) The coordinated dual-arm capturing of a moving target when the base is free-floating; (b) one arm is used for target capturing, and the other for keeping the base fixed inertially. Instead of solving all the variables in a unified differential equation, the solution equation of the first case is simplified into two sub-equations and practical methods are used to solve them. Therefore, the computation loads are largely reduced, and feasible trajectories can be determined. For the second case, we propose to deal with the linear and angular momentums of the system separately. The linear momentum conservation equation is used to design the configuration and the mounted pose of a balance arm to keep the inertial position of the base's center of mass, and the angular momentum conservation equation is used to estimate the desired momentum generated by the reaction wheels for maintaining the inertial attitude of the base. Finally, two typical tasks are simulated. Simulation results verify the corresponding approaches.

Bubble Analogy and Stabilization of Core-Annular Flow

2000 ◽  
Vol 123 (2) ◽  
pp. 127-132 ◽  
Author(s):  
Antonio C. Bannwart
Keyword(s):  
Cross Section ◽  
Annular Flow ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Interface Shape ◽  
Laboratory Measurements ◽  
Horizontal Pipe ◽  
The Core ◽  
Oil Water ◽  
Momentum Conservation Equation

A theory for the stabilization of annular liquid-liquid flow (i.e., core-annular flow) in a horizontal pipe is proposed. Based upon the analysis of the momentum conservation equation in the cross section of the flow, including the effects of peripheral flow in the annulus and interfacial tension, an equation is obtained which describes the interface shape. Results for the height-to-width aspect ratio of the core are compared with laboratory measurements done by the author for a heavy oil-water core-annular flow. A criterion for stabilization of this interesting flow pattern is proposed.

scholarly journals Thermodynamically consistent Darcy–Brinkman–Forchheimer framework in matrix acidization

2021 ◽  
Vol 76 ◽  
pp. 8
Author(s):  
Yuanqing Wu ◽  
Jisheng Kou ◽  
Shuyu Sun ◽  
Yu-Shu Wu
Keyword(s):  
Numerical Experiments ◽  
Good Description ◽  
Energy Balance Equation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Scale Model ◽  
Recovery Stage ◽  
Tertiary Recovery ◽  
Matrix Acidization ◽  
Momentum Conservation Equation

Matrix acidization is an important technique used to enhance oil production at the tertiary recovery stage, but its numerical simulation has never been verified. From one of the earliest models, i.e., the two-scale model (Darcy framework), the Darcy–Brinkman–Forchheimer (DBF) framework is developed by adding the Brinkman term and Forchheimer term to the momentum conservation equation. However, in the momentum conservation equation of the DBF framework, porosity is placed outside of the time derivation term, which prevents a good description of the change in porosity. Thus, this work changes the expression so that the modified momentum conservation equation can satisfy Newton’s second law. This modified framework is called the improved DBF framework. Furthermore, based on the improved DBF framework, a thermal DBF framework is given by introducing an energy balance equation to the improved DBF framework. Both of these frameworks are verified by former works through numerical experiments and chemical experiments in labs. Parallelization to the complicated framework codes is also realized, and good scalability can be achieved.

On the Streamwise Development of Density Jumps

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
A. Regev ◽  
S. Hassid
Keyword(s):  
Energy Conservation ◽  
Software Package ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Entrainment Ratio ◽  
Layer Height ◽  
Energy Conservation Equation ◽  
Linear Expression ◽  
Momentum Conservation Equation ◽  
Good Agreement

The analysis of density jumps in two-layer channel flows of miscible fluids controlled by a downstream obstruction, in which one of the layers is infinitely deep and at rest, is extended to consider the dependence of its features on its streamwise dimension. The momentum conservation equation in the entrainment and roller regions, and the energy conservation equation after the jump are corrected to account for friction. The streamwise coordinate is related to the increase in the density layer height through a linear expression derived from CFD calculations. Three regimes are distinguished: (1) for short distances from the origin to the obstruction, only an entrainment region exists; (2) for medium distances, two regions can be distinguished, i.e., the entrainment region, and the roller region, in which no entrainment is assumed; and (3) for long distances, three regions can be distinguished—the entrainment, the roller, and the postjump regions, characterized by approximate energy conservation. It is shown that initially the dimensionless total entrainment ratio increases as the distance to the obstruction increases, until a roller region appears. A further increase in distance to the obstruction does not have a significant effect on the total entrainment, until the appearance of a postjump region, resulting in a gradual decrease in the total entrainment. These results are supported by numerical calculations using the FLUENT CFD software package, which are in good agreement with experimental results.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

scholarly journals INDOOR AIR TEMPERATURE DISTRIBUTION – AN ALTERNATIVE APPROACH TO BUILDING SIMULATION

2003 ◽  
Vol 2 (1) ◽  
Author(s):  
A. T. Franco ◽  
C. O. R. Negrão
Keyword(s):  
Temperature Distribution ◽  
Air Temperature ◽  
Indoor Air ◽  
Linear Equations ◽  
Three Dimensional ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Algebraic Equations ◽  
Conservation Of Energy ◽  
Energy Conservation Equation

The current paper presents a model to predict indoor air temperature distribution. The approach is based on the energy conservation equation which is written for a certain number of finite volumes within the flow domain. The magnitude of the flow is estimated from a scale analysis of the momentum conservation equation. Discretized two or three-dimensional domains provide a set of algebraic equations. The resulting set of non-linear equations is iteratively solved using the line-by-line Thomas Algorithm. As long as the only equation to be solved is the conservation of energy and its coefficients are not strongly dependent on the temperature field, the solution is considerably fast. Therefore, the application of such model to a whole building system is quite reasonable. Two case studies involving buoyancy driven flows were carried out and comparisons with CFD solutions were performed. The results are quite promising for cases involving relatively strong couplings between heat and airflow.

Mathematical Modelling of Thermo-Hydro-Mechanical Behaviour for Concrete under Elevated Temperature

2014 ◽  
Vol 670-671 ◽  
pp. 355-364
Author(s):  
Shao Bo Zhang ◽  
Xiao Chun Wang ◽  
Xin Pu Shen
Keyword(s):  
Elevated Temperature ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Gaseous Mixture ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Energy Conservation Equation

A hydro-thermo-mechanical model was presented for concrete at elevated temperature. Three phases of continuum were adopted in this model: gaseous mixture of water vapor and dry air, liquid water, and solid skeleton of concrete. Mass conservation equations, linear momentum conservation equation, and energy conservation equation were derived on the basis of the macroscopic Navier-Stokes equations for a general continuum, along with assumptions made for the purpose of simplification. Mathematical relationships between selected primary variables and secondary variables were given with existing data from references. Specifications of the constitutive relations were made for the kinetic variables and their conjugate forces.

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