Spatial Localisation, Mass Conservation, and Boundaries

2012 ◽  
pp. 44-70
Author(s):  
A. Ian Murdoch
Keyword(s):  
Mass Conservation ◽  
Spatial Localisation

Mixed Layer Models and Their Application to Water Quality Problems

1994 ◽  
Vol 29 (2-3) ◽  
pp. 221-232
Author(s):  
M.J. McCormick
Keyword(s):  
Water Quality ◽  
Mixed Layer ◽  
Thermal Structure ◽  
Mass Conservation ◽  
Eddy Diffusion ◽  
Rate Of Change ◽  
Surface Mixed Layer ◽  
Storm Events ◽  
Quality Model ◽  
Mixing Processes

Abstract Four one-dimensional models which have been used to characterize surface mixed layer (ML) processes and the thermal structure are described. Although most any model can be calibrated to mimic surface water temperatures, it does not imply that the corresponding mixing processes are well described. Eddy diffusion or "K" models can exhibit this problem. If a ML model is to be useful for water quality applications, then it must be able to resolve storm events and, therefore, be able to simulate the ML depth, h, and its time rate of change, dh/dt. A general water quality model is derived from mass conservation principles to demonstrate how ML models can be used in a physically meaningful way to address water quality issues.

Transport of Microorganisms in the Underground – Processes, Experiments and Simulation Models

1991 ◽  
Vol 24 (2) ◽  
pp. 309-314 ◽  
Author(s):  
G. Teutsch ◽  
K. Herbold-Paschke ◽  
D. Tougianidou ◽  
T. Hahn ◽  
K. Botzenhart
Keyword(s):  
Simulation Models ◽  
Mass Conservation ◽  
Breakthrough Curves ◽  
Conservation Equation ◽  
Retardation Factor ◽  
Natural Systems ◽  
Laboratory Setup ◽  
Preliminary Model ◽  
Sand And Gravel ◽  
Mass Conservation Equation

In this paper the major processes governing the persistence and underground transport of viruses and bacteria are reviewed in respect to their importance under naturally occurring conditions. In general, the simulation of the governing processes is based on the macroscopic mass-conservation equation with the addition of some filter and/or retardation factor and a decay coefficient, representing the natural “die-off” of the microorganisms. More advanced concepts try to incorporate growth and decay coefficients together with deposition and declogging factors. At present, none of the reported concepts has been seriously validated. Due to the complexity of natural systems and the pathogenic properties of some of the microorganisms, experiments under controlled laboratory conditions are required. A laboratory setup is presented in which a great variety of natural conditions can be simulated. This comprises a set of 1 metre columns and an 8 metre stainless-steel flume with 24 sampling ports. The columns are easily filled and conditioned and therefore used to study the effects of different soil-microorganism combinations under various environmental conditions. In the artificial flume natural underground conditions are simulated using sand and gravel aquifer material from the river Neckar alluvium. A first set of results from the laboratory experiments is presented together with preliminary model simulations. The large variety of observed breakthrough curves and recovery for the bacteria and viruses under investigation demonstrates the great uncertainty encountered in microbiological risk assessment.

scholarly journals A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1639
Author(s):  
Abdelkrim Aharmouch ◽  
Brahim Amaziane ◽  
Mustapha El Ossmani ◽  
Khadija Talali
Keyword(s):  
Finite Volume ◽  
Coastal Aquifers ◽  
Nonlinear Partial Differential Equations ◽  
Time Integration ◽  
Mass Conservation ◽  
Coupled System ◽  
Finite Volume Scheme ◽  
Time Step ◽  
Volume Scheme ◽  
Fully Implicit

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu X . The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method.

Influence of new surface micro-structures on the performance behaviours of fluid film tilting pad thrust bearings

2021 ◽  
pp. 095440622110309
Author(s):  
JC Atwal ◽  
RK Pandey
Keyword(s):  
Mass Conservation ◽  
Performance Parameters ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Thrust Bearings ◽  
Lubrication Equation ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Newton Raphson ◽  
Micro Structures

Performance parameters such as power loss, minimum film thickness, and maximum oil temperature of the sector-shaped tilting pad thrust bearings employing the new micro-structural geometries on pad surfaces have been investigated. The lubrication equation incorporating the mass-conservation issue is discretized using the finite element method and the solution of resulting algebraic equations is obtained employing a Newton-Schur method. The pad equilibrium in the analysis is established using the Newton-Raphson and Braydon methods. The influence of attributes of micro-structures such as depth, circumferential and radial positioning extents have been explored on the performance behaviours. It is found that with the new micro-structured pad surfaces, the performance parameters significantly improved in comparison to conventional plain and conventional rectangular pocketed pads.

scholarly journals A Mass- and Energy-Conserving Numerical Model for a Fractional Gross–Pitaevskii System in Multiple Dimensions

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1765
Author(s):  
Adán J. Serna-Reyes ◽  
Jorge E. Macías-Díaz
Keyword(s):  
Initial Conditions ◽  
Type System ◽  
Continuous System ◽  
Mass Conservation ◽  
Continuous Model ◽  
Manuscript Studies ◽  
Multiple Dimensions ◽  
Negative Constant ◽  
Energy Conserving ◽  
Finite Difference Discretization

This manuscript studies a double fractional extended p-dimensional coupled Gross–Pitaevskii-type system. This system consists of two parabolic partial differential equations with equal interaction constants, coupling terms, and spatial derivatives of the Riesz type. Associated with the mathematical model, there are energy and non-negative mass functions which are conserved throughout time. Motivated by this fact, we propose a finite-difference discretization of the double fractional Gross–Pitaevskii system which inherits the energy and mass conservation properties. As the continuous model, the mass is a non-negative constant and the solutions are bounded under suitable numerical parameter assumptions. We prove rigorously the existence of solutions for any set of initial conditions. As in the continuous system, the discretization has a discrete Hamiltonian associated. The method is implicit, multi-consistent, stable and quadratically convergent. Finally, we implemented the scheme computationally to confirm the validity of the mass and energy conservation properties, obtaining satisfactory results.

Simulation of the wind fields over complex terrain with coupling of CFD and WRF

2021 ◽  
pp. 1-12
Author(s):  
Xiaoyu Luo ◽  
Yiwen Cao
Keyword(s):  
Wind Speed ◽  
Wind Field ◽  
Complex Terrain ◽  
Civil Engineering ◽  
Meteorological Data ◽  
Mass Conservation ◽  
Coupling Method ◽  
Wind Fields ◽  
Civil Structures ◽  
Civil Engineers

In the field of civil engineering, the meteorological data available usually do not have the detailed information of the wind near a certain site. However, the detailed information of the wind field during typhoon is important for the wind-resistant design of civil structures. Furthermore, the resolution of the meteorological data available by the civil engineers is too coarse to be applicable. Therefore it is meaningful to obtain the detailed information of the wind fields based on the meteorological data provided by the meteorological department. Therefore, in the present study, a one-way coupling method between WRF and CFD is adopted and a method to keep the mass conservation during the simulation in CFD is proposed. It is found that using the proposed one-way coupling method, the predicted wind speed is closer to the measurement. And the curvature of the wind streamline during typhoon is successfully reproduced.

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