The book presents advanced stochastic models and simulation methods for random flows and transport of particles by turbulent velocity fields and flows in porous media. Two main classes of models are constructed: (1) turbulent flows are modeled as synthetic random fields which have certain statistics and features mimicing those of turbulent fluid in the regime of interest, and (2) the models are constructed in the form of stochastic differential equations for stochastic Lagrangian trajectories of particles carried by turbulent flows. The book is written for mathematicians, physicists, and engineers studying processes associated with probabilistic interpretation, researchers in applied and computational mathematics, in environmental and engineering sciences dealing with turbulent transport and flows in porous media, as well as nucleation, coagulation, and chemical reaction analysis under fluctuation conditions. It can be of interest for students and post-graduates studying numerical methods for solving stochastic boundary value problems of mathematical physics and dispersion of particles by turbulent flows and flows in porous media.

ThisbookcontainstheproceedingsoftheFourthInternationalConference onComputationalFluidDynamics(ICCFD4),heldinGent,Belgiumfrom July10through16,2006. TheICCFDconferenceseriesisanoutcomeofthe mergeroftwoimportantstreamsofconferencesinComputationalFluid- namics:InternationalConferenceonNumericalMethodsinFluidDynamics, ICNMFD(since1996)andInternationalSymposiumonComputationalFluid Dynamics,ISCFD(since1985). In1998itwasdecidedtojointhetwoand ICCFD emerged as a biannual meeting, held in Kyoto in 2000, Sydney in 2002, Toronto in 2004 and Gent in 2006. Thus, the ICCFD series became theleadinginternationalconferenceseriesforscientists,mathematiciansand engineersinterestedinthecomputationof?uid?ow. The4theditionoftheconferencehasattracted200participantsfromall overtheworld;270abstractswerereceived,ofwhich135wereselectedina carefulpeerreviewprocessbytheexecutivecommittee(C. H. Bruneau,J. -J. Chattot,D. Kwak,N. Satofuka,D. W. Zingg,E. DickandH. Deconinck)for oralpresentationandafurther21forposterpresentation. Thepaperscontainedintheseproceedingsprovideanexcellentsnapshot of the ?eld of Computational Fluid Dynamics as of 2006. Invited keynote lecturesbyrenownedresearchersareincluded,withcontributionsinthe?eld ofdiscretizationschemes,high-endcomputingandengineeringchallenges,and two-phase?ow. Thesekeynotecontributionsarecomplementedby137regular papersonthemostdiverseaspectsofCFD: -Innovativealgorithmdevelopmentfor?owsimulation,optimisationandc- trol:higher-ordermethods(DG,FV,FEandRDmethods),iterativemethods andmultigrid,solutionadaptivemeshtechniques,errorestimationandc- trol,parallelalgorithms. -Innovativemodelingof?owphysicsintheareaofcompressibleandinc- pressible ?ows: hypersonic and reacting ?ows, two-phase ?ows, turbulence (LES,DES,DNS,andtransition),vortexdynamics,boundarylayerstability, multi-scalephysics,magnetohydrodynamics. Preface VII -advancedapplicationsusingtheabovementionedinnovativetechnology,and multidisciplinaryapplicationsincludingaero-elasticityandaero-acoustics. ThanksareduetooursponsorsNASA,theFWOResearchFoundation FlandersandtheEuropeanUnionthroughtheEUA4XMarieCurieproject. Inparticular,thegenerousgrantfromNASAisakeyfactorinthesuccessof thisconferenceseriesandthepublicationoftheseProceedings. Wealsowouldliketothankthesta?andPhDstudentsofthevonKarman InstituteandtheDepartmentof?ow,heatandcombustionmechanicsofthe University of Gent, for the help they provided toward the success of this conference. Sint-Genesius-Rode,Belgium HermanDeconinck vonKarmanInstituteforFluidDynamics Ghent,Belgium ErikDick GhentUniversity September2006 ConferenceChair Contents PartIInvitedSpeakers Twonewtechniquesforgeneratingexactlyincompressible approximatevelocities BernardoCockburn...3 RoleofHigh-EndComputinginMeetingNASA'sScience andEngineeringChallenges RupakBiswas,EugeneL. Tu,WilliamR. VanDalsem...14 RecentAdvancesofMulti-phaseFlowComputationwiththe AdaptiveSoroban-gridCubicInterpolatedPropagation(CIP) Method TakashiYabe,YouichiOgata,KenjiTakizawa...29 PartIISchemes OntheComputationofSteady-StateCompressibleFlows UsingaDGMethod HongLuo,JosephD. Baum,RainaldL..ohner...47 Space-TimeDiscontinuousGalerkinMethodforLarge AmplitudeNonlinearWaterWaves YanXu,JaapJ. W. vanderVegt...53 AdiscontinuousGalerkinmethodwithHancock-typetime integrationforhyperbolicsystemswithsti?relaxationsource terms YoshifumiSuzuki,BramvanLeer...59 Contents IX VeryHighOrder,Non-OscillatoryFluctuationDistribution Schemes M. E. Hubbard,N. Z. Mebrate...65 High-orderresidualdistribution:discontinuitycapturing crosswinddissipationanddi?usion N. Villedieu-Ligout,M. Ricchiuto,H. Deconinck...7 1 High-OrderFluctuation-SplittingSchemesforAdvection- Di?usionEquations HiroakiNishikawaandPhilipRoe...77 ConstructionofHigherOrderResidualDistributionSchemes R'emiAbgrallandC'edricTav'e...83 Stableandconvergentresidualdistributionforti- dependentconservationlaws MarioRicchiuto,R'emiAbgrall...89 AnALEFormulationoftheMultidimensionalResidual DistributionSchemeforComputationsonMovingMeshes Jir'?Dobes,HermanDeconinck...95 SolutionofthesteadyEulerequationsusingFluctuation Splittingschemesonquadrilateralelements D. T. Rubino,P. DePalma,G. Pascazio,M. Napolitano ...101 AResidual-BasedCompactSchemeforAll-SpeedFlowson UnstructuredGrids ChristopheCorre,AlbertoBeccantini,ThibaudKloczko ...107 VorticityPreservingSchemeforUnsteadyCompressible Flows FabriceFalissard,AlainLerat,JacquesSid'es ...113 ExtensionoftheSDMethodtoViscousFlowonUnstructured Grids Z. J. Wang,YuzhiSun,C. Liang,Yen,Liu...119 StrictlyStableHighOrderDi?erenceMethodsforthe CompressibleEulerandNavier-StokesEquations BernhardMul ..ler...125 UniformFlowPreservingPropertyofHighOrderUpwind FiniteDi?erenceSchemesonGeneralizedCoordinateSystem TakuNonomura,NobuyukiIizuka,KozoFujii...1 31 X Contents ImplementationofanEnhancedFluxFormulationfor UnsteadyNavier-StokesSolutions G. Xia,S. Sardeshmukh,V. Sankaran,C. L. Merkle...137 ComputationofEigenspacesofHyperbolicSystems S. K. Godunov,O. B. Feodoritova,V. T. Zhukov...143 AProposedCuretotheCarbunclePhenomenon FarzadIsmail,PhilipL. Roe,HiroakiNishikawa ...149 TheHighOrderWLSQRSchemeanditsApplicationsin Turbomachinery Jivr'?Furst ...

Mathematical Modeling in Diffraction Theory: Based on A Priori Information on the Analytical Properties of the Solution provides the fundamental physical concepts behind the theory of wave diffraction and scattered wave fields as well as its application in radio physics, acoustics, optics, radio astronomy, biophysics, geophysics, and astrophysics. This book provides a coherent discussion of several advanced topics that have the potential to push forward progress in this field. It begins with examples illustrating the importance of taking a priori information into account when developing algorithms for solving diffraction problems, with subsequent chapters discussing the basic analytical representations of wave fields, the auxiliary current and source methods for solving the problems of diffraction at compact scatterers, the null field and matrix methods that are widely used to solve problems in radio-physics, radio-astronomy, and biophysics, and the continued boundary condition and pattern equation method.

This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's function approach. For the first time, Green's functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.

1 Grundlagen der Dynamik regelungstechnischer Systeme.- 1.1 Allgemeine Zielsetzung der Regelungstechnik.- 1.2 Regelkreis.- 1.3 Voraussetzungen fur Blockorientierung und Regelkreisbildung.- 1.4 Aufgaben der Regelungstechnik.- 1.5 UEbertragungsfunktion und Regelungssystemtheorie.- 1.6 Anfangsbedingungen und Nullstellen der UEbertragungsfunktion.- 1.7 Ausgangssignal Xa(s) bei x a(k)(0?)=0.- 1.8 Nichtverschwindende Vorgeschichte xa(k)(0?)?0.- 1.9 Analyse im Spektralbereich. Verknupfung mehrerer Elemente.- 1.10 Regelstrecke und Stoergroessen.- 1.11 Einschleifiger Standardregelkreis.- 1.12 Sensitivitat.- 1.13 Differentielle Sensitivitat fur den Standardregelkreis.- 1.14 Linearisierung.- 1.15 Regelkreis im Signalflussdiagramm.- 1.16 Spezielle Elemente regelungstechnischer Systeme.- 1.16.1 Rationale UEbertragungselemente.- 1.16.2 Totzeit-Elemente.- 1.16.3 Allpass-Elemente.- 1.16.4 Laufzeitelemente.- 2 Regelkreisanalyse im Zeitbereich.- 2.1 Regelkreis-Reaktion auf einfache Signale.- 2.2 Mehrfache Polstellen von Xa(s).- 2.3 Naherung fur kleine Zeitwerte.- 2.4 Naherung fur grosse Zeitwerte.- 2.5 Faltungsintegral und Naherung durch Faltungssumme.- 2.6 Regelungen mit Totzeitelementen.- 3 Formulierung kontinuierlicher Regelungssysteme im Zustandsraum.- 3.1 Grundlagen.- 3.2 Transitionsmatrix (Fundamentalmatrix).- 3.3 Potenzreihenentwicklung der Transitionsmatrix.- 3.4 Zustandsregler. Fuhrungs- und Stoerungsverhalten.- 3.5 Vorfilterbemessung.- 4 Analyseverfahren im Frequenzbereich.- 4.1 Frequenzgang.- 4.2 Ortskurven des Frequenzgangs.- 4.3 Ortskurven von typischen stabilen Regelkreis-Element en.- 4.4 Ortskurven instabiler Regelkreiselemente.- 4.5 Frequenzgangsortskurve des Regelkreises.- 4.6 Ermittlung von Zeitbereichssignalen aus dem Frequenzbereich.- 4.7 Ermittlung des Frequenzganges aus der gemessenen Systemantwort.- 4.8 Bode-Diagramm.- 4.9 Phasenminimum-Beziehungen.- 4.10 Knickstellen der Regelschleife und des Regelkreises.- 4.11 H?-Norm einer UEbertragungsfunktion.- 5 Regelstrecken im Regelkreis.- 5.1 Antriebe. Allgemeines.- 5.2 Stromrichtergespeiste Gleichstromantriebe.- 5.3 Stromleitverfahren.- 5.4 Begrenzungsregelung.- 5.5 Kupplungselastizitat.- 5.6 Umrichtergespeiste Asynchronmaschine.- 5.7 Thermische Regelstrecken.- 5.7.1 Durchlauferhitzer, Warmetauscher.- 5.7.2 Kessel und Turbine.- 5.8 Hydraulische Regelstrecken.- 5.9 Pneumatische Regelstrecke.- 5.10 Mechanische Positionsregelstrecken.- 5.10.1 Einfache Fahrzeuglenkung.- 5.10.2 Balancierung.- 5.10.3 Passagierflugzeug.- 5.10.4 Raketenantrieb.- 5.11 Verfahrenstechnische Regelstrecken.- 5.12 Elektronische und nachrichtentechnische Regelstrecken.- 5.12.1 Verstarkungsausgleich.- 5.12.2 Scharfabstimmung.- 5.12.3 Zeilensynchronisierung.- 5.12.4 Rauschunterdruckung.- 5.13 Phase-Locked Loops (PLL).- 5.13.1 Phase-Locked Loop in analoger Ersatzrechnung.- 5.13.2 Regelungen an einem CD-Player.- 5.14 Schaltzeichen (Sinnbilder) fur technische Regelstrecken.- 5.15 Volkswirtschaftliche Regelungen.- 5.16 Physiologische und psychische Regelkreise.- 5.17 Soziologische Regelungen.- 6 Stellglieder und Verstarker.- 6.1 Stromrichterstellglieder.- 6.2 Umrichter fur Drehfeldmaschinen.- 6.3 Stellmotoren fur mechanische Positionierung.- 6.4 Stellglieder fur Flussigkeits-, Gasstroeme u. koernige Stoffe.- 6.5 Schaltzeichen fur Stellglieder und Verstarker.- 7 Regelungstechnischer Einsatz von Sensoren und Messumformern.- 7.1 Anforderungen.- 7.2 Messrauschen.- 7.3 Leistung eines Rauschsignales.- 8 Identifikationsverfahren.- 8.1 Auswertung der Sprungantwort von PDT1-Elementen.- 8.2 Auswertung der Sprungantwort von PT2-Elementen.- 8.3 Wendetangentenmethode bei PT2-Elementen.- 8.4 Auswertung der Sprungantwort von IT1-Elementen.- 8.5 Momentenmethode an der Gewichtsfunktion.- 8.6 Identifikation mit Hilfsregler.- 8.7 Identifikation mit fiktivem Serienelement.- 8.8 Regressionsanalyse. Quadratische Ausgleichsrechnung.- 9 Regler. Ausfuhrung und Dimensionierung.- 9.1 Operationsverstarker.- 9.2 Elektr

This volume presents the Proceedings of the 10th International Conference on Vibration Problems, 2011, Prague, Czech Republic. ICOVP 2011 brings together again scientists from different backgrounds who are actively working on vibration-related problems of engineering both in theoretical and applied fields, thus facilitating a lively exchange of ideas, methods and results between the many different research areas. The aim is that reciprocal intellectual fertilization will take place and ensure a broad interdisciplinary research field. The topics, indeed, cover a wide variety of vibration-related subjects, from wave problems in solid mechanics to vibration problems related to biomechanics. The first ICOVP conference was held in 1990 at A.C. College, Jalpaiguri, India, under the co-chairmanship of Professor M.M. Banerjee and Professor P. Biswas. Since then it has been held every 2 years at various venues across the World.

This book describes significant tractable models used in solid mechanics - classical models used in modern mechanics as well as new ones. The models are selected to illustrate the main ideas which allow scientists to describe complicated effects in a simple manner and to clarify basic notations of solid mechanics. A model is considered to be tractable if it is based on clear physical assumptions which allow the selection of significant effects and relatively simple mathematical formulations. The first part of the book briefly reviews classical tractable models for a simple description of complex effects developed from the 18th to the 20th century and widely used in modern mechanics. The second part describes systematically the new tractable models used today for the treatment of increasingly complex mechanical objects - from systems with two degrees of freedom to three-dimensional continuous objects.

This book is written for scientists involved in the calibration of viscometers. A detailed description for stepping up procedures to establish the viscosity scale and obtaining sets of master viscometers is given in the book. Uncertainty considerations for standard oils of known viscosity are presented. The modern viscometers based on principles oftuning fork, ultrasonic, PZT, plate waves, Love waves, micro-cantilever and vibration of optical fiber are discussed to inspire the reader to further research and to generate improved versions. The primary standard for viscosity is pure water. Measurements of its viscosity with accuracy/uncertainty achieved are described. The principles of rotational and oscillation viscometers are explained to enhance the knowledge in calibration work. Devices used for specific materials and viscosity in non SI units are discussed with respect to the need to correlate viscosity values obtained by various devices. The description of commercial viscometers meets the needs of the user."

This volume collects the edited and reviewed contributions presented in the 5th iTi Conference in Bertinoro covering fundamental aspects in turbulent flows. In the spirit of the iTi initiative, the volume is produced after the conference so that the authors had the possibility to incorporate comments and discussions raised during the meeting.

Turbulence presents a large number of aspects and problems, which are still unsolved and which challenge research communities in engineering and physical sciences both in basic and applied research. The book presents recent advances in theory related to new statistical approaches, effect of non-linearities and presence of symmetries. This edition presents new contributions related to the physics and control of laminar-turbulent transition in wall-bounded flows, which may have a significant impact on drag reduction applications. Turbulent boundary layers, at increasing Reynolds number, are the main subject of both computational and experimental long research programs aimed at improving our knowledge on scaling, energy distribution at different scales, structure eduction, roughness effects to name only a few. Like previous editions several numerical and experimental analysis of complex flows, mostly related to applications, are presented.

The structure of the present book is as such that contributions have been bundled according to covering topics i.e. I Theory, II Stability, III Wall bounded flows, IV, Complex flows, V Acoustic, VI Numerical methods.

The volume is dedicated to the memory of Prof. Rudolf Friedrich who prematurely died in Munster/Germany on the 16th of August 2012. In his honor the conference has started with a special session dedicated to his work.

"

This work contains the proceedings of an International Astronomical Symposium devoted to the interactions between physics and dynamics in the solar system, especially with regard to the small bodies (asteroids, comets, meteors). These two topics were traditionally considered as almost independent, but their interactions are increasingly being reviewed as the key to an understanding of the formation and evolution of the solar system. For instance, the rotational dynamics of planets have a profound influence on their climate. On the other hand, a good understanding of the complicated dynamics of asteroids and the identification of families of bodies born from the break-up of a parent body may tell us much about the formation and the evolution of the solar system. All these, and several related questions are discussed in these proceedings, which should be of interest to both physicists and dynamicists.

This volume contains 27 contributions to the Forth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing presented in October 2009 in Freiburg, Germany. The workshop was organized jointly by the High Performance Computing Center Stuttgart (HLRS), the Institute of Computational Technologies of the Siberian Branch of the Russian Academy of Sciences (ICT SB RAS) and the Section of Applied Mathematics of the University of Freiburg (IAM Freiburg) The contributions range from computer science, mathematics and high performance computing to applications in mechanical and aerospace engineering. They show a wealth of theoretical work and simulation experience with a potential of bringing together theoretical mathematical modelling and usage of high performance computing systems presenting the state of the art of computational technologies.

This thesis presents valuable contributions to several aspects of the rapidly growing field of gravitational wave astrophysics. The potential sources of gravitational waves in globular clusters are analyzed using sophisticated dynamics simulations involving intermediate mass black holes and including, for the first time, high-order post-Newtonian corrections to the equations of motion. The thesis further demonstrates our ability to accurately measure the parameters of the sources involved in intermediate-mass-ratio inspirals of stellar-mass compact objects into hundred-solar-mass black holes. Lastly, it proposes new techniques for the computationally efficient inference on gravitational waves. On 14 September 2015, the LIGO observatory reported the first direct detection of gravitational waves from the merger of a pair of black holes. For a brief fraction of a second, the power emitted by this merger exceeded the combined output of all stars in the visible universe. This has since been followed by another confirmed detection and a third candidate binary black hole merger. These detections heralded the birth of an exciting new field: gravitational-wave astrophysics.

Mathematics is undoubtedly the key to state-of-the-art high technology. It is aninternationaltechnicallanguageandprovestobeaneternallyyoungscience to those who have learned its ways. Long an indispensable part of research thanks to modeling and simulation, mathematics is enjoying particular vit- ity now more than ever. Nevertheless, this stormy development is resulting in increasingly high requirements for students in technical disciplines, while general interest in mathematics continues to wane at the same time. This book and its appendices on the Internet seek to deal with this issue, helping students master the di?cult transition from the receptive to the productive phase of their education. The author has repeatedly held a three-semester introductory course - titled Higher Mathematics at the University of Stuttgart and used a series of "handouts" to show further aspects, make the course contents more motiv- ing, and connect with the mechanics lectures taking place at the same time. One part of the book has more or less evolved from this on its own. True to the original objective, this part treats a variety of separate topics of varying degrees of di?culty; nevertheless, all these topics are oriented to mechanics. Anotherpartofthisbookseekstoo?eraselectionofunderstandablereal- ticmodelsthatcanbeimplementeddirectlyfromthemultitudeofmathema- calresources.TheauthordoesnotattempttohidehispreferenceofNumerical Mathematics and thus places importance on careful theoretical preparation.

Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence. Particular emphasis is given to low- dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiment is illustrated, and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of basic, underlying physics. This monograph will appeal to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program. It will also be of use to researchers working on both applied, fundamental theoretical and experimental aspects of thin film flows, as well as engineers and technologists dealing with processes involving isothermal or heated films. This monograph is largely self-contained and no background on interfacial fluid mechanics is assumed.

This book deals in a modern manner with a family of named problems from an old and mature subject, classical elasticity. These problems are formulated over either a half or the whole of a linearly elastic and isotropic two- or three-dimensional space, subject to loads concentrated at points or lines. The discussion of each problem begins with a careful examination of the prevailing symmetries, and proceeds with inverting the canonical order, in that it moves from a search for balanced stress fields to the associated strain and displacement fields. The book, although slim, is fairly well self-contained; the only prerequisite is a reasonable familiarity with linear algebra (in particular, manipulation of vectors and tensors) and with the usual differential operators of mathematical physics (gradient, divergence, curl, and Laplacian); the few nonstandard notions are introduced with care. Support material for all parts of the book is found in the final Appendix.

Ultrasound has found an increasing number of applications in recent years due to greatly increased computing power. Ultrasound devices are often preferred over other devices because of their lower cost, portability, and non-invasive nature. Patients using ultrasound can avoid the dangers of radiological imaging devices such as x-rays, CT scans, and radioactive media injections. Ultrasound is also a preferred and practical method of detecting material fatique and defects in metals, composites, semiconductors, wood, etc.
Detailed appendices contain useful formulas and their derivations, technical details of relevant theories
The FAQ format is used where a concept in one answer leads to a new Q&A

This volume collects contributions to the 14th Symposium of the STAB (German Aerospace Aerodynamics Association). The association involves German scientists and engineers from universities, research establishments and industry who are doing research and project work in numerical and experimental fluid mechanics and aerodynamics, mainly for aerospace but for other applications, too. The volume gives a broad overview of ongoing work in Germany in this field.

This work represents one of the first comprehensive attempts to seamlessly integrate two highly active interdisciplinary domains in soft matter science - microfluidics and liquid crystals (LCs). Motivated by the lack of fundamental experiments, Dr. Sengupta initiated systematic investigation of LC flows at micro scales, gaining new insights that are also suggestive of novel applications. By tailoring the surface anchoring of the LC molecules and the channel dimensions, different topological constraints were controllably introduced within the microfluidic devices. These topological constraints were further manipulated using a flow field, paving the way for Topological Microfluidics. Harnessing topology on a microfluidic platform, as described in this thesis, opens up capabilities beyond the conventional viscous-dominated microfluidics, promising potential applications in targeted delivery and sorting systems, self-assembled motifs, and novel metamaterial fabrications.

This book focuses on the phenomenon of sediment erosion and resuspension in the Yellow River delta, China, which is a vital issue involved in understanding the sediment transport processes in estuarine and coastal environments, and how these contribute to the nature and distribution of geohazards in the subaqueous Yellow River delta and Bohai Sea. The most important sections of this book will be the detailed physical mechanisms and theoretical models of sediment erosion and resuspension problem fully considering the wave-induced seabed dynamic response to waves, which are particularly useful for postgraduate students and junior researchers entering the discipline of estuary and coastal sedimentation, marine geotechnical engineering, estuary and coastal engineering, harbor and waterway engineering and coastal environmental protection. This book can also serve as a textbook for advanced graduate students of Marine Engineering Geology and Estuarine Sediment Dynamics.

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science.

Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows.

"Mathematical and Numerical Foundations of Turbulence Models and Applications" is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.

This volume presents applications of the Pi-Theorem to fluid mechanics and heat and mass transfer. The Pi-theorem yields a physical motivation behind many flow processes and therefore it constitutes a valuable tool for the intelligent planning of experiments in fluids. After a short introduction to the underlying differential equations and their treatments, the author presents many novel approaches how to use the Pi-theorem to understand fluid mechanical issues. The book is a great value to the fluid mechanics community, as it cuts across many subdisciplines of experimental fluid mechanics.

This book is a comprehensive state-of-the-knowledge summation of shock wave reflection phenomena from a phenomenological point of view. It includes a thorough introduction to oblique shock wave reflections, dealing with both regular and Mach types. It also covers in detail the corresponding two- and three-shock theories. The book moves on to describe reflection phenomena in a variety of flow types, as well as providing the resolution of the Neumann paradox.

This book presents the theory of continuum mechanics for mechanical, thermodynamical, and electrodynamical systems. It shows how to obtain governing equations and it applies them by computing the reality. It uses only open-source codes developed under the FEniCS project and includes codes for 20 engineering applications from mechanics, fluid dynamics, applied thermodynamics, and electromagnetism. Moreover, it derives and utilizes the constitutive equations including coupling terms, which allow to compute multiphysics problems by incorporating interactions between primitive variables, namely, motion, temperature, and electromagnetic fields. An engineering system is described by the primitive variables satisfying field equations that are partial differential equations in space and time. The field equations are mostly coupled and nonlinear, in other words, difficult to solve. In order to solve the coupled, nonlinear system of partial differential equations, the book uses a novel collection of open-source packages developed under the FEniCS project. All primitive variables are solved at once in a fully coupled fashion by using finite difference method in time and finite element method in space.