TIME DOMAIN SIMULATION FOR SOUND PROPAGATION OVER VARIOUS OBJECTS AND UNDER VORTICAL BACKGROUND CONDITIONS

Acoustic wave propagations have been studied for a long time with both experimental and numerical methods. Most of the analytical solutions for wave propagations are considered for simple environments such as a homogeneous atmospheres. As a result, the analytical solutions are unable to be applied for complicated environments. Numerical methods have become more and more important in acoustics studies after decades of development. The finite difference time-domain method (FDTD) is one of the most commonly used numerical methods in wave propagation studies. Compared with the other methods, the FDTD method is able to include many aspects of sound wave behaviors such as reflection, refraction, and diffraction in the physical problems. In this thesis, the linearized acoustic Euler equations coupled with the immersed boundary method are applied to investigate the sound wave propagation over complex environments. For the three-dimensional simulations of sound wave propagation in long distance, the moving domain method and parallel computing techniques are applied. Based on these approaches, the computational costs are significantly reduced and the simulation efficiency is greatly improved. When looking into the effects of high subsonic vortical flow, a high order WENO scheme is applied for the simulation. In this way the simulation stability can be achieved and the sound scattering of vortical flow can be studied. Then, the numerical scheme is applied to simulate an ultrasonic plane wave propagating through biological tissue. The linearized Euler acoustic equations coupled with the spatial fractional Laplacian operators are used for numerical simulations. The absorption and attenuation effects of the biological lossy media are successfully observed from the simulation results. Throughout this thesis, the simulation results are compared with either experimental measurements or analytical solutions so that the accuracy of the implemented numerical scheme is validated

TIME DOMAIN SIMULATION FOR SOUND PROPAGATION OVER VARIOUS OBJECTS AND UNDER VORTICAL BACKGROUND CONDITIONS

Acoustic wave propagations have been studied for a long time with both experimental and numerical methods. Most of the analytical solutions for wave propagations are considered for simple environments such as a homogeneous atmospheres. As a result, the analytical solutions are unable to be applied for complicated environments. Numerical methods have become more and more important in acoustics studies after decades of development. The finite difference time-domain method (FDTD) is one of the most commonly used numerical methods in wave propagation studies. Compared with the other methods, the FDTD method is able to include many aspects of sound wave behaviors such as reflection, refraction, and diffraction in the physical problems. In this thesis, the linearized acoustic Euler equations coupled with the immersed boundary method are applied to investigate the sound wave propagation over complex environments. For the three-dimensional simulations of sound wave propagation in long distance, the moving domain method and parallel computing techniques are applied. Based on these approaches, the computational costs are significantly reduced and the simulation efficiency is greatly improved. When looking into the effects of high subsonic vortical flow, a high order WENO scheme is applied for the simulation. In this way the simulation stability can be achieved and the sound scattering of vortical flow can be studied. Then, the numerical scheme is applied to simulate an ultrasonic plane wave propagating through biological tissue. The linearized Euler acoustic equations coupled with the spatial fractional Laplacian operators are used for numerical simulations. The absorption and attenuation effects of the biological lossy media are successfully observed from the simulation results. Throughout this thesis, the simulation results are compared with either experimental measurements or analytical solutions so that the accuracy of the implemented numerical scheme is validated

Linear and nonlinear wave equation models with power law attenuation

Motivated by the need to model high intensity focused ultrasound in lossy media we study linear and nonlinear wave equations that contain non local time fractional derivatives, whose inclusion in our models incorporates the effects of acoustic attenuation. This is characterized by a frequency dependent power law parametrized by a non integer γ ∈ (0, 2), leading to the need for fractional derivative damping. Issues with such integro-differential equations arise in the continuous and discrete analysis due to singularities that occur at t = 0 and as a result of their non local nature. To address these issues we present results that carefully show how to treat such equations for smooth and non smooth solutions, and we derive fast and efficient numerical schemes that pay particular attention to the handling of these non local operators. As well as acoustic attenuation the models we consider will need to account for nonlinear propagation effects that result from the focusing of the ultrasound waves and be modelled on an unbounded domain. To combat this issue, we use a perfectly matched layer. That is, we truncate the unbounded domain to a finite computational domain and impose an absorbing, non reflecting boundary layer around it.Engineering and Physical Sciences Research Council (grant EP/L016508/01

Parallel Lagrangian particle transport : application to respiratory system airways

This thesis is focused on particle transport in the context of high computing performance (HPC) in its widest range, from the numerical modeling to the physics involved, including its parallelization and post-process. The main goal is to obtain a general framework that enables understanding all the requirements and characteristics of particle transport using the Lagrangian frame of reference. Although the idea is to provide a suitable model for any engineering application that involves particle transport simulation, this thesis uses the respiratory system framework. This means that all the simulations are focused on this topic, including the benchmarks for testing, verifying and optimizing the results. Other applications, such as combustion, ocean residuals, or automotive, have also been simulated by other researchers using the same numerical model proposed here. However, they have not been included here in the interest of allowing the project to advance in a specific direction, and facilitate the structure and comprehension of this work. Human airways and respiratory system simulations are of special interest for medical purposes. Indeed, human airways can be significantly different in every individual. This complicates the study of drug delivery efficiency, deposition of polluted particles, etc., using classic in-vivo or in-vitro techniques. In other words, flow and deposition results may vary depending on the geometry of the patient and simulations allow customized studies using specific geometries. With the help of the new computational techniques, in the near future it may be possible to optimize nasal drugs delivery, surgery or other medical studies for each individual patient though a more personalized medicine. In summary, this thesis prioritizes numerical modeling, wide usability, performance, parallelization, and the study of the physics that affects particle transport. In addition, the simulation of the respiratory system should carry out interesting biological and medical results. However, the interpretation of these results will be only done from a pure numerical point of view.Aquesta tesi se centra en el transport de partícules dins el context de la computació d'alt rendiment (HPC), en el seu ventall més ampli; des del model numèric fins a la física involucrada, incloent-hi la part de paral·lelització del codi i de post-procés. L'objectiu principal és obtenir un esquema general que permeti entendre tant els requeriments com les característiques del transport de partícules fent servir el marc de referència Lagrangià. Encara que la idea sigui definir un model capaç¸ de simular qualsevol aplicació en el camp de l'enginyeria que involucri el transport de partícules, aquesta tesi utilitza el sistema respiratori com a temàtica de referència. Això significa que totes les simulacions estan emmarcades en aquest camp d'estudi, incloent-hi els tests de referència, verificacions i optimitzacions de resultats. L'estudi d'altres aplicacions, com ara la combustió, els residus oceànics, l'automoció o l'aeronàutica també han estat dutes a terme per altres investigadors utilitzant el mateix model numèric proposat aquí. Tot i així, aquests resultats no han estat inclosos en aquesta tesi per simplificar-la i avançar en una sola direcció; facilitant així l'estructura i millor comprensió d'aquest treball. Pel que fa al sistema respiratori humà i les seves simulacions, tenen especial interès per a propòsits mèdics. Particularment, la geometria dels conductes respiratoris pot variar de manera considerable en cada persona. Això complica l'estudi en aspectes com el subministrament de medicaments o la deposició de partícules contaminants, per exemple, utilitzant les tècniques clàssiques de laboratori (in-vivo o in-vitro). En altres paraules, tant el flux com la deposició poden canviar en funció de la geometria del pacient i aquí és on les simulacions permeten estudis adaptats a geometries concretes. Gràcies a les noves tècniques de computació, en un futur proper és probable que puguem optimitzar el subministrament de medicaments per via nasal, la cirurgia o altres estudis mèdics per a cada pacient mitjançant una medicina més personalitzada. En resum, aquesta tesi prioritza el model numèric, l'amplitud d'usos, el rendiment, la paral·lelització i l'estudi de la física que afecta directament a les partícules. A més, el fet de basar les nostres simulacions en el sistema respiratori dota aquesta tesi d'un interès biològic i mèdic pel que fa als resultats

Variationally consistent methods for Lagrangian dynamics in continuum mechanics

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (p. 135-143).Rapid dynamics are commonly encountered in industrial applications such as forging, crash tests and many others. These problems are typically non-linear due to large deformations and/or non-linear constitutive relations. Such problems are typically modelled from a Lagrangian viewpoint, where the mesh is attached to the body; hence, large deformations lead to large distortions in the mesh. Explicit numerical methods are considered to be efficient in these cases where large meshes and small time-steps are employed for spatial and temporal resolution. However, incompressible and nearly incompressible materials pose a problem as the timestep stability restriction in explicit methods becomes increasingly severe. Most of the numerical methods employed for such simulations, are developed from discretization of the equations of motion. Recently, Variational Integrators have been developed where the numerical time integration scheme is developed from a variational principle based on Hamilton's principle of stationary action. Such methods ensure conservation of linear and angular momentum, which lead to more physically consistent simulations.(cont.) In this research, numerical methods addressing incompressibility and mesh distortions have been developed under a variational framework. A variational formulation for mesh adaptation procedures, involving local mesh changes for triangular meshes, is presented. Such procedures are very well suited for explicit methods, without significant expense. Conservation properties of such methods are proved and demonstrated. Further, a Fractional Time-Step method is developed, from a variational framework, for incompressible and nearly incompressible problems. Algorithmic details are presented, followed by examples demonstrating the performance of the method.by Sudeep K. Lahiri.Ph.D

Nonlinear Acoustic Waves in Complex Media

[EN] Nature is nonlinear. The linear description of physical phenomena is useful for explain observations with the simplest mathematical models, but they are only accurate for a limited range of input values. In the case of intense acoustics waves, linear models obviate a wide range of physical phenomena that are necessary for accurately describe such high-amplitude waves, indispensable for explain other exotic acoustic waves and mandatory for developing new applied techniques based on nonlinear processes. In this Thesis we study the interactions between nonlinearity and other basic wave phenomena such as non-classical attenuation, anisotropic dispersion and periodicity, and diffraction in specific configurations. First, we present intense strain waves in a chain of cations coupled by realistic interatomic potentials. Here, the nonlinear ionic interactions and lattice dispersion lead to the formation of supersonic kinks. These intrinsically-nonlinear localized dislocations travel long distances without changing its properties and explain the formation of dark traces in mica crystals. Then, we analyze nonlinear wave processes in a system composed of multilayered acoustic media. The rich nonlinear dynamics of this system is characterized by its strong dispersion. Here, harmonic generation processes and the relation with its band structure are presented, showing that the nonlinear processes can be enhanced, strongly minimized or simply modified by tuning the layer parameters. In this way, we show how the dynamics of intense monochromatic waves and acoustic solitons can be controlled by artificial layered materials. In a second part, we include diffraction and analyze four types of singular beams. First, we study nonlinear beams in two dimensional sonic crystals. In this system, the inclusion of anisotropic dispersion is tuned for obtain simultaneous self-collimation for fundamental and second harmonic beams. The conditions for optimal second harmonic generation are presented. Secondly, we present limited diffraction beam generation using equispaced axisymmetric diffraction gratings. The obtained beams are truncated version of zero-th order Bessel beams. Third, the grating spacing can be modified to achieve focusing, where the generated nonlinear beams presents high gain, around 30 dB, with a focal width which is between the diffraction limit and the sub-wavelength regime, but with its characteristic high amplitude side lobes strongly reduced. Finally, we observe that waves diffracted by spiral-shaped gratings generate high-order Bessel beams, conforming nonlinear acoustic vortex. The conditions to obtain arbitrary-order Bessel beams by these passive elements are presented. Finally, the interplay of nonlinearity and attenuation in biological media is studied in the context of medical ultrasound. First, a numerical method is developed. The method solves the constitutive relations for nonlinear acoustics and the frequency power law attenuation of biological media is modeled as a sum of relaxation processes. A new technique for reducing numerical dispersion based on artificial relaxation is included. Second, this method is used to study the harmonic balance as a function of the power law, showing the role of weak dispersion and its impact on the efficiency of the harmonic generation in soft-tissues. Finally, the study concerns the nonlinear behavior of acoustic radiation forces in frequency power law attenuation media. We present how the interplay between nonlinearity and the specific frequency power law of biological media can modify the value for acoustic radiation forces. The relation of the nonlinear acoustic radiation force with thermal effects are also discussed. The broad range of nonlinear processes analyzed in this Thesis contributes to understanding the behavior of intense acoustic waves traveling trough complex media, while its implications for enhancing existent applied acoustics techniques are presented.[ES] La Naturaleza es no lineal. La descripción lineal de los fenómenos físicos es de gran utilidad para explicar nuestras observaciones con modelos matemáticos simples, pero éstos sólo son precisos en un limitado rango de validez. En el caso de onda acústica de alta intensidad, los modelos lineales obvian un amplio rango de fenómenos físicos que son necesarios para describir con precisión las ondas de gran amplitud, pero además son necesarios para explicar otros procesos más exóticos e indispensables para desarrollar nuevas aplicaciones basadas en propagación no lineal. En esta Tesis, estudiamos las interacciones entre no linealidad y otros procesos complejos como atenuación no-clásica, dispersión anisotrópica y periodicidad, y difracción en configuraciones específicas. En primer lugar, presentamos ondas de deformación en una cadena de cationes acoplados por potenciales realísticas. Aquí, las interacciones no lineales entre iones, producen la conformación de kinks supersónicos. Estas dislocaciones localizadas intrínsecamente no lineales viajan por la red largas distancias sin variar sus propiedades, y pueden explicar la formación de trazas en minerales como la mica. Aumentando la escala del problema, estudiamos los procesos acústicos no lineales en medios multicapa. La rica dinámica de estos medios está caracterizada por la fuerte dispersión debido a la periodicidad del sistema. Aquí, estudiamos los procesos de generación de harmónicos, mostrando como modificando la estructura podemos potenciar, minimizar, o simplemente modificar artificialmente la transferencia de energía entre las componentes espectrales, y de esta manera controlar la dinámica de las ondas y solitones en el interior de la estructura. En la segunda parte, incluimos difracción y analizamos cuatro tipos de haces singulares. En primer lugar, analizamos haces ultrasónicos no lineales en cristales de sonido bidimensionales. En este sistema, las propiedades de anisotropía del medio son ajustadas para obtener la auto-colimación simultánea del primer y segundo harmónico. Así, se obtiene la propagación no difractiva para las dos componentes. En segundo lugar, presentamos haces de difracción limitada empleando rejillas de difracción axisimétricas. Por último, demostramos la generación de haces de Bessel de orden superior mediante estructuras en espiral. En la última parte, estudiamos la competición entre no linealidad y la atenuación y dispersión observable en medios biológicos en el contexto de las aplicaciones de biomédicas de los ultrasonidos. En primer lugar desarrollamos un nuevo método computacional para la dependencia frecuencial en forma de ley de potencia de la absorción característica de los tejidos. Este método en dominio temporal es usado posteriormente para revisar los procesos básicos no lineales prestando especial interés en el paper de la dispersión del tejido. Por último, la resolución de las ecuaciones constitutivas nos permite abordar la descripción no lineal de la fuerza de radiación acústica producida en tejidos biológicos, y las implicaciones existentes con la deposición de energía y transferencia de momento para ondas ultrasónicas de alta intensidad. El amplio abanico de procesos no lineales analizados en esta tesis contribuye a una mejor comprensión de la dinámica de las ondas acústicas de alta intensidad en medios complejos, donde las implicaciones existentes en cuanto a la mejora de sus aplicaciones prácticas son puestas de manifiesto.[CA] La Naturalesa és no lineal. La descripció lineal dels fenòmens físics és de gran utilitat per a explicar les nostres observacions amb models matemàtics simples, però aquests sol són precisos en un limitat rang de validesa. En el cas d'ona acústica d'alta intensitat, els models lineals obvien un ampli rang de fenòmens físics que són necessaris per a descriure amb precisió les ones de gran amplitud, però a més són necessaris per a explicar altres processos més exòtics i indispensables per a desenvolupar noves aplicacions basades en propagació no lineal. En aquesta Tesi, estudiem les interaccions entre no-linealitat i altres processos complexos com atenuació no-clàssica, dispersió anisotròpica i periodicitat, i difracció en configuracions específiques. En primer lloc, presentem ones de deformació en una cadena de cations acoblats per potencials realistes. Ací, les interaccions no lineals entre ions, produeixen la conformació de kinks supersònics. Aquestes dislocacions localitzades intrínsecament no lineals viatgen per la xarxa llargues distàncies sense variar les seues propietats, i poden explicar la formació de traces en minerals com la mica. Augmentant l'escala del problema, estudiem els processos acústics no lineals en mitjans multicapa. La rica dinàmica d'aquests mitjans es caracteritza per la forta dispersió a causa de la periodicitat del sistema. Ací, estudiem els processos de generació d'harmònics, mostrant com modificant l'estructura podem potenciar, minimitzar, o simplement modificar artificialment la transferència d'energia entre les components espectrals, i d'aquesta manera controlar la dinàmica de les ones i solitons a l'interior de l'estructura. En la segona part, incloem difracció i analitzem quatre tipus de feixos singulars. En primer lloc, analitzem feixos ultrasònics no lineals en cristalls de so bidimensionals. En aquest sistema, les propietats d'anisotropia del medi són ajustades per a obtenir l'acte-col·limació simultània del primer i segon harmònic. Així, s'obté la propagació no difractiva per a les dues components. En segon lloc, presentem feixos de difracció limitada emprant reixetes de difracció axisimètriques. Per últim, vam demostrar la generació de feixos de Bessel d'ordre superior mitjançant estructures en espiral. En l'última part, estudiem la competició entre no linealitat i l'atenuació i dispersió observable en medis biològics en el context de les aplicacions biomèdiques dels ultrasons. En primer lloc desenvolupem un nou mètode computacional per a la dependència freqüencial en forma de llei de potència de l'absorció característica dels teixits biològics. Aquest mètode en domini temporal és usat posteriorment per a revisar els processos bàsics no lineals prestant especial interés en el paper de la dispersió del teixit. Per últim, la resolució de les equacions constitutives ens permet abordar la descripció no lineal de la força de radiació acústica produïda en teixits biològics, i les implicacions existents amb la deposició d'energia i transferència de moment per a ones ultrasòniques d'alta intensitat. L'ampli ventall de processos no lineals analitzats en aquesta tesi contribueix a una millor comprensió de la dinàmica de les ones acústiques d'alta intensitat en medis complexos, on les implicacions existents quant a la millora de les seues aplicacions practiques són posades de manifest.Jiménez González, N. (2015). Nonlinear Acoustic Waves in Complex Media [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/53237TESISPremios Extraordinarios de tesis doctorale

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal