scholarly journals Hydroelastic interaction of nonlinear waves with floating sheets

2021 ◽  
Author(s):  
Vasily Kostikov ◽  
Masoud Hayatdavoodi ◽  
R. Cengiz Ertekin
Keyword(s):  
Wave Field ◽  
Nonlinear Waves ◽  
Wave Reflection ◽  
Numerical Solutions ◽  
Beam Theory ◽  
Wave Structure ◽  
Elastic Plates ◽  
Wide Range ◽  
Local Wave ◽  
Elastic Surfaces

AbstractHydroelastic responses of floating elastic surfaces to incident nonlinear waves of solitary and cnoidal type are studied. There are N number of the deformable surfaces, and these are represented by thin elastic plates of variable properties and different sizes and rigidity. The coupled motion of the elastic surfaces and the fluid are solved simultaneously within the framework of linear beam theory for the structures and the nonlinear Level I Green–Naghdi theory for the fluid. The water surface elevation, deformations of the elastic surfaces, velocity and pressure fields, wave reflection and transmission coefficients are calculated and presented. Results of the model are compared with existing laboratory measurements and other numerical solutions. In the absence of any restriction on the nonlinearity of the wave field, number of surfaces, their sizes and rigidities, a wide range of wave–structure conditions are considered. It is found that wave reflection from an elastic surface changes significantly with the rigidity, and the highest reflection is observed when the plate is rigid (not elastic). It is also found that due to the wave–structure interaction, local wave fields with different length and celerity are formed under the plates. In the case of multiple floating surfaces, it is observed that the spacing between plates has more significant effect on the wave field than their lengths. Also, the presence of relatively smaller floating plates upwave modifies remarkably the deformation and response of the downwave floating surface.

The Interaction of Nonlinear Waves With the Submerged Caissons of a Gravity Based Structure

2008 ◽  
Author(s):  
Marios Christou ◽  
Jannicke S. Roos ◽  
Chris Swan ◽  
Ove T. Gudmestad
Keyword(s):  
Wave Field ◽  
Incident Wave ◽  
Nonlinear Waves ◽  
Wave Structure ◽  
Boundary Integral ◽  
Numerical Predictions ◽  
Water Region ◽  
Geometric Discontinuities ◽  
The Waves ◽  
Wave Structure Interaction

This paper concerns the numerical description of nonlinear waves propagating over the storage caissons of a gravity based structure. This process produces a steepening of the incident wave-field, which occurs when the waves propagate into the shallower water region above the storage caissons, resulting in the focussing of wave energy. A fully nonlinear Multiple-flux Boundary Element Method (MF-BEM) is applied to simulate this effect. The MF-BEM differs from traditional boundary integral approaches in two important respects: first, a multiple-flux approach is employed to overcome the problem of geometric discontinuities; and, second, no filtering, smoothing, re-gridding or redistribution of the nodes is performed at any stage during the simulations. These two aspects are believed to play an important role in accurately predicting the steepening of the incident wave-field. The numerical predictions are compared to new laboratory observations that examine the extent of this wave-structure interaction and, particularly, the steepening of the incident wave-field.

scholarly journals Nematic Dispersive Shock Waves from Nonlocal to Local

2021 ◽  
Vol 11 (11) ◽  
pp. 4736
Author(s):  
Saleh Baqer ◽  
Dimitrios J. Frantzeskakis ◽  
Theodoros P. Horikis ◽  
Côme Houdeville ◽  
Timothy R. Marchant ◽  
...  
Keyword(s):  
Shock Wave ◽  
Liquid Crystals ◽  
Shock Waves ◽  
Numerical Solutions ◽  
Wave Structure ◽  
Beam Power ◽  
Input Beam ◽  
Shock Wave Structure ◽  
Wave Solutions ◽  
Modulation Theory

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

Wave-Vessel Interactions in Beam Seas

2009 ◽  
Author(s):  
Eirini Spentza ◽  
Chris Swan
Keyword(s):  
Wave Field ◽  
Incident Wave ◽  
Laboratory Data ◽  
Wave Structure ◽  
Wave Pattern ◽  
Scaled Model ◽  
Beam Seas ◽  
Wave Basin ◽  
Wave Slamming ◽  
Speed Of Propagation

This paper concerns the nonlinear interaction of waves with a floating vessel. A detailed experimental study has been undertaken in a 3-D wave basin, using a scaled model tanker subject to a variety of incident wave conditions. The vessel, which is free to move in heave, pitch and roll, has a draft of 14m (at full-scale) and is subject to a range of incident wave periods propagating at right angles to the side shell of the vessel. Measurements undertaken with and without the vessel in place allow the diffracted-radiated wave field to be identified. The laboratory data indicate that the diffracted-radiated wave pattern varies significantly with the incident wave period. Detailed analysis of the experimental results has identified a hitherto unexpected second-order freely propagating wave harmonic generated due to the presence of the vessel. Given its frequency content and its relatively slow speed of propagation, this harmonic leads to a significant steepening of the wave field around the vessel and therefore has an important role to play in terms of the occurrence of wave slamming. Physical insights are provided concerning the latter and the practical implications of the overall wave-structure interactions are considered.

scholarly journals Derivation of Global Parametric Performance of Mixed Flow Hydraulic Turbine Using CFD

1970 ◽  
Vol 7 ◽  
pp. 60-64 ◽  
Author(s):  
Ruchi Khare ◽  
Vishnu Prasad Prasad ◽  
Sushil Kumar
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Numerical Solutions ◽  
Guide Vane ◽  
Hydraulic Turbine ◽  
Francis Turbine ◽  
Mixed Flow ◽  
Flow Equations ◽  
Laboratory Setup ◽  
Wide Range

The testing of physical turbine models is costly, time consuming and subject to limitations of laboratory setup to meet International Electro technical Commission (IEC) standards. Computational fluid dynamics (CFD) has emerged as a powerful tool for funding numerical solutions of wide range of flow equations whose analytical solutions are not feasible. CFD also minimizes the requirement of model testing. The present work deals with simulation of 3D flow in mixed flow (Francis) turbine passage; i.e., stay vane, guide vane, runner and draft tube using ANSYS CFX 10 software for study of flow pattern within turbine space and computation of various losses and efficiency at different operating regimes. The computed values and variation of performance parameters are found to bear close comparison with experimental results.Key words: Hydraulic turbine; Performance; Computational fluid dynamics; Efficiency; LossesDOI: 10.3126/hn.v7i0.4239Hydro Nepal Journal of Water, Energy and EnvironmentVol. 7, July, 2010Page: 60-64Uploaded date: 31 January, 2011

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

An Approximate Method for Transient Radial Flow

1962 ◽  
Vol 2 (03) ◽  
pp. 225-256 ◽  
Author(s):  
G. Rowan ◽  
M.W. Clegg
Keyword(s):  
Infinite Series ◽  
Analytical Solutions ◽  
Radial Flow ◽  
Numerical Solutions ◽  
Basic Theory ◽  
Variable Pressure ◽  
Flow Problems ◽  
Disturbed Zone ◽  
Approximate Analytical Solutions ◽  
Wide Range

Abstract The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including; gravity drainage of depletion-type reservoirs; multiple well systems; well interference. Introduction A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages - the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov, whopostulated a disturbed zone in the reservoir, the radius of which increases with time, andreplaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following:That the flow is irrotational.That the formation is of constant thickness.Darcy's Law is valid.The formation is saturated with a single homogeneous fluid. SPEJ P. 225^

NUMERICAL SOLUTIONS OF SMOLUCHOWSKI'S EQUATIONS FOR THE COAGULATION OF UNCHARGED AEROSOLS

1965 ◽  
Vol 43 (8) ◽  
pp. 2312-2318 ◽  
Author(s):  
J. M. Beeckmans
Keyword(s):  
Particle Size ◽  
Numerical Solutions ◽  
Coagulation Factor ◽  
Dispersion Parameter ◽  
Particle Size Range ◽  
Mean Particle Size ◽  
A Value ◽  
Wide Range ◽  
Differential Sedimentation ◽  
Smoluchowski’S Equation

Smoluchowski's equations for the coagulation of uncharged aerosol particles were programmed for solution by electronic computer. Terms representing differential sedimentation, turbulence, and mean aggregate density in solid aerosols were included. The effect of heterogeneity in the particle-size distribution of the aerosols on their rate of coagulation was illustrated by means of a slip-corrected coagulation factor Fc, which assumes a value of unity in all non-turbulent homogeneous aerosols. Curves of Fc vs. σg, the geometrical standard deviation, were calculated for aerosols of various mean particle-size. The effects due to turbulence, and to differential sedimentation, were illustrated in a similar manner. It was also found that the process of coagulation gives rise to a degree of dispersion which is independent of the original dispersion parameter, and depends only slightly on the mean particle-size of the aerosol over a wide range of particle-sizes. In the particle-size range in which differential sedimentation is inappreciable, the relatively constant value of the dispersion parameter implies that heterogeneous aerosols must obey the simplified integrated form of Smoluchowski's equation, which is applicable to homogeneous aerosols. The coagulation constant exceeds that predicted by the simple theory by about 10% for liquid aerosols of 0.1 μ or less.

Application of minimal mathematical models for the dynamics of the signaling pathway of the p53 - miRNA to the analysis of laboratory data

2021 ◽  
pp. 4-49
Author(s):  
Софья Дмитриевна Сенотрусова ◽  
Ольга Фалалеевна Воропаева ◽  
Юрий Иванович Шокин
Keyword(s):  
Mathematical Models ◽  
Signaling Pathway ◽  
Numerical Solutions ◽  
Laboratory Data ◽  
Minimal Models ◽  
Basic Model ◽  
P53 Signaling ◽  
Wide Range ◽  
P53 Signaling Pathway

Работа посвящена практическому использованию минимальных математических моделей динамики сигнального пути p53 для описания достаточно широкого круга лабораторных экспериментов, в которых взаимодействие p53 и белковингибиторов p53 опосредуется микроРНК, образующими с p53 петлю положительной обратной связи. Представлены базовая модель, разработанные на ее основе новые минимальные модели, алгоритм численного решения прямых и обратных коэффициентных задач и результаты сопоставления полученных численных решений с экспериментальными данными о динамике уровней белков p53, p21, Bax, белков-ингибиторов Mdm2, Wip1, Sirt1 и различных микроРНК (miR-16, miR-34a, miR-192, miR-194, miR-215) в условиях стрессовых воздействий. С привлечением полученных математических моделей исследованы базовые механизмы функционирования сигнального пути p53 в условиях, приближенных к условиям конкретных лабораторных экспериментов in vitro и in vivo. Продемонстрированы синергический эффект гиперактивации сигнального пути p53, в котором задействованы микроРНК, и механизмы бимодального переключения. Показана ключевая роль p53-зависимых микроРНК в реализации некоторых гипотетических терапевтических стратегий, связанных с управлением механизмом активации апоптоза клеток. В рамках принятой базовой модели даны оценки вероятности рассогласования в диагностике дегенеративных заболеваний, основанной на анализе уровня p53зависимых микроРНК и p53, при слабой и умеренной дерегуляции микроРНК. This study addresses the practical use of minimal mathematical models of the dynamics of a hypothetical system of the p53 signaling pathway to describe a fairly wide range of laboratory experiments. In such system, the interaction of p53 and p53 inhibitor proteins is mediated by microRNAs that form a positive feedback loop with p53. A basic model, new minimal models developed on its basis, an algorithm for the numerical solution of direct and inverse coefficient problems, and the results of comparing the obtained numerical solutions with experimental data on the dynamics of the levels of p53, p21, Bax proteins, inhibitor proteins Mdm2, Wip1, Sirt1, and various microRNAs (miR-16, miR-34a, miR-192, miR-194, miR-215) under stress conditions are presented. In numerical experiments, the main mechanisms of the p53 signaling pathway were investigated. A synergistic effect of hyperactivation of the p53 signaling pathway and bimodal switching mechanisms has been demonstrated. We show the key role of p53-dependent microRNAs in the implementation of some hypothetical therapeutic strategies associated with the control mechanism for activation of cells apoptosis. Within the framework of the accepted basic model, we estimated the probability of mismatch in the diagnosis of the patient’s status. The status is based on the analysis of the level of p53-dependent microRNAs and p53, with weak and moderate deregulation of microRNAs.

Wave Reflection/Transmission Analysis of Thick Multi-Layered Structures Using the Numerical Truncation Approximation for the Transfer Matrix Technique

1999 ◽  
Author(s):  
Krishnan Balasubramaniam
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Wave Reflection ◽  
Layered Structures ◽  
Numerical Instability ◽  
Wide Range

Abstract In this paper, the authors describe a numerical truncation technique for handling the numerical instability problems associated with the utilization of the transfer matrix method. This, rather simplistic modification to the numerical coding extends the transfer matrix method to a wide range of applications.

scholarly journals Constitutive relations for compressible granular flow in the inertial regime

2019 ◽  
Vol 874 ◽  
pp. 926-951 ◽  
Author(s):  
D. G. Schaeffer ◽  
T. Barker ◽  
D. Tsuji ◽  
P. Gremaud ◽  
M. Shearer ◽  
...  
Keyword(s):  
Steady State ◽  
Granular Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Practical Interest ◽  
Time Dependent ◽  
Direct Result ◽  
Wide Range ◽  
Inertial Regime

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology that does not suffer from such defects is proposed. In the framework of compressible $I$-dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations.

Sign in / Sign up

Export Citation Format

Share Document