A Typical RAM Approach: Boussinesq Model Equations

2011 ◽  
pp. 81-94
Author(s):  
Radyadour Kh. Zeytounian
Keyword(s):  
Boussinesq Model ◽  
Model Equations

A fully nonlinear Boussinesq model for surface waves. Part 2. Extension to O(kh)4

2000 ◽  
Vol 405 ◽  
pp. 181-210 ◽  
Author(s):  
MAURÍCIO F. GOBBI ◽  
JAMES T. KIRBY ◽  
GE WEI
Keyword(s):  
Velocity Potential ◽  
Model Performance ◽  
Weighted Average ◽  
Type Model ◽  
Surface Boundary ◽  
Boussinesq Model ◽  
Weakly Nonlinear ◽  
Surface Boundary Condition ◽  
Full Solution ◽  
Model Equations

A Boussinesq-type model is derived which is accurate to O(kh)4 and which retains the full representation of the fluid kinematics in nonlinear surface boundary condition terms, by not assuming weak nonlinearity. The model is derived for a horizontal bottom, and is based explicitly on a fourth-order polynomial representation of the vertical dependence of the velocity potential. In order to achieve a (4,4) Padé representation of the dispersion relationship, a new dependent variable is defined as a weighted average of the velocity potential at two distinct water depths. The representation of internal kinematics is greatly improved over existing O(kh)2 approximations, especially in the intermediate to deep water range. The model equations are first examined for their ability to represent weakly nonlinear wave evolution in intermediate depth. Using a Stokes-like expansion in powers of wave amplitude over water depth, we examine the bound second harmonics in a random sea as well as nonlinear dispersion and stability effects in the nonlinear Schrödinger equation for a narrow-banded sea state. We then examine numerical properties of solitary wave solutions in shallow water, and compare model performance to the full solution of Tanaka (1986) as well as the level 1, 2 and 3 solutions of Shields & Webster (1988).

scholarly journals APPLICATION OF A TVD SOLVER IN A SUITE OF COASTAL ENGINEERING MODELS

2012 ◽  
Vol 1 (33) ◽  
pp. 31 ◽  
Author(s):  
Fengyan Shi ◽  
Gangfeng Ma ◽  
James T. Kirby ◽  
Tian-Jian Tom Hsu
Keyword(s):  
Circulation Model ◽  
Breaking Waves ◽  
Coastal Engineering ◽  
Shock Capturing ◽  
Tvd Scheme ◽  
Boussinesq Model ◽  
Recent Developments ◽  
Engineering Models ◽  
Hydrostatic Model ◽  
Model Equations

This paper describes the recent developments in a suite of coastal engineering models using Godunov-type shock-capturing schemes. The developments include a depth-integrated, wave resolving Boussinesq model, a hydrostatic, wave-averaged circulation model, and a fully 3-D non-hydrostatic model in a surface-following $\sigma$ coordinate formulation. The models implemented with the shock-capturing TVD scheme show robust performances in modeling breaking waves, nearshore circulation and coastal inundation. In this paper, we present model equations in a conservative form, MUSCLE-TVD numerical scheme and model applications. We also point out some problems caused by the TVD scheme in the recent model applications.

Model Equations for Quasi-Twodimensional Pattern Forming Systems

1994 ◽  
Vol 19 (6) ◽  
pp. 721-733 ◽  
Author(s):  
M. Neufeld ◽  
R. Friedrich
Keyword(s):  
Model Equations ◽  
Pattern Forming

Modelling Of Transport And Capture Of Particles In A Porous Medium

2019 ◽  
pp. 56-60
Keyword(s):  
Porous Medium ◽  
Asymptotic Solution ◽  
Retention Mechanism ◽  
Inverse Filtering ◽  
Underground Structures ◽  
Loose Soil ◽  
Monodisperse Suspension ◽  
Homogeneous Porous Medium ◽  
Model Equations ◽  
Pass Through

The study of the transport and capture of particles moving in a fluid flow in a porous medium is an important problem of underground hydromechanics, which occurs when strengthening loose soil and creating watertight partitions for building tunnels and underground structures. A one-dimensional mathematical model of long-term deep filtration of a monodisperse suspension in a homogeneous porous medium with a dimensional particle retention mechanism is considered. It is assumed that the particles freely pass through large pores and get stuck at the inlet of small pores whose diameter is smaller than the particle size. The model takes into account the change in the permeability of the porous medium and the permissible flow through the pores with increasing concentration of retained particles. A new spatial variable obtained by a special coordinate transformation in model equations is small at any time at each point of the porous medium. A global asymptotic solution of the model equations is constructed by the method of series expansion in a small parameter. The asymptotics found is everywhere close to a numerical solution. Global asymptotic solution can be used to solve the inverse filtering problem and when planning laboratory experiments.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

Reduction of Acquisition Time for RIL, SDL, and LADA

2007 ◽  
Author(s):  
Arjan Mels ◽  
Frank Zachariasse
Keyword(s):  
Background Noise ◽  
Signal Strength ◽  
Acquisition Time ◽  
Optimal Conditions ◽  
Signal Collection ◽  
Defect Localization ◽  
Model Equations ◽  
Set Up ◽  
Main Operating ◽  
Quantitative Tool

Abstract Although RIL, SDL and LADA are slightly different, the main operating principle is the same and the theory for defect localization presented in this paper is applicable to all three methods. Throughout this paper the authors refer to LADA, as all experimental results in this paper were obtained with a 1064nm laser on defect free circuits. This paper first defines mathematically what 'signal strength' actually means in LADA and then demonstrates a statistical model of the LADA situation that explains the optimal conditions for signal collection and the parameters involved. The model is tested against experimental data and is also used to optimise the acquisition time. Through this model, equations were derived for the acquisition time needed to discern a LADA response from the background noise. The model offers a quantitative tool to estimate the feasibility of a given LADA measurement and a guide to optimising the required experimental set-up.

PREDICTIVE SIMULATION AND OPTIMIZATION ORIENTED MODELING FOR THE EXTRACTION OF METAL IONS FROM SOLUTIONS INTO A NOVEL BIS-SCHIFF BASE

2019 ◽  
pp. 1-8
Author(s):  
F. S. Nworie ◽  
S. O. Ngele ◽  
J. C. Onah
Keyword(s):  
Metal Ions ◽  
Metal Concentration ◽  
Acid Concentration ◽  
Aqueous Media ◽  
Industrial Effluents ◽  
Ligand Concentration ◽  
Simulation And Optimization ◽  
Chemometric Technique ◽  
Model Equations ◽  
Level Of Significance

Metal ions present in waste samples, industrial effluents, acid mines and other aqueous media constitute a serious challenge in different human activities. Solvent extraction a technique for preconcentration, separation and identification of trace amount of metal ions coupled with multivariate chemometric technique was used for the determination of Fe(II) and Cr(III) from solutions in the presence of bis(salicylidene)ethylenediamine (SALEN). The influence of main extraction variables affecting the extraction efficiency was simultaneously studied and regression model equations illustrating the relationship between variables predicted. The extraction parameters (time of extraction, acid concentration, ligand concentration, temperature and metal concentration) were optimized using experimental designs with the contributions of the various parameters to extraction of the metal ions bound to the complexone evaluated using SPSS19.0 software. The statistically determined simulated models for the parameters were R2 = 0.946, 0.727, 0.793, 0.53, 0.53, 1.000 and F- values of 70.400, 13. 285, 15.348, 4.646 and 2.569×105 respectively for time of extraction, acid concentration, ligand concentration, temperature and metal concentration for Cr (III). For Fe (II), R2 = 0.243, 0.371, 0.519, 0.446, 1.000 and F-values of 0.964, 2.953, 4.310, 3.216 and 2.516×105 for time of extraction, acid concentration, ligand concentration, temperature and metal concentration respectively. The level of significance of the models as predicted was both lower than 5% making it feasible, efficient, reproducible and accurate. This means that metal ions at the conditions stated could be removed from waste samples, industrial effluents, acid mines and other aqueous media with extension in industrial scale application.

Simple explicit model of liquid mean flow in region above axial impeller

1985 ◽  
Vol 50 (11) ◽  
pp. 2396-2410
Author(s):  
Miloslav Hošťálek ◽  
Ivan Fořt
Keyword(s):  
Vortex Flow ◽  
Flow Model ◽  
Quantitative Agreement ◽  
Mean Flow ◽  
Flat Bottom ◽  
Proposed Model ◽  
Minimum Number ◽  
The Mean ◽  
Model Equations ◽  
Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

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