Computations of Physical Transport and Regeneration of Phosphorus in Lake Erie, Fall 1970

1976 ◽  
Vol 33 (3) ◽  
pp. 550-563 ◽  
Author(s):  
D. C. L. Lam ◽  
J.-M. Jaquet
Keyword(s):  
Total Phosphorus ◽  
Lake Erie ◽  
Mesh Size ◽  
Time Dependent ◽  
Time Step ◽  
Satisfactory Model ◽  
Mean Grain Size ◽  
Wave Orbital Velocity ◽  
High Winds ◽  
Good Agreement

A one-layer, two-dimensional computer model for the time-dependent, lakewide advective and diffusive transports as well as physical regeneration of total phosphorus in Lake Erie has been developed. It has 60 × 16 square grid cells of 6.67-km mesh size and uses a time step of 12 h. The model has been verified and found to be in reasonably good agreement with the Canada Centre for Inland Waters (CCIW) monitor cruise data for October, November, and December during which period there were high winds with high phosphorus concentrations being observed. Computed, daily averaged currents from a hydrodynamic model developed at CCIW are used for the transport terms and actual data for the lake boundary conditions. The physical regeneration is attributed to wave motions induced by wind. A formula is proposed which expresses the regenerated amount of total phosphorus in terms of wave orbital velocity and sediment mean grain size. A discussion is presented on the choice of the settling rate and the regeneration coefficient which produce satisfactory model results.

scholarly journals Development of a Time-Dependent Friction Model for Frictional Aging at the Nanoscale

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Seung Yub Baek ◽  
Kyungmok Kim
Keyword(s):  
Fracture Energy ◽  
Cohesive Zone ◽  
Hold Time ◽  
Mesh Size ◽  
Friction Model ◽  
Time Dependent ◽  
Element Simulation ◽  
Silica Materials ◽  
Simulation Results ◽  
Good Agreement

A model for describing frictional aging of silica is developed at the nanoscale. A cohesive zone is applied to the contact surface between self-mated silica materials. Strengthening of interfacial bonding during frictional aging is reproduced by increasing fracture energy of a cohesive zone. Fracture energy is expressed as a function of hold time between self-mated silica materials. Implicit finite element simulation is employed, and simulation results are compared with experimental ones found in the literature. Calculated friction evolutions with various hold times are found to be in good agreement with experimental ones. Dependence of mesh size and cohesive thickness is identified for obtaining accurate simulation result.

scholarly journals A NEW DOMAIN DECOMPOSITION PARALLEL ALGORITHM FOR CONVECTION–DIFFUSION PROBLEM

2014 ◽  
Vol 19 (4) ◽  
pp. 589-605 ◽  
Author(s):  
Jiansong Zhang ◽  
Danping Yang
Keyword(s):  
Approximate Solution ◽  
Domain Decomposition ◽  
Parallel Algorithm ◽  
Mesh Size ◽  
Diffusion Problem ◽  
Time Dependent ◽  
Time Step ◽  
Convection Diffusion ◽  
Overlapping Domain Decomposition ◽  
Iteration Number

Basing on overlapping domain decomposition, we construct a new parallel algorithm combined the method of subspace correction with least-squares procedure for solving time-dependent convection–diffusion problem. This algorithm is fully parallel. We analyze the convergence of approximate solution, and study the dependence of the convergent rate on the spacial mesh size, time increment, iteration number and sub-domains overlapping degree. Both theoretical analysis and numerical results suggest that only one or two iterations are needed to reach to given accuracy at each time step.

scholarly journals A high-fidelity realization of the Euclid code comparison N-body simulation with Abacus

2019 ◽  
Vol 485 (3) ◽  
pp. 3370-3377 ◽  
Author(s):  
Lehman H Garrison ◽  
Daniel J Eisenstein ◽  
Philip A Pinto
Keyword(s):  
Power Spectrum ◽  
High Performance ◽  
High Fidelity ◽  
Step Size ◽  
Time Step ◽  
Code Comparison ◽  
Force Accuracy ◽  
Integration Errors ◽  
Better Than ◽  
Good Agreement

Abstract We present a high-fidelity realization of the cosmological N-body simulation from the Schneider et al. code comparison project. The simulation was performed with our AbacusN-body code, which offers high-force accuracy, high performance, and minimal particle integration errors. The simulation consists of 20483 particles in a $500\ h^{-1}\, \mathrm{Mpc}$ box for a particle mass of $1.2\times 10^9\ h^{-1}\, \mathrm{M}_\odot$ with $10\ h^{-1}\, \mathrm{kpc}$ spline softening. Abacus executed 1052 global time-steps to z = 0 in 107 h on one dual-Xeon, dual-GPU node, for a mean rate of 23 million particles per second per step. We find Abacus is in good agreement with Ramses and Pkdgrav3 and less so with Gadget3. We validate our choice of time-step by halving the step size and find sub-percent differences in the power spectrum and 2PCF at nearly all measured scales, with ${\lt }0.3{{\ \rm per\ cent}}$ errors at $k\lt 10\ \mathrm{Mpc}^{-1}\, h$. On large scales, Abacus reproduces linear theory better than 0.01 per cent. Simulation snapshots are available at http://nbody.rc.fas.harvard.edu/public/S2016.

Numerical Simulation of Ship Collision and Validations With Experimental Results

2021 ◽  
Author(s):  
Xiangbiao Wang ◽  
Chun Bao Li ◽  
Ling Zhu
Keyword(s):  
Numerical Simulation ◽  
Model Test ◽  
Structural Damage ◽  
Added Mass ◽  
Ship Motion ◽  
Time Dependent ◽  
Structural Deformation ◽  
Structure Interaction ◽  
Ship Collision ◽  
Good Agreement

Abstract Ship collision accidents occur from time to time in recent years, and this would cause serious consequences such as casualties, environmental pollution, loss of cargo on board, damage to the ship and its equipment, etc. Therefore, it is of great significance to study the response of ship motion and the mechanism of structural damage during the collision. In this paper, model experiments and numerical simulation are used to study the ship-ship collision. Firstly, the Coupled Eulerian-Lagrangian (CEL) was used to simulate the fluid-structure interaction for predicting structural deformation and ship motion during the normal ship-ship collision. Meanwhile, a series of model tests were carried out to validate the numerical results. The validation presented that the CEL simulation was in good agreement with the model test. However, the CEL simulation could not present the characteristics the time-dependent added mass.

An Accelerated Retarded Potential Method for Time Dependent Acoustic Wave Scattering

1995 ◽  
Author(s):  
Toufic S. Abboud ◽  
Joseph M. Gharib ◽  
Jean Claude Nédélec ◽  
Toni G. Sayah
Keyword(s):  
Finite Element Method ◽  
Integral Equation ◽  
Wave Scattering ◽  
Numerical Approximation ◽  
Mesh Size ◽  
Integral Equation Method ◽  
Potential Method ◽  
Boundary Integral ◽  
Time Dependent ◽  
Acoustic Wave Scattering

Abstract We are interested in the numerical approximation of the problem of the scattering of a transient acoustic plane wave by a bounded obstacle in IR2 or IR3, using the boundary integral equation method. In the frequency domain it has been recently developed a boundary finite element method where the mesh size is like O(λ1/3) instead of O(λ) (λ is the wavelength) and where the obstacle is convex. This paper presents the implementation of the idea on the retarted potential representation.

scholarly journals Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

2013 ◽  
Vol 14 (5) ◽  
pp. 1228-1251 ◽  
Author(s):  
Yan Li ◽  
I-Liang Chern ◽  
Joung-Dong Kim ◽  
Xiaolin Li
Keyword(s):  
Upper Bound ◽  
Mesh Size ◽  
Front Tracking ◽  
Time Step ◽  
Mass System ◽  
Ode System ◽  
Spring System ◽  
Fabric Surface ◽  
Mass Spring ◽  
Eigen Frequency

AbstractWe use front tracking data structures and functions to model the dynamic evolution of fabric surface. We represent the fabric surface by a triangulated mesh with preset equilibrium side length. The stretching and wrinkling of the surface are modeled by the mass-spring system. The external driving force is added to the fabric motion through the “Impulse method” which computes the velocity of the point mass by superposition of momentum. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

scholarly journals Estimation of Optimal Time Step and Compare with of ODE Solver of MATLAB Package of RLC Circuit using Numerical Methods

1970 ◽  
Vol 7 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Sheikh Md Rabiul Islam
Keyword(s):  
Mesh Size ◽  
Paper Analysis ◽  
Optimal Time ◽  
Time Step ◽  
Minimum Error ◽  
Optimal Output ◽  
Runge Kutta Method ◽  
Rlc Circuit ◽  
Matlab Package ◽  
Theoretical Results

In this paper analysis of a RLC circuit model that has been described optimal time step and minimize of error using numerical method. The goal is to reach the optimal time response due to the input for which optimal output response reaches a minimum error and also compared with ODE solver of MATLAB packages for the different cell (mesh) size of the RLC model. Table is constructed of the model to evaluate optimal time step and also CPU time into the simulation using MATLAB 7.6.0(R2008a).The values of register, capacitor and inductor as well as electromagnetic force are obtained through the mathematical relations of the model. The general analysis of the RLC circuit due to the optimal time step and minimum error is developed after several analysis and operations. The theoretical results show effectiveness of optimized of the model. Keywords: Optimal time step; MATLAB; Trapezoidal; Implicit Euler; Runge-Kutta method; RLC circuit. DOI: http://dx.doi.org/10.3329/diujst.v7i1.9650   Daffodil International University Journal of Science and Technology Vol.7(1) 2012 67-73

Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers

1998 ◽  
Vol 360 ◽  
pp. 249-271 ◽  
Author(s):  
H. DÜTSCH ◽  
F. DURST ◽  
S. BECKER ◽  
H. LIENHART
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Time Step ◽  
Time Resolved ◽  
Reynolds Number Flow ◽  
Line Force ◽  
Number Flow ◽  
Weakly Stable ◽  
Fluid Behaviour ◽  
Good Agreement

Time-averaged LDA measurements and time-resolved numerical flow predictions were performed to investigate the laminar flow induced by the harmonic in-line oscillation of a circular cylinder in water at rest. The key parameters, Reynolds number Re and Keulegan–Carpenter number KC, were varied to study three parameter combinations in detail. Good agreement was observed for Re=100 and KC=5 between measurements and predictions comparing phase-averaged velocity vectors. For Re=200 and KC=10 weakly stable and non-periodic flow patterns occurred, which made repeatable time-averaged measurements impossible. Nevertheless, the experimentally visualized vortex dynamics was reproduced by the two-dimensional computations. For the third combination, Re=210 and KC=6, which refers to a totally different flow regime, the computations again resulted in the correct fluid behaviour. Applying the widely used model of Morison et al. (1950) to the computed in-line force history, the drag and the added-mass coefficients were calculated and compared for different grid levels and time steps. Using these to reproduce the force functions revealed deviations from those originally computed as already noted in previous studies. They were found to be much higher than the deviations for the coarsest computational grid or the largest time step. The comparison of several in-line force coefficients with results obtained experimentally by Kühtz (1996) for β=35 confirmed that force predictions could also be reliably obtained by the computations.

scholarly journals Dynamical analysis of a reduced model for the North Atlantic Oscillation

2021 ◽  
Author(s):  
Courtney Quinn ◽  
Dylan Harries ◽  
Terence J. O’Kane
Keyword(s):  
North Atlantic Oscillation ◽  
North Atlantic ◽  
Growth Rates ◽  
Time Dependent ◽  
Unstable State ◽  
Time Step ◽  
Atlantic Sector ◽  
The North ◽  
The North Atlantic ◽  
The North Atlantic Oscillation

AbstractThe dynamics of the North Atlantic Oscillation (NAO) are analyzed through a data-driven model obtained from atmospheric reanalysis data. We apply a regularized vector autoregressive clustering technique to identify recurrent and persistent states of atmospheric circulation patterns in the North Atlantic sector (110°W-0°E, 20°N-90°N). In order to analyze the dynamics associated with the resulting cluster-based models, we define a time-dependent linear delayed map with a switching sequence set a priori by the cluster affiliations at each time step. Using a method for computing the covariant Lyapunov vectors (CLVs) over various time windows, we produce sets of mixed singular vectors (for short windows) and approximate the asymptotic CLVs (for longer windows). The growth rates and alignment of the resulting time-dependent vectors are then analyzed. We find that the window chosen to compute the vectors acts as a filter on the dynamics. For short windows, the alignment and changes in growth rates are indicative of individual transitions between persistent states. For long windows, we observe an emergent annual signal manifest in the alignment of the CLVs characteristic of the observed seasonality in the NAO index. Analysis of the average finite-time dimension reveals the NAO− as the most unstable state relative to the NAO+, with persistent AR states largely stable. Our results agree with other recent theoretical and empirical studies that have shown blocking events to have less predictability than periods of enhanced zonal flow.

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