Relevant bibliographies by topics / 2D non-linear wave equation

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic '2D non-linear wave equation'

Author: Grafiati
Published: 4 June 2025
Last updated: 23 June 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic '2D non-linear wave equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "2D non-linear wave equation"

1

Deya, Aurélien. "On a non-linear 2D fractional wave equation." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 56, no. 1 (2020): 477–501. http://dx.doi.org/10.1214/19-aihp969.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Vivas-Cortez, Miguel, Maham Nageen, Muhammad Abbas, and Moataz Alosaimi. "Investigation of Analytical Soliton Solutions to the Non-Linear Klein–Gordon Model Using Efficient Techniques." Symmetry 16, no. 8 (2024): 1085. http://dx.doi.org/10.3390/sym16081085.

Full text
Abstract:
Nonlinear distinct models have wide applications in various fields of science and engineering. The present research uses the mapping and generalized Riccati equation mapping methods to address the exact solutions for the nonlinear Klein–Gordon equation. First, the travelling wave transform is used to create an ordinary differential equation form for the nonlinear partial differential equation. This work presents the construction of novel trigonometric, hyperbolic and Jacobi elliptic functions to the nonlinear Klein–Gordon equation using the mapping and generalized Riccati equation mapping methods. In the fields of fluid motion, plasma science, and classical physics the nonlinear Klein–Gordon equation is frequently used to identify of a wide range of interesting physical occurrences. It is considered that the obtained results have not been established in prior study via these methods. To fully evaluate the wave character of the solutions, a number of typical wave profiles are presented, including bell-shaped wave, anti-bell shaped wave, W-shaped wave, continuous periodic wave, while kink wave, smooth kink wave, anti-peakon wave, V-shaped wave and flat wave solitons. Several 2D, 3D and contour plots are produced by taking precise values of parameters in order to improve the physical description of solutions. It is noteworthy that the suggested techniques for solving nonlinear partial differential equations are capable, reliable, and captivating analytical instruments.
APA, Harvard, Vancouver, ISO, and other styles
3

Flores, Jesús, Ángel García, Mihaela Negreanu, Eduardo Salete, Francisco Ureña, and Antonio M. Vargas. "Numerical Solutions to Wave Propagation and Heat Transfer Non-Linear PDEs by Using a Meshless Method." Mathematics 10, no. 3 (2022): 332. http://dx.doi.org/10.3390/math10030332.

Full text
Abstract:
The applications of the Eikonal and stationary heat transfer equations in broad fields of science and engineering are the motivation to present an implementation, not only valid for structured domains but also for completely irregular domains, of the meshless Generalized Finite Difference Method (GFDM). In this paper, the fully non-linear Eikonal equation and the stationary heat transfer equation with variable thermal conductivity and source term are solved in 2D. The explicit formulae for derivatives are developed and applied to the equations in order to obtain the numerical schemes to be used. Moreover, the numerical values that approximate the functions for the considered domain are obtained. Numerous examples for both equations on irregular 2D domains are exposed to underline the effectiveness and practicality of the method.
APA, Harvard, Vancouver, ISO, and other styles
4

Elmandouh, Adel, Aqilah Aljuaidan, and Mamdouh Elbrolosy. "The Integrability and Modification to an Auxiliary Function Method for Solving the Strain Wave Equation of a Flexible Rod with a Finite Deformation." Mathematics 12, no. 3 (2024): 383. http://dx.doi.org/10.3390/math12030383.

Full text
Abstract:
Our study focuses on the governing equation of a finitely deformed flexible rod with strain waves. By utilizing the well-known Ablowita–Ramani–Segur (ARS) algorithm, we prove that the equation is non-integrable in the Painlevé sense. Based on the bifurcation theory for planar dynamical systems, we modify an auxiliary equation method to obtain a new systematic and effective method that can be used for a wide class of non-linear evolution equations. This method is summed up in an algorithm that explains and clarifies the ease of its applicability. The proposed method is successfully applied to construct wave solutions. The developed solutions are grouped as periodic, solitary, super periodic, kink, and unbounded solutions. A graphic representation of these solutions is presented using a 3D representation and a 2D representation, as well as a 2D contour plot.
APA, Harvard, Vancouver, ISO, and other styles
5

P., Parameshwari, and Pushpalatha G. "Application of Nonlinear Two Dimension Wave Equation Dual Reciprocity Boundary Element Method." International Journal of Trend in Scientific Research and Development 2, no. 3 (2019): 2041–42. https://doi.org/10.31142/ijtsrd11584.

Full text
Abstract:
The constructive numerical implementation of the two dimensional dual boundary element method. This paper present to solve nonlinear 2 D wave equation defined over a rectangular spatial domain the boundary conditions. Two dimension wave equation is a time domain problem, with three independent variables u,v,t. The applied to 2 D wave equation satisfactory authority. P. Parameshwari | G. Pushpalatha "Application of Nonlinear Two-Dimension Wave Equation Dual Reciprocity Boundary Element Method" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-3 , April 2018, URL: https://www.ijtsrd.com/papers/ijtsrd11584.pdf
APA, Harvard, Vancouver, ISO, and other styles
6

Макаренко, Николай Иванович, Валерий Юрьевич Ляпидевский, Данила Сергеевич Денисенко, and Дмитрий Евгеньевич Кукушкин. "Nonlinear internal wave packets in shelf zone." Вычислительные технологии, no. 2(24) (April 17, 2019): 90–98. http://dx.doi.org/10.25743/ict.2019.24.2.008.

Full text
Abstract:
В рамках модели невязкой слабостратифицированной жидкости рассматривается длинноволновое приближение, описывающее нелинейные волновые пакеты типа кноидальных волн. Построены семейства асимптотических решений, одновременно описывающие периодические последовательности приповерхностных волн в форме впадин и придонных волн типа возвышений. Показано, что картины расчетных профилей качественно согласуются со структурами внутренних волн, наблюдавшихся авторами в натурных экспериментах в шельфовой зоне моря. The problem on nonlinear internal waves propagating permanently in shallow fluid is studied semi-analytically in comparison with the field data measured on the sea shelf. At present, the most studied in this context are nonlinear solitary-type waves generated due to the tidal activity over continental slope. This paper deals with periodic cnoidaltype wave packets considered in the framework of mathematical model of continuously stratified fluid. Basic model involves the Dubreil-Jacotin-Long equation for a stream function that results from stationary fully non-linear 2D Euler equations. The longwave approximate equation describing periodic non-harmonic waves is derived by means of scaling procedure using small Boussinesq parameter. This parameter characterizes slight stratification of the fluid layer with the density profile being close to the linear stratification. The fine-scale density plays important role here because it determines the non-linearity rate of model equation, so it permits to consider strongly non-linear dispersive waves of large amplitude. As a result, constructed asymptotic solutions can simulate periodic wave-trains of sub-surface depression coupled with near-bottom wavetrains of isopycnal elevation. It is demonstrated that calculated wave profiles are in good qualitative agreement with internal wave structures observed by the authors in the field experiments performed annually during 2011-2018 in expeditions on the shelf of the Japanese sea.
APA, Harvard, Vancouver, ISO, and other styles
7

Jayewardene, Indra FW, Aliasghar Golshani, and Ed Couriel. "MAXIMUM MOMENTUM FLUX FOR STABILITY ANALYSIS OF MODEL AND PROTOTYPE BREAKWATERS." Coastal Engineering Proceedings, no. 37 (September 1, 2023): 6. http://dx.doi.org/10.9753/icce.v37.papers.6.

Full text
Abstract:
None of the established formulae for breakwater armour stone stability, Hudson (1958) or van der Meer (1987), explicitly account for the water depth at the toe of the structure. More recently, Hughes (2004), Melby and Hughes (2004), Melby and Kobayashi (2011) have developed equations for stability and runup utilising the concept of wave momentum flux which explicitly accounts for the water depth of the wave probe(s) in close proximity to the structure. The equations are adapted to three forms; namely (1) linear, (2) extended-linear and (3) non-linear. In the paper linearity is assessed by using the Ursell number at each probe depth. Also, due to the placement of probes at various depths in MHL’s 2D wave flume it is possible to correlate the linearity of the wave measurement for the same time series and subsequently test the appropriateness of the momentum flux equation applied for assessment of stability and runup. The stability and runup data from 43 2D physical model tests where stability was previously assessed using van der Meer’s and Hudson’s equations are assessed using the momentum flux equations and an evaluation of the results has been made. It was found that the estimation of notional permeability and selection of the use of the plunging or surging formulae was critical to obtaining a closer match between measurement and prediction. The equations were also utilised in conjunction with numerical models to evaluate the armour size for repair of two breakwater heads in South Camden Haven and Bellambi. The maximum momentum flux equations were found to perform satisfactorily at these locations where the Ursell numbers were found to be high and the waves non-linear.
APA, Harvard, Vancouver, ISO, and other styles
8

Ansar, Rimsha, Muhammad Abbas, Pshtiwan Othman Mohammed, Eman Al-Sarairah, Khaled A. Gepreel, and Mohamed S. Soliman. "Dynamical Study of Coupled Riemann Wave Equation Involving Conformable, Beta, and M-Truncated Derivatives via Two Efficient Analytical Methods." Symmetry 15, no. 7 (2023): 1293. http://dx.doi.org/10.3390/sym15071293.

Full text
Abstract:
In this study, the Jacobi elliptic function method (JEFM) and modified auxiliary equation method (MAEM) are used to investigate the solitary wave solutions of the nonlinear coupled Riemann wave (RW) equation. Nonlinear coupled partial differential equations (NLPDEs) can be transformed into a collection of algebraic equations by utilising a travelling wave transformation. This study’s objective is to learn more about the non-linear coupled RW equation, which accounts for tidal waves, tsunamis, and static uniform media. The variance in the governing model’s travelling wave behavior is investigated using the conformable, beta, and M-truncated derivatives (M-TD). The aforementioned methods can be used to derive solitary wave solutions for trigonometric, hyperbolic, and jacobi functions. We may produce periodic solutions, bell-form soliton, anti-bell-shape soliton, M-shaped, and W-shaped solitons by altering specific parameter values. The mathematical form of each pair of travelling wave solutions is symmetric. Lastly, in order to emphasise the impact of conformable, beta, and M-TD on the behaviour and symmetric solutions for the presented problem, the 2D and 3D representations of the analytical soliton solutions can be produced using Mathematica 10.
APA, Harvard, Vancouver, ISO, and other styles
9

Iqbal, Mujahid, Aly R. Seadawy, Dianchen Lu, and Xianwei Xia. "Construction of bright–dark solitons and ion-acoustic solitary wave solutions of dynamical system of nonlinear wave propagation." Modern Physics Letters A 34, no. 37 (2019): 1950309. http://dx.doi.org/10.1142/s0217732319503097.

Full text
Abstract:
The nonlinear (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) equations deal with the nonlinear behavior of waves in collision-less plasma, which contains non-isothermal cold ions and electrons. Two-dimensional dust acoustic solitary waves (DASWs) in magnetized plasma, which consist of trapped electrons and ions are leading to (2 + 1)-dim (ZK) equation by using the perturbation technique. We found the solitary wave solutions of (2 + 1)-dimensional (ZK)-equation, generalized (ZK)-equation and generalized form of modified (ZK)-equation by implementing the modified mathematical method. As a result, we obtained the bright–dark solitons, traveling wave and solitary wave solutions. The physical structure of obtained solutions is represented in 2D and 3D, graphically with the help of Mathematica.
APA, Harvard, Vancouver, ISO, and other styles
10

MAAS, LEO R. M. "WAVE ATTRACTORS: LINEAR YET NONLINEAR." International Journal of Bifurcation and Chaos 15, no. 09 (2005): 2757–82. http://dx.doi.org/10.1142/s0218127405013733.

Full text
Abstract:
A number of physical mechanisms give rise to confined linear wave systems whose spatial structure is governed by a hyperbolic equation. These lack the discrete set of regular eigenmodes that are found in classical wave systems governed by an elliptic equation. In most 2D hyperbolic cases the discrete eigenmodes are replaced by a continuous spectrum of wave fields that possess a self-similar spatial structure and have a (point, line or planar) singularity in the interior. These singularities are called wave attractors because they form the attracting limit set of an iterated nonlinear map, which is employed in constructing exact solutions of this hyperbolic equation. While this is an inviscid, ideal fluid result, observations support the physical relevance of wave attractors by showing localization of wave energy onto their predicted locations. It is shown that in 3D, wave attractors may co-exist with a regular kind of trapped wave. Wave attractors are argued to be of potential relevance to fluids that are density-stratified, rotating, or subject to a magnetic field (or a combination of these) all of which apply to geophysical media.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "2D non-linear wave equation"

1

Scheidt, Torsten. "Non-linear optical diagnostics of non-centrosymmetric opto-electronic semiconductor materials." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/17332.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Hoq, Qazi Enamul. "Quantization Of Spin Direction For Solitary Waves in a Uniform Magnetic Field." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4210/.

Full text
Abstract:
It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data)and have nonzero spin (nonzero intrinsic angular momentum in the centre of momentum frame). In this paper we consider vector-valued solitary wave solutions to a nonlinear Klein-Gordon equation and investigate the behavior of these spinning solitary waves under the influence of an externally imposed uniform magnetic field. We find that the only stationary spinning solitary wave solutions have spin parallel or antiparallel to the magnetic field direction.
APA, Harvard, Vancouver, ISO, and other styles
3

Talib, Ahmed Abedelhussain. "Optimal system of subalgebras and invariant solutions for a nonlinear wave equation." Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-2675.

Full text
Abstract:
This thesis is devoted to use Lie group analysis to obtain all invariant solutions by constructing optimal system of one-dimensional subalgebras of the Lie algebra L5 for a nonlinear wave equation. I will show how the given symmetries ( Eq.2) are admitted by using partial differential equation (Eq.1), In addition to obtain the commutator table by using the same given symmetries. Subsequently, I calculate the transformations of the generators with the Lie algebra L5, which provide the 5-parameter group of linear transformations for the operators. Finally, I construct the invariant solutions for each member of the optimal system.
APA, Harvard, Vancouver, ISO, and other styles
4

Nascimento, Wanderley Nunes do. "Klein-Gordon models with non-effective time-dependent potential." Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/7453.

Full text
Abstract:
Submitted by Livia Mello (liviacmello@yahoo.com.br) on 2016-09-23T20:38:51Z No. of bitstreams: 1 TeseWNN.pdf: 1247691 bytes, checksum: 63f743255181169a9bb4ca1dfd2312c2 (MD5)<br>Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:35:27Z (GMT) No. of bitstreams: 1 TeseWNN.pdf: 1247691 bytes, checksum: 63f743255181169a9bb4ca1dfd2312c2 (MD5)<br>Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-26T20:35:33Z (GMT) No. of bitstreams: 1 TeseWNN.pdf: 1247691 bytes, checksum: 63f743255181169a9bb4ca1dfd2312c2 (MD5)<br>Made available in DSpace on 2016-09-26T20:35:40Z (GMT). No. of bitstreams: 1 TeseWNN.pdf: 1247691 bytes, checksum: 63f743255181169a9bb4ca1dfd2312c2 (MD5) Previous issue date: 2016-02-19<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>In this thesis we study the asymptotic properties for the solution of the Cauchy problem for the Klein-Gordon equation with non-effective time-dependent potential. The main goal was define a suitable energy related to the Cauchy problem and derive decay estimates for such energy. Strichartz’ estimates and results of scattering and modified scattering was established. The C m theory and the stabilization condition was applied to treat the case where the coefficient of the potential term has very fast oscillations. Moreover, we consider a semi-linear wave model scale-invariant time- dependent with mass and dissipation, in this step we used linear estimates related with the semi-linear model to prove global existence (in time) of energy solutions for small data and we show a blow-up result for a suitable choice of the coefficients.<br>Nesta tese estudamos as propriedades assintóticas para a solução do problema de Cauchy para a equação de Klein-Gordon com potencial não efetivo dependente do tempo. O principal objetivo foi definir uma energia adequada relacionada ao problema de Cauchy e derivar estimativas para tal energia. Estimativas de Strichartz e resultados de scatering e scatering modificados também foram estabelecidos. A teoria C m e a condição de estabilização foram aplicados para tratar o caso em que o coeficiente da massa oscila muito rápido. Além disso, consideramos um mod- elo de onda semi-linear scale-invariante com massa e dissipação dependentes do tempo, nesta etapa usamos as estimativas lineares de tal modelo para provar ex- istência global (no tempo) de solução de energia para dados iniciais suficientemente pequenos e demonstramos um resultado de blow-up para uma escolha adequada dos coeficientes.
APA, Harvard, Vancouver, ISO, and other styles
5

Civin, Damon. "Stability of charged rotating black holes for linear scalar perturbations." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247397.

Full text
Abstract:
In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and trapping occur in disjoint regions of phase space and can be dealt with individually. Trapping is a high frequency obstruction to the proof whereas superradiance occurs at both high and low frequencies. The construction of energy currents for superradiant frequencies gives rise to an unfavourable boundary term. In the high frequency regime, this boundary term is controlled by exploiting the presence of a large parameter. For low superradiant frequencies, no such parameter is available. This difficulty is overcome by proving quantitative versions of mode stability type results. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions of the wave equation restricted to a bounded frequency regime. The (ILED) statement is necessarily degenerate due to the trapping effect. This implies that a nondegenerate (ILED) statement must lose differentiability. If one uses an (ILED) result that loses differentiability to prove (NEB), this loss is passed onto the (NEB) statement as well. Here, the geometry of the subextremal Kerr-Newman background is exploited to obtain the (NEB) statement directly from the degenerate (ILED) with no loss of differentiability.
APA, Harvard, Vancouver, ISO, and other styles
6

Sun, Ruoci. "Comportement en grand temps et intégrabilité de certaines équations dispersives sur l'espace de Hardy Long time behavior of the NLS-Szegö equation Traveling waves of the quintic focusing NLS-Szegö equation Complete integrability of the Benjamin-Ono equation on the multi-soliton manifolds." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASS111.

Full text
Abstract:
On s'intéresse dans cette thèse à trois modèles d'équations hamiltoniennes dispersives non linéaires : l'équation de Schrödinger cubique défocalisante sur le cercle, filtrée par le projecteur de Szegö, qui enlève tous les modes de Fourier strictement négatifs (NLS--Szegö cubique), l'équation de Schrödinger quintique focalisante filtrée par le projecteur de Szegö sur la droite (NLS--Szegö quintique) et l'équation de Benjamin--Ono (BO) sur la droite. Comme pour les deux modèles précédents, l'équation de BO peut encore s'écrire sous la forme d'une équation de Schrödinger quadratique filtrée par le projecteur de Szegö. Ces trois modèles nous donnent l'occasion d'étudier les propriétés qualitatives de certaines ondes progressives, le phénomène de croissance des normes de Sobolev, le phénomène de diffusion non linéaire et certaines propriétés d'intégrabilité de systèmes dynamiques hamiltoniens. Le but de cette thèse est de comprendre l'influence des opérateurs de Szegö (non locaux) sur les équations de type Schrödinger, et d'adapter les outils liés à l'espace de Hardy sur le cercle et sur la droite. On applique aussi la méthode de forme normale de Birkhoff, l'argument de concentration--compacité, qui est précisé à travers le théorème de d'ecomposition en profils, et la transformée spectrale inverse pour résoudre ces problèmes. Dans le troisième modèle, la théorie de l'intégrabilité permet de faire le lien avec certains aspects algébriques et géométriques<br>We are interested in three non linear dispersive Hamiltonian equations: the defocusing cubic Schrödinger equation filtered by the Szegö projector on the torus that cancels every negative Fourier modes, leading to the cubic NLS--Szegö equation on the torus; the focusing quintic Schrödinger equation, which is filtered by the Szegö projector on the line, leading to the quintic NLS--Szegö equation on the line and the Benjamin--Ono (BO) equation on the line. Similarly to the other two models, the BO equation on the line can be written as a quadratic Schrödinger-type equation that is filtered by the Szegö projector on the line. These three models allow us to study their qualitative properties of some traveling waves, the phenomenon of the growth of Sobolev norms, the phenomenon of non linear scattering and some properties about the complete integrability of Hamiltonian dynamical systems. The goal of this thesis is to investigate the influence of the Szegö projector on some one-dimensional Schrödinger-type equations and to adapt the tools of the Hardy space on the torus and on the line. We also use the Birkhoff normal form transform, the concentration--compactness argument, refined as the profile decomposition theorem, and the inverse spectral transform in order to solve these problems. In the third model, the integrability theory allows to establish the connection with some algebraic and geometric aspects
APA, Harvard, Vancouver, ISO, and other styles
7

Pocovnicu, Oana. "Etude d'une équation non linéaire, non dispersive et complètement integrable et de ses perturbations." Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00834518.

Full text
Abstract:
On étudie dans cette thèse l'équation de Szegö sur la droite réelle ainsi que ses perturbations. Cette équation a été introduite il y a quelques années par Gérard et Grellier comme modèle mathématique d'une équation non linéaire totalement non dispersive.L'équation de Szegöapparait naturellement dans l'étude de l'équation de Schrödinger non linéaire (NLS) danscertaines situations sur-critiques où l'on constate un manque de dispersion, par exemplelorsque l'on considère NLS sur le groupe de Heisenberg. Par conséquent, une des motivationsde cette thèse est d'établir des résultats concernant l'équation de Szegö qui pourrontéventuellement être utilisés dans le contexte de l'équation de Schrödinger non linéaire.Le premier résultat de cette thèse est la classification des solitons de l'équation de Szegö.On montre que ce sont tous des fonctions rationnelles ayant un unique pôle qui est simple.De plus, on prouve que les solitons sont orbitalement stables.La propriété la plus remarquable de l'équation de Szegö est le fait qu'elle est complètement intégrable, ce qui permet notamment d'établir une formule explicite de sa solution.Comme applications de cette formule, on obtient les trois résultats suivants. (A) On montreque les solutions fonctions rationnelles génériques se décomposent en une somme de solitonset d'un reste qui est petit lorsque le temps tend vers l'infini. (B) On met en évidence unexemple de solution non générique dont les grandes normes de Sobolev tendent vers l'infiniavec le temps. (C) On détermine des coordonnées action-angle généralisées lorsque l'on restreintl'équation de Szegö à une sous-variété de dimension finie. En particulier, on en déduitqu'une grande partie des trajectoires de cette équation sont des spirales autour de cylindrestoroïdaux.Comme l'équation de Szegö est complètement intégrable, il est ensuite naturel d'étudierses perturbations et d'établir de nouvelles propriétés pour celles-ci à partir des résultatsconnus pour l'équation de Szegö. Une des perturbations de l'équation de Szegö est une équation desondes non linéaire (NLW) de donnée bien préparée.On prouve que si la donnée initiale de NLW est petite et à support dans l'ensemble desfréquences positives, la solution de NLW est alors approximée pour un temps long par lasolution de l'équation de Szegö. Autrement dit, on démontre ainsi que l'équation de Szegöest la première approximation de NLW. On construit ensuite une solution de NLW dont lesgrandes normes de Sobolev augmentent (relativement à la norme de la donnée initiale).Sur le tore T, Gérard et Grellier ont démontré un résultat analogue d'approximation deNLW. On améliore ce résultat en trouvant une approximation plus fine, de deuxième ordre.Dans une dernière partie, on s'intéresse à l'équation de Szegö perturbée par un potentielmultiplicatif petit. On étudie l'interaction de ce potentiel avec les solitons. Plus précisément,on montre que, si la donnée initiale est celle d'un soliton pour l'équation non perturbée, lasolution de l'équation perturbée garde la forme d'un soliton sur un long temps. De plus, ondéduit la dynamique effective, i.e. les équations différentielles satisfaites par les paramètresdu soliton.
APA, Harvard, Vancouver, ISO, and other styles
8

Colin, Thierry. "Problème de Cauchy et effets régularisants pour des équations aux dérivées partielles dispersives." Cachan, Ecole normale supérieure, 1993. http://www.theses.fr/1993DENS0003.

Full text
Abstract:
Dans la première partie, on traite une équation de Schrödinger non linéaire et non locale qui intervient en physique des plasmas: problème de Cauchy local et global, ondes stationnaires et leur stabilité. Dans la deuxième partie, on étudie le problème de Cauchy local pour une classe d'équations dispersives en utilisant des effets régularisant globaux. Dans la troisième partie, on démontre des effets régularisant pour des équations dispersives grâce a une transformée de Wigner généralisée. Ceci fournit de nouvelles estimations
APA, Harvard, Vancouver, ISO, and other styles
9

Kian, Yavar. "Equations des ondes avec des perturbations dépendantes du temps." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14101/document.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Meunier, Claude. "Quelques problèmes non-linéaires en hydrodynamique et en physique des plasmas : théorèmes de moyennisation et théorèmes adiabatiques." Paris 6, 1986. http://www.theses.fr/1986PA066126.

Full text
Abstract:
Etude de l'intermittence, un type de transition vers la turbulence rencontre en convection et dans la réaction de Belousov-Zhabotinsky. La mesure invariante dépend continument du paramètre de bifurcation. Etude d'un modèle de couplage résonnant d'ondes de dérivé dans une limite de dissipation forte par des méthodes perturbatives et l'utilisation du théorème de la variété stable. Etude de la génération périodique de solitons dans l'équation de Schrödinger cubique avec source. Travail de synthèse sur les méthodes de moyennisation et les théorèmes adiabatiques.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "2D non-linear wave equation"

1

M, Greco Antonio, Ruggeri Tommaso, Boillat G, and Circolo matematico di Palermo, eds. Non linear hyperbolic fields and waves: A tribute to Guy Boillat. Sede della Società, 2006.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
2

Yousuff, Hussaini M., and Institute for Computer Applications in Science and Engineering., eds. Non-linear evolution of a second mode wave in supersonic boundary layers. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1989.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Yousuff, Hussaini M., and Institute for Computer Applications in Science and Engineering., eds. Non-linear evolution of a second mode wave in supersonic boundary layers. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1989.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Reed, Michael. Abstract Non Linear Wave Equations. Springer London, Limited, 2006.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Zeitlin, Vladimir. RSW Modons and their Surprising Properties: RSW Turbulence. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0009.

Full text
Abstract:
By using quasi-geostrophic modons constructed in Chapter 6 as initial conditions, rotating-shallow-water modons are obtained through the process of ageostrophic adjustment, both in one- and in two-layer configurations. Scatter plots show that they are solutions of the rotating shallow-water equations. A special class of modons with an internal front (shock) is shown to exist. A panorama of collision processes of the modons, leading to formation of tripoles, nonlinear modons, or elastic scattering is presented. The modon solutions are then used for initialisations of numerical simulations of decaying rotating shallow-water turbulence. The results are analysed and compared to those obtained with standard in 2D turbulence initializations, and differences are detected, showing non-universality of decaying 2D turbulence. The obtained energy spectra are steeper than theoretical predictions for ‘pure’ 2D turbulence, and pronounced cyclone–anticyclone asymmetry and dynamical separation of waves and vortices are observed.
APA, Harvard, Vancouver, ISO, and other styles
6

Asano, N., and Y. Kato. Algebraic and Spectral Methods for Non-Linear Wave Equations (Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 49). Longman Sc & Tech, 1991.

Find full text
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "2D non-linear wave equation"

1

Torrisi, M., R. Tracinà, and A. Valenti. "On Equivalence Transformations Applied to a Non-Linear Wave Equation." In Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2050-0_39.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Durur, Hülya, Asıf Yokuş, and Mehmet Yavuz. "Behavior Analysis and Asymptotic Stability of the Traveling Wave Solution of the Kaup-Kupershmidt Equation for Conformable Derivative." In Fractional Calculus: New Applications in Understanding Nonlinear Phenomena. BENTHAM SCIENCE PUBLISHERS, 2022. http://dx.doi.org/10.2174/9789815051933122030010.

Full text
Abstract:
This article suggests solving the traveling wave solutions of the time.fractional Kaup-Kupershmidt (KK) equation via 1/ G -expansion and sub-equation methods. Non-local fractional derivatives have some advantages over local fractional derivatives. The most important of these advantages are the chain rule and the Leibniz rule. The conformable derivative, which has a local fractional derivative feature, is taken into account in this study. Different types of traveling wave solutions of the time-fractional KK equation have been produced by using the important benefits of the time-dependent conformable derivative operator. These wave types are dark, singular, rational, trigonometric and hyperbolic type solitons. 2D, 3D and contour graphics are presented by giving arbitrary values to the constants in the solutions produced by analytical methods. These presented graphs represent the shape of the standing wave at any given moment. Besides, the advantages and disadvantages of the two analytical methods are discussed and presented in the result and discussion section. In addition, wave behavior analysis for different velocity values of the dark soliton produced by the analytical method is analyzed by simulation. The conditional convergence and asymptotic stability of the dark soliton discussed are analyzed. Computer software is also used in operations such as drawing graphs, complex operations, and solving algebraic equation systems.
APA, Harvard, Vancouver, ISO, and other styles
3

Carretero-González, R., D. J. Frantzeskakis, and P. G. Kevrekidis. "The Gross–Pitaevskii (GP) Equation." In Nonlinear Waves & Hamiltonian Systems. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/oso/9780192843234.003.0024.

Full text
Abstract:
Abstract In the next few chapters we cover some further techniques based on NLS-type equations by focusing on a particularly attractive application in atomic physics: Bose-Einstein condensates (BECs). The mean-field dynamics of BECs can be modeled by the Gross-Pitaevskii (GP) equation which is a generalization of the NLS equation that includes an external potential. In this chapter we introduce BECs and some basic properties of the GP equation. In particular, we show how the external potential may render the, originally 3D, BEC into an effective 1D or 2D system. We also describe the large mass (Thomas-Fermi) limit and the low mass (linear) limit.
APA, Harvard, Vancouver, ISO, and other styles
4

Carretero-González, R., D. J. Frantzeskakis, and P. G. Kevrekidis. "From Boussinesq to KdV – Boussinesq Solitons as KdV Solitons." In Nonlinear Waves & Hamiltonian Systems. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/oso/9780192843234.003.0005.

Full text
Abstract:
Abstract In this chapter we focus on the asymptotic reduction of the Boussinesq equation to the KdV equation. We show how the slow variables and the scales of the unknown fields involved in the problem are chosen. We will see that relevant choices stem from "first principles", such as the structure of the linear dispersion relation, and the balance between dispersion and nonlinear effects. In addition, we will go a step further: relying on the formal asymptotic connection between the Boussinesq and KdV equations, we will show that the soliton solution of the former is nothing but the small-amplitude limit of the latter. Finally, we will show how results pertaining to the 1D setting can be generalized to higher-dimensions. In particular, we will present the asymptotic reduction of the 2D Boussinesq equation to the Kadomtsev-Petviashvili (KP) equation, which is the higher-dimensional generalization of the KdV.
APA, Harvard, Vancouver, ISO, and other styles
5

Aigulim, Bayegizova, and Dadayeva Assiyat. "Boundary Integral Equations of no Stationary Boundary Value Problems for the Klein-Gordon Equation." In Mathematical Theorems - Boundary Value Problems and Approximations. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.91693.

Full text
Abstract:
The non-stationary boundary value problems for Klein-Gordon equation with Dirichlet or Neumann conditions on the boundary of the domain of definition are considered; a uniqueness of boundary value problems is proved. Based on the generalized functions method, boundary integral equations method is developed to solve the posed problems in strengths of shock waves. Dynamic analogs of Green’s formulas for solutions in the space of generalized functions are obtained and their regular integral representations are constructed in 2D and 3D over space cases. The singular boundary integral equations are obtained which resolve these tasks.
APA, Harvard, Vancouver, ISO, and other styles
6

Carretero-González, R., D. J. Frantzeskakis, and P. G. Kevrekidis. "Direct Perturbation Theory for Solitons*." In Nonlinear Waves & Hamiltonian Systems. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/oso/9780192843234.003.0012.

Full text
Abstract:
Abstract In this chapter, we study the behavior of solitons and traveling waves under the action of weak perturbations. We consider the case of transverse perturbations occurring in higher-dimensional settings. Our prototypical example will be the perturbed KdV equation. In particular, we will present the cases of (i) a KdV incorporating weak linear losses and (ii) a Kadomtsev-Petviashvili (KP) equation, which is the suitable generalization of the KdV to study the transverse dynamics of 2D line solitons. We show how direct perturbation theory can be applied to problems involving dynamics of solitons and, in general, traveling waves under perturbations.
APA, Harvard, Vancouver, ISO, and other styles
7

Akhmanov, S. A., and S. YU Nikitin. "Theoretical non-linear optics." In Physical Optics. Oxford University PressOxford, 1997. http://dx.doi.org/10.1093/oso/9780198517955.003.0023.

Full text
Abstract:
Abstract Optical second-harmonic generation. Stimulated Raman scattering. Self-focusing of light. The theory of non-linear optical effects is based on Maxwell’s equations and the material equations. From Maxwell’s equations one can obtain the wave equation (see Chapter 22).
APA, Harvard, Vancouver, ISO, and other styles
8

Boroviks, Sergejs, and Olivier J. F. Martin. "Fundamentals of Non-linear Optics in Nanostructures." In Laser-based Techniques for Nanomaterials. Royal Society of Chemistry, 2024. https://doi.org/10.1039/9781837673513-00015.

Full text
Abstract:
This chapter provides an overview of the formalism required to describe non-linear optical phenomena, including the non-linear wave equation and the different orders of susceptibilities, up to the third-order. Second- and third-order non-linear phenomena are reviewed, including second- and third-harmonic generation, as well as three-wave mixing. The remainder of the chapter is devoted to the description of important non-linear effects that can occur in nanostructures and stem either from surface or bulk non-linearities; the chapter concludes by discussing the enhancement mechanisms for the non-linear response of nanostructures.
APA, Harvard, Vancouver, ISO, and other styles
9

"Stability of Lie groups of the perturbed non-linear wave equation." In Proceedings of the seventh International Colloquium on Differential Equations. De Gruyter, 1997. http://dx.doi.org/10.1515/9783112319185-041.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Pearle, Philip. "CSL Expressed as a Schrödinger Stochastic DE." In Introduction to Dynamical Wave Function Collapse. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/oso/9780198901372.003.0016.

Full text
Abstract:
Abstract Chapter 16 uses the results of Chapter 15 to show how to construct the CSL Stratonovich and Ito Schrödinger equations for the normalized state vector. It is emphasized that there is a non-linear dependence on the state vector. It then goes on to show how the (linear) density matrix evolution equation follows is constructed from that. The chapter ends with a discussion regarding specialization to non-relativistic CSL.
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "2D non-linear wave equation"

1

Qiao, Hongdong, Weidong Ruan, Zhaohui Shang, and Yong Bai. "Non-Linear Static Analysis of 2D Steep Wave Riser Under Current Load." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54460.

Full text
Abstract:
A new solution combining finite difference method and shooting method is developed to analyze the behavior of steep wave riser subjected to current loading. Based on the large deformation beam theory and mechanics equilibrium principle, a set of non-linear ordinary differential equations describing the motion of the steep wave riser are obtained. Then, finite difference method and shooting method are adopted and combined to solve the ordinary differential equations with zero moment boundary conditions at both the seabed end and surface end of the steep wave riser. The resulting non-linear finite difference formulations can be solved effectively by Newton-Raphson method. To improve iterative efficiency, shooting method is also employed to obtain the initial value for Newton-Raphson method. Results are compared with that of FEM by OrcaFlex, to verify the accuracy and reliability of the numerical method. Finally, a series of sensitivity analyses are also performed to highlight the influencing parameters in the steep wave riser.
APA, Harvard, Vancouver, ISO, and other styles
2

Middleton, M., D. Murphy, and L. Savioja. "The application of Fourier neural operator networks for solving the 2D linear acoustic wave equation." In 10th Convention of the European Acoustics Association Forum Acusticum 2023. European Acoustics Association, 2022. http://dx.doi.org/10.61782/fa.2023.0047.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Capdeville, Yann, Laurent Guillot, and Jean‐Jacques Marigo. "2D/3D Elastic model up‐scaling for the wave equation based on non‐periodic homogenization." In SEG Technical Program Expanded Abstracts 2009. Society of Exploration Geophysicists, 2009. http://dx.doi.org/10.1190/1.3255387.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Li, Yabin, Ming He, Bing Ren, and Guoyu Wang. "Numerical Simulation of Wave Interaction With a Hinged Multi-Module Floating Structure." In ASME 2017 36th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/omae2017-61079.

Full text
Abstract:
This paper studies the interaction of water waves with a hinged multi-module floating structure, using a numerical model based on smoothed particle hydrodynamics (SPH) method. The simulation is performed in a 2D nonlinear numerical wave tank (NWT) equipped with an active absorbing wave maker and a sponge layer. The motion of the multi-module floating structure is calculated follow the Newton’s second law. The hydrodynamic forces on the floating modules are evaluated using the volume integration of the stress tensors obtained from the momentum equation in its compact support. A linear spring model is employed to calculate the mooring force. The collision forces acting on neighboring modules are acquired based on the strain-stress relationship of rubber bumper between the neighboring modules, and a continuity condition of linear acceleration at the hinge joint is built and implicit equations are solved utilizing Gauss-Jordan elimination method. To validate the numerical model, a laboratory experiment is conducted in a wave flume. Comparisons of the computed and measured data show reasonable agreements in terms of the wave surface profiles, mooring forces, connector forces and motion attitudes of the hinged multi-module floating structure in spite of slight discrepancies of the peak values of connector forces and the valley values of mooring forces.
APA, Harvard, Vancouver, ISO, and other styles
5

Bihs, Hans, Arun Kamath, Ankit Aggarwal, and Csaba Pakozdi. "Efficient Wave Modeling Using Non-Hydrostatic Pressure Distribution and Free Surface Tracking on Fixed Grids." In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/omae2018-78158.

Full text
Abstract:
For the estimation of wave loads on offshore structures, relevant extreme wave events need to be identified. In order to achieve this, long term wave simulations of relatively large scales need to be performed. Computational Fluid Dynamics (CFD) based Numerical Wave Tanks (NWT) with an interface capturing two-phase flow approach typically require too large computational resources to achieve this efficiently. They are more suitable for the near-field hydrodynamics of steep and breaking wave impacts on the structures. In the current paper, a three-dimensional non-hydrostatic wave model is presented. While it also solves the Navier-Stokes equations, it employs an interface tracking method for the calculation of the free surface location. The algorithm for the simulation of the free surface is based on the continuity of the horizontal velocities along the vertical water column. With this approach, relatively fewer cells are needed in the vicinity of the air-water interface compared to CFD based NWTs. With coarser grids and larger time steps, the wave propagation can be accurately predicted. The numerical model solves the governing equations on an rectilinear grid, which allows for the employment of high-order finite differences. For time stepping, a fractional step method with implicit treatment of the diffusion terms is employed. The projection method is used for the calculation of the non-hydrostatic pressure. The resulting Poisson equation is solved with Hypres geometric multigrid preconditioned conjugated gradient algorithm. The numerical model is parallelized following the domain decomposition strategy and MPI communication between the individual processors. In the current paper, the capabilities of the new wave model are presented by comparing the wave propagation in the tank with the CFD approach in a 2D simulation. Further, a 3D simulation is carried out to determine the wave forces on a vertical cylinder. The calculated wave forces using the new approach is compared to that obtained using the CFD approach and experimental data. It is seen that the new approach provides a similar accuracy to that from the CFD approach while providing a large reduction in the time taken for the simulation. The gain is calculated to be about 4.5 for the 2D simulation and about 7.1 for the 3D simulation.
APA, Harvard, Vancouver, ISO, and other styles
6

Chun, Wang, Danmei Xie, Xiong Yangheng, Yu Xinggang, Nie Chu, and Hengliang Zhang. "Research of Temperature Characteristics of Non-Equilibrium Condensation in Transonic Steam Flow." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-26455.

Full text
Abstract:
The non-equilibrium phase transition model in CFX is used to simulate the non-equilibrium condensation flow in Laval nozzles. The Eulerian-Eulerian governing equation of multi-phase computational fluid dynamics model is utilized to solve the two-phase flow with k-ε turbulence model. By simulating the spontaneous condensation flow in 2D and 3D models Laval nozzles with different geometries, non-equilibrium phase transition and condensation shock are captured. Our numerical results indicate that the pressure distributions and water droplet diameters are compared with the experimental ones under the same situation. It is shown that the results of 3D model agree with the experimental results better, while the pressure distribution curve of 2D model exhibits the “2D effect”, which may cause calculated errors. Finally, the temperature characteristics of non-equilibrium condensation in transonic steam flow are computed with 3D model and the influence of the inlet temperature on the condensation characteristics and position of shock wave is analyzed.
APA, Harvard, Vancouver, ISO, and other styles
7

Valentine, Daniel T. "Nonlinear Internal Waves: A Numerical Investigation of 2D Sloshing." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51002.

Full text
Abstract:
This paper examines internal sloshing motions in 2-D numerical wave tanks subjected to horizontal excitation. In all of the cases studied, the rectangular tank of liquid has a width-to-depth ratio of 2. The results presented are from simulations of internal waves induced by sloshing a density-stratified liquid. Non-linear, viscous flow equations of a Newtonian, Boussinesq liquid are solved. Some of the features of the evolution of sloshing in nearly two-layer and three-layer fluid systems are described. Initially, the middle of the two layers and the center of the middle layer of the three layers are horizontal and located at the center of the tank. The two-layer cases are forced at resonance. The evolution of sloshing from rest is examined. The maximum amplitude of sloshing occurs during the initial transient. If breaking occurs it is at the center of the container in the two-layer cases. The subharmonic forcing of a three-layer case induces a resonant response with the middle layer moving in such a way that motion is perpendicular to the isopycnals within this layer. These model problems provide some insights into the relatively complex sloshing that can occur in density-stratified liquids.
APA, Harvard, Vancouver, ISO, and other styles
8

Phan, L., S. L. Post, and A. Narain. "The Classical Nusselt Problem of Film Condensation: Direct Steady and Unsteady Computational Simulations That Yield Results on Stability and Wave Effects." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80221.

Full text
Abstract:
Accurate steady and unsteady numerical solutions of the full 2D governing equations for the Nusselt problem (film condensation of quiescent saturated vapor on a vertical wall) are presented and related to known results. The problem, solved accurately up to film Reynolds number of 60 (Reδ ≤ 60), establishes various features of the well known steady solution and reveals the interesting phenomena of stability, instability and non-linear wave effects. The wave effects are shown to arise from the intrinsic flow instabilities as well as sensitivity to ever present minuscule transverse vibrations of the condensing surface. The results also suggest ways to enhance wave fluctuations and heat transfer rates.
APA, Harvard, Vancouver, ISO, and other styles
9

Grotle, Erlend Liavåg, Hans Bihs, Eilif Pedersen, and Vilmar Æsøy. "CFD Simulations of Non-Linear Sloshing in a Rotating Rectangular Tank Using the Level Set Method." In ASME 2016 35th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/omae2016-54533.

Full text
Abstract:
In this paper, numerical simulations of non-linear sloshing in rectangular tanks are presented. Model implementations in the open source software REEF3D are tested and results compared with experimental data. Three different conditions are compared with experiments in 2D. First, the free surface time-evolution is compared for both linear and non-linear sloshing. In the last case, video images from the SPHERIC project are compared with simulations images of the free surface. A condition with lateral wave impacts in sloshing, with a frequency closer to the natural frequency of the first mode, can be found in this case. The non-linear sloshing, case 2, is also simulated in 3D. The numerical model is solving the RANS equations with the k-ω turbulence model. The level set method is used to capture the interface. Higher order discretization schemes are implemented to handle time-evolution and convective fluxes. A ghost cell method is used to account for solid boundaries and multiple grids for parallel computations. It is found that the limiting factor for the eddy-viscosity has significant influence in case 2 and 3. As the sloshing becomes more violent, the increased strain at the gas-liquid interface overproduces turbulence energy with unrealistically high damping of the motion. 3D simulations are only performed in case 2, which shows slightly better comparison than with 2D. Due to non-linearities and small damping, the time to reach steady-state may take several cycles, but no information is given in the paper [1]. The last case shows promising results for the global motion. As expected, the break up of the liquid surface makes it difficult to resolve each phase. But overall, the numerical model predicts the sloshing motion reasonably well.
APA, Harvard, Vancouver, ISO, and other styles
10

Masuda, Mitsuhiro, Tomoki Ikoma, Koichi Masuda, and Hisaaki Maeda. "A Study on Predictions of Fully Nonlinear Motion Aircushion Type Floating Structures Using 2D MPS Method." In ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2008. http://dx.doi.org/10.1115/omae2008-57387.

Full text
Abstract:
Very large floating structures (VLFSs) have been proposed for new ocean space utilization and many researches have been carried out. VLFSs are elastically deformed due to ocean waves because the rigidity of the structure decreases relatively. The authors examine the aircushion type floating structure in order to reduce hydroelastic motion. An aircushion type floating structure to which air-chambers are installed can reduce the wave drifting force and hydroelastic motion at the same time. Most theoretical calculations of motion of aircushion type floating structures in water waves have been done based on a linear potential theory so far. As a result, the utility of the aircushion has been proved. However fully nonlinear phenomena such as deck wetness, slamming and air-leakage cannot be investigated by using existing calculations based on the linear theory. In this study, a computer program code of the two-dimensional MPS method that can consider fully nonlinear influence is developed and then the air layer inside an aircushion is expressed with particles of the MPS. Moreover, the numerical technique for introducing directly the mooring force into the motion equation of the particle is developed. Motion response of aircushion type floating structures in a billow is computed. As a result, the usefulness of this numerical calculation method is confirmed.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic '2D non-linear wave equation' for particular source types:
Journal articles Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography