Modeling and Analysis of Modern Fluids helps researchers solve physical problems observed in fluid dynamics and related fields, such as heat and mass transfer, boundary layer phenomena, and numerical heat transfer. These problems are characterized by nonlinearity and large system dimensionality, and 'exact' solutions are impossible to provide using the conventional mixture of theoretical and analytical analysis with purely numerical methods. To solve these complex problems, this work provides a toolkit of established and novel methods drawn from the literature across nonlinear approximation theory. It covers Pade approximation theory, embedded-parameters perturbation, Adomian decomposition, homotopy analysis, modified differential transformation, fractal theory, fractional calculus, fractional differential equations, as well as classical numerical techniques for solving nonlinear partial differential equations. In addition, 3D modeling and analysis are also covered in-depth.

Developing clean energy and utilizing waste energy has become increasingly vital. Research targeting the advancement of thermally powered adsorption cooling technologies has progressed in the past few decades, and the awareness of fuel cells and thermally activated (heat pipe heat exchangers) adsorption systems using natural refrigerants and/or alternatives to hydrofluorocarbon-based refrigerants is becoming ever more important. Heat Pipes and Solid Sorption Transformations: Fundamentals and Practical Applications concentrates on state-of-the-art adsorption research and technologies for relevant applications based on the use of efficient heat transfer devices-heat pipe and two-phase thermosyphons-with the objectives of energy efficiency and sustainability. This book also discusses heat pipe thermal control as it relates to spacecraft applications. The first few chapters of Heat Pipes and Solid Sorption Transformations: Fundamentals and Practical Applications focus on heating and cooling, the principles of adsorption, adsorption dynamics, and the availability of three-phase boundaries. Other chapters cover successful heat pipe applications and heat-pipe-based thermal control of fuel cells, solid sorption transformers, and electronic components and air-condition devices. The final chapters summarize the achievements in the field of heat and mass transfer study in heat pipes with variable properties such as gas loaded heat pipes. Several configurations of thermosyphons are showcased, with suggested applications. A number of examples of equipment using the thermosyphon technology are presented and, in the final chapter, the concept of flow boiling and flow condensation heat transfer in micochannels is analyzed in detail.

A comprehensive presentation of wicking models developed in academia and industry, Wicking in Porous Materials: Traditional and Modern Modeling Approaches contains some of the most important approaches and methods available, from the traditional Washburn-type models to the latest Lattice-Boltzmann approaches developed during the last few years. It provides a sound conceptual framework for learning the science behind different mathematical models while at the same time being aware of the practical issues of model validation as well as measurement of important properties and parameters associated with various models. Top experts in the field reveal the secrets of their wicking models. The chapters cover the following topics: Wetting and wettability Darcy's law for single- and multi-phase flows Traditional capillary models, such as the Washburn-equation based approaches Unsaturated-flow based methodologies (Richard's Equation) Sharp-front (plug-flow) type approaches using Darcy's law Pore network models for wicking after including various micro-scale fluid-flow phenomena Studying the effect of evaporation on wicking using pore network models Fractal-based methods Modeling methods based on mixture theory Lattice-Boltzmann method for modeling wicking in small scales Modeling wicking in swelling and non-rigid porous media This extensive look at the modeling of porous media compares various methods and treats traditional topics as well as modern technologies. It emphasizes experimental validation of modeling approaches as well as experimental determination of model parameters. Matching models to particular media, the book provides guidance on what models to use and how to use them.

Elastohydrodynamic Lubrication for Line and Point Contacts: Asymptotic and Numerical Approaches describes a coherent asymptotic approach to the analysis of lubrication problems for heavily loaded line and point contacts. This approach leads to unified asymptotic equations for line and point contacts as well as stable numerical algorithms for the solution of these elastohydrodynamic lubrication (EHL) problems. A Unique Approach to Analyzing Lubrication Problems for Heavily Loaded Line and Point Contacts The book presents a robust combination of asymptotic and numerical techniques to solve EHL problems for lightly and heavily loaded line and point contacts. It also proposes a reasonably simple and naturally based regularization approach that produces stable solutions in heavily loaded EHL contacts. The book offers a clear understanding of the processes taking place in heavily loaded line and point EHL contacts as well as of the proper solution structure for EHL problems. It outlines concrete ways to determine important design parameters such as lubrication film thickness and frictional stresses and forces. The book establishes a close link between EHL problems for heavily loaded point and line contacts. Fine Tune Your Methods for Solving Elastohydrodynamic Lubrication Problems In most cases, the equations in the book are derived from first principles. The author describes each of the asymptotic and numerical methods in detail, making it easier for readers to apply them to various problems. The problem solutions are presented in the form of simple analytical formulas, graphs, and tables. Almost all the chapters include exercises that highlight key points and skills. Suitable for engineering and applied mathematics students, this is also a unique resource for researchers and practitioners who want to fine tune their solution methods and design better numerical methods to tackle elastohydrodynamic lubrication problems.

Detailing the major developments of the last decade, the Handbook of Hydraulic Fluid Technology, Second Edition updates the original and remains the most comprehensive and authoritative book on the subject. With all chapters either revised (in some cases, completely) or expanded to account for new developments, this book sets itself apart by approaching hydraulic fluids as a component of a system and focusing on key technological aspects. Written by experts from around the world, the handbook covers all major classes of hydraulic fluids in detail, delving into chemistry, design, fluid maintenance and selection, and other key concepts. It also offers a rigorous overview of hydraulic fluid technology and evaluates the ecological benefits of water and its use as an important alternative technology. This complete overview discusses pumps and motors, valves, and reservoir design, as well as fluid properties and associated topics. These include air entrainment, modulus, lubrication and wear assessment by bench and pump testing, biodegradability, and fire resistance. Contributors also present particularly important material on biodegradable fluids and the use of water as a hydraulic fluid. As the foremost resource on the design, selection, and testing of hydraulic systems and fluids used in engineering applications, this book contains new illustrations, data tables, and practical examples, all updated with essential information on the latest methods. To streamline presentation, relevant content from the first edition has been integrated into this new version, where appropriate. The result is a reference that helps readers develop an unparalleled understanding of the total hydraulic system, including essential hardware, fluid properties, and hydraulic lubricants.

This series of books forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations such as the incompressible and compressible NavierStokes equations. The main emphasis in the first volume is on the mathematical analysis of incompressible models. The second volume is an attempt to achieve a mathematical understanding of compressible Navier-Stokes equations. It is probably the first reference covering the issue of global solutions in the large. It includes entirely new material on compactness properties of solutions for the Cauchy problem, the existence and regularity of stationary solutions, and the existence of global weak solutions. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise, and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena. Pierre-Louis Lions is Professor of Mathematics at the University Paris-Dauphine and of Applied Mathematics at the Ecole Polytechnique.

This textbook provides a concise introduction to the mathematical theory of fluid motion with the underlying physics. Different branches of fluid mechanics are developed from general to specific topics. At the end of each chapter carefully designed problems are assigned as homework, for which selected fully worked-out solutions are provided. This book can be used for self-study, as well as in conjunction with a course in fluid mechanics.

One of the most challenging topics in applied mathematics over the past decades has been the developent of the theory of nonlinear partial differential equations. Many of the problems in mechanics, geometry, probability, etc lead to such equations when formulated in mathematical terms. However, despite a long history of contributions, there exists no central core theory, and the most important advances have come from the study of particular equations and classes of equations arising in specific applications. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models. These models consist of systems of nonlinear partial differential equations like the incompressible and compressible Navier-Stokes equations. The main emphasis in Volume 1 is on the mathematical analysis of incompressible models. After recalling the fundamental description of Newtonian fluids, an original and self-contained study of both the classical Navier-Stokes equations (including the inhomogenous case) and the Euler equations is given. Known results and many new results about the existence and regularity of solutions are presented with complete proofs. The discussion contiatns many interesting insights and remarks. The text highlights in particular the use of modern analytical tools and methods and also indicates many open problems. Volume 2 will be devoted to essentially new results for compressible models. Written by one of the world's leading researchers in nonlinear partial differential equations, Mathematical Topics in Fluid Mechanics will be an indispensable reference for every serious researcher in the field. Its topicality and the clear, concise, and deep presentation by the author make it an outstanding contribution to the great theoretical problems in science concerning rigorous mathematical modelling of physical phenomena. Pierre-Louis Lions is Professor of Mathematics at the University of Paris-Dauphine and of Applied Mathematics at the Ecole Polytechnique.

1. Bursting and Structure of the Turbulence in an Internal Flow Manipulated by Riblets; S. Tardu, T.V. Truong, B. Tanguay. 2. On Near-Wall Turbulence-Generating Events in a Turbulent Boundary Layer on a Riblet Surface; Y.P. Tang, D.G. Clark. 3. Friction Velocity and Virtual Origin Estimates for Mean Velocity Profiles above Smooth and Triangular Riblet Surfaces; A.D. Schwarz-van Manen, A.F.M. van Geloven, J. Nieuwenhuizen, J.C. Stouthart, K.K. Prasad, F.T.M. Nieuwstadt. 4. Viscous Sublayers Analysis of Riblets and Wire Arrays; P. Luchini. 5. Riblet Flow Calculations with a Low Reynolds Number K - epsilon model; L. Djenidi, R.A. Antonia. 6. On the Prediction of Riblet Performance with Engineering Turbulence Models; B.E. Launder, S.P. Li. 7. Modelling the Time Dependent Flow over the Viscous Wall Region; S. Tullis, A. Pollard. 8. Possibility of Drag Reduction using d-Type Roughness; K.S. Choi, N. Fujisawa. 9. The Drag of Three-Dimensional Rectangualr Cavities; E. Savory, N. Toy, P.J. Disimile, R.G. DiMicco. 10. Turbulence Structure of Dilute Polymer and Surfactant Solutions in Artificially Roughened Pipes; H.-W. Bewersdorff, H. Thiel. 11. Effect of External Manipulators on the Heat Transfer on a Flat Plate Turbulent Boundary Layer; A. Hamdouni, J.P. Bonnet.

Fluidization Engineering, Second Edition, expands on its original scope to encompass these new areas and introduces reactor models specifically for these contacting regimes. Completely revised and updated, it is essentially a new book. Its aim is to distill from the thousands of studies those particular developments that are pertinent for the engineer concerned with predictive methods, for the designer, and for the user and potential user of fluidized beds.
Covers the recent advances in the field of fluidization.
Presents the studies of developments necessary to the engineers, designers, and users of fluidized beds.

This newly-translated book takes the reader from the basic principles and conservation laws of hydrodynamics to the description of general atmospheric circulation. Among the topics covered are the Kelvin, Ertel and Rossby-Obukhov invariants, quasi-geostrophic equation, thermal wind, singular Helmholtz vortices, derivation of the Navier-Stokes equation, Kolmogorov's flow, hydrodynamic stability, and geophysical boundary layers. Generalizing V. Arnold's approach to hydrodynamics, the author ingeniously brings in an analogy of Coriolis forces acting on fluid with motion of the Euler heavy top and shows how this is used in the analysis of general atmospheric circulation.

This book is based on popular graduate and undergraduate courses given by F.V.Dolzhansky at the Moscow Institute of Physics and Technology, and is the result of the author's highly acclaimed work in Moscow's Laboratory of Geophysical Hydrodynamics. Each chapter is full of examples and figures, exercises and hints, motivating and illustrating both theoretical and experimental results. The exposition is comprehensive yet user-friendly in engaging and exploring the broad range of topics for students and researchers in mathematics, physics, meteorology and engineering. "

Biofluid mechanics is the study of a certain class of biological problems from the viewpoint of fluid mechanics. Though biofluid mechanics does not involve any new development of the general principles of fluid mechanics, it does involve some new applications of its methods. Complex movements of fluids in the biological system demand for an analysis achievable only with professional fluid mechanics skills, and this volume aims to equip readers with the knowledge needed.This second edition is an enlarged version of the book published in 1992. While retaining the general plan of the first edition, this new edition presents an engineering analysis of the cardiovascular system relevant to the treatment of cardiovascular diseases and combines engineering principles. Included in the material of this volume are: the emerging interdisciplinary field of tissue engineering, which deals with the principles of engineering and life sciences toward the development of biological substitutes that restore, maintain and improve tissue function, and cellular and molecular bioengineering, which involves the mechanical, electrical and chemical processes of the human cell and tries to explain how cellular behaviour arises from molecular-level interactions.The added material in this edition is specifically designed for biomedical engineering professionals and students, and looks at the important applications of biofluid mechanics from an engineering perspective.

Microscale and Nanoscale Heat Transfer: Analysis, Design, and Applications features contributions from prominent researchers in the field of micro- and nanoscale heat transfer and associated technologies and offers a complete understanding of thermal transport in nano-materials and devices. Nanofluids can be used as working fluids in thermal systems; the thermal conductivity of heat transfer fluids can be increased by adding nanoparticles in fluids. This book provides details of experimental and theoretical investigations made on nanofluids for use in the biomechanical and aerospace industries. It examines the use of nanofluids in improving heat transfer rates, covers the numerical approaches for computational fluid dynamics (CFD) simulation of nanofluids, and reviews the experimental results of commonly used nanofluids dispersed in both spherical and nonspherical nanoparticles. It also focuses on current and developing applications of microscale and nanoscale convective heat transfer. In addition, the book covers a wide range of analysis that includes: Solid-liquid interface phonon transfer at the molecular level The validity of the continuum hypothesis and Fourier law in nanochannels Conventional methods of using molecular dynamics (MD) for heat transport problems The molecular dynamics approach to calculate interfacial thermal resistance (ITR) A review of experimental results in the field of heat pipes and two-phase flows in thermosyphons Microscale convective heat transfer with gaseous flow in ducts The application of the lattice Boltzmann method for thermal microflows A numerical method for resolving the problem of subcooled convective boiling flows in microchannel heat sinks Two-phase boiling flow and condensation heat transfer in mini/micro channels, and more Microscale and Nanoscale Heat Transfer: Analysis, Design, and Applications addresses the need for thermal packaging and management for use in cooling electronics and serves as a resource for researchers, academicians, engineers, and other professionals working in the area of heat transfer, microscale and nanoscale science and engineering, and related industries.

Reactive flows encompass a broad range of physical phenomena, interacting over many different time and space scales. Such flows occur in combustion, chemical lasers, the earth's oceans and atmosphere, and in stars. Because of a similarity in their descriptive equations, procedures for constructing numerical models of these systems are also similar, and these similarities can be exploited. Moreover, using the latest technology, what were once difficult and expensive computations can now be done on desktop computers. This new edition of a highly successful book presents algorithms useful for reactive flow simulations, describes trade-offs involved in their use, and gives guidance for building and using models of complex reactive flows. It takes account of the explosive growth in computer technology and the greatly increased capacity for solving complex reactive-flow problems that has occurred since the previous edition was published more than fifteen years ago. An indispensable guide on how to construct, use, and interpret numerical simulations of reactive flows, this book will be welcomed by advanced undergraduate and graduate students, and a wide range of researchers and practitioners in engineering, physics, and chemistry.

Contains Fluid Flow Topics Relevant to Every Engineer Based on the principle that many students learn more effectively by using solved problems, Solved Practical Problems in Fluid Mechanics presents a series of worked examples relating fluid flow concepts to a range of engineering applications. This text integrates simple mathematical approaches that clarify key concepts as well as the significance of their solutions, and fosters an understanding of the fundamentals encountered in engineering. Comprised of nine chapters, this book grapples with a number of relevant problems and asks two pertinent questions to extend understanding and appreciation: What should we look out for? and What else is interesting? This text can be used for exam preparation and addresses problems that include two-phase and multi-component flow, viscometry and the use of rheometers, non-Newtonian fluids, and applications of classical fluid flow principles. While the author incorporates terminology recognized by all students of engineering and provides a full understanding of the basics, the book is written for engineers who already have a rudimentary understanding and familiarity of fluid flow phenomena. It includes engineering concepts such as dimensionless numbers and requires a fluency in basic mathematical skills, such as differential calculus and the associated application of boundary conditions to reach solutions. Solved Practical Problems in Fluid Mechanics thoroughly explains the concepts and principles of fluid flow by highlighting various problems frequently encountered by engineers with accompanying solutions. This text can therefore help you gain a complete understanding of fluid mechanics and draw on your own practical experiences to tackle equally tricky problems.

First concise textbook on Large-Eddy Simulation, a very important method in scientific computing and engineering

From the foreword to the third edition written by Charles Meneveau: ..". this meticulously assembled and significantly enlarged description of the many aspects of LES will be a most welcome addition to the bookshelves of scientists and engineers in fluid mechanics, LES practitioners, and students of turbulence in general."

This book uses the Lagrangian approach, especially useful and convenient for studying large-scale transport and mixing in the ocean, to present a detailed view of ocean circulation. This approach focuses on simulations and on monitoring the trajectories of fluid particles, which are governed by advection equations. The first chapter of the book is devoted to dynamical systems theory methods, which provide the framework, methodology and key concepts for the Lagrangian approach. The book then moves on to an analysis of chaotic mixing and cross-stream transport in idealized models of oceanic meandering currents like the Gulfstream in the Atlantic, the Kuroshio in the Pacific, and Antarctic Circumpolar Current, after which the current state of physical oceanography is reviewed. The latter half of the book applies the techniques and methods already described in order to study eddies, currents, fronts and large-scale mixing and transport in the Far-Eastern seas and the north-western part of the Pacific Ocean. Finally, the book concludes with a discussion of Lagrangian simulation and monitoring of water contamination after the Fukushima disaster of 2011. The propagation of Fukushima-derived radionuclides, surface transport across the Kuroshio Extension current, and the role of mesoscale eddies in the transport of Fukushima-derived cesium isotopes in the ocean are examined, and a comparison of simulation results with actual measurements are presented.Written by some of the world leaders in the application of Lagrangian methods in oceanography, this title will be of benefit to the oceanographic community by presenting the necessary background of the Lagrangian approach in an accessible manner.

This book reports on the German research initiative AeroStruct, a three-year collaborative project between universities and the aircraft industry. It describes the development of an integrated multidisciplinary simulation environment for aircraft analysis and optimization using high-fidelity methods. This system is able to run at a high level of automatism, thus representing a step forward with respect to previous ones. Its special features are: a CAD description that is independent from the disciplines involved, an automated CFD mesh generation and an automated structure model generation including a sizing process. The book also reports on test cases by both industrial partners and DLR demonstrating the advantages of the new environment and its suitability for the industry. These results were also discussed during the AeroStruct closing Symposium, which took place on 13-14 October 2015 at the DLR in Braunschweig, Germany. The book provides expert readers with a timely report on multidisciplinary aircraft design and optimization. Thanks to a good balance between theory and practice, it is expected to address an audience of both academics and professional, and to offer them new ideas for future research and development.

Waves and oscillations are found in large scales (galactic) and microscopic scales (neutrino) in nature. Their dynamics and behavior heavily depend on the type of medium through which they propagate. Waves and Oscillations in Nature: An Introduction clearly elucidates the dynamics and behavior of waves and oscillations in various mediums. It presents different types of waves and oscillations that can be observed and studied from macroscopic to microscopic scales. The book provides a thorough introduction for researchers and graduate students in assorted areas of physics, such as fluid dynamics, plasma physics, optics, and astrophysics. The authors first explain introductory aspects of waves and electromagnetism, including characteristics of waves, the basics of electrostatics and magnetostatics, and Maxwell's equations. They then explore waves in a uniform media, waves and oscillations in hydrodynamics, and waves in a magnetized medium for homogeneous and nonhomogeneous media. The book also describes types of shock waves, such as normal and oblique shocks, and discusses important details pertaining to waves in optics, including polarization from experimental and observational points of view. The book concludes with a focus on plasmas, covering different plasma parameters, quasilinear and nonlinear aspects of plasma waves, and various instabilities in hydrodynamics and plasmas.

This book covers classical and modern aerodynamics, theories and related numerical methods, for senior and first-year graduate engineering students, including: -The classical potential (incompressible) flow theories for low speed aerodynamics of thin airfoils and high and low aspect ratio wings. - The linearized theories for compressible subsonic and supersonic aerodynamics. - The nonlinear transonic small disturbance potential flow theory, including supercritical wing sections, the extended transonic area rule with lift effect, transonic lifting line and swept or oblique wings to minimize wave drag. Unsteady flow is also briefly discussed. Numerical simulations based on relaxation mixed-finite difference methods are presented and explained. - Boundary layer theory for all Mach number regimes and viscous/inviscid interaction procedures used in practical aerodynamics calculations. There are also four chapters covering special topics, including wind turbines and propellers, airplane design, flow analogies and hypersonic (rotational) flows. A unique feature of the book is its ten self-tests and their solutions as well as an appendix on special techniques of functions of complex variables, method of characteristics and conservation laws and shock waves. The book is the culmination of two courses taught every year by the two authors for the last two decades to seniors and first-year graduate students of aerospace engineering at UC Davis.

The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations.The global unique solvability (well-posedness) of initial boundary value problems for the Navier-Stokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the Navier-Stokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.

This monograph presents a synopsis of fluid dynamics based on the personal scientific experience of the author who has contributed immensely to the field. The interested reader will also benefit from the general historical context in which the material is presented in the book. The book covers a wide range of relevant topics of the field, and the main tool being rational asymptotic modelling (RAM) approach. The target audience primarily comprises experts in the field of fluid dynamics, but the book may also be beneficial for graduate students.

This book discusses the recent advances in aircraft design methodologies. It provides an overview of topics such as shape optimization, robust design and aeroelasticity, focusing on fluid-structure numerical methodologies to address static and dynamic aeroelastic problems. It demonstrates that the capability to evaluate the interaction between aerodynamics, inertia and elastic forces is important to avoid drag penalties, control system efficiency loss and generation of potentially dangerous phenomena, such as divergence, control reversal and flutter. The book particularly highlights the advances in "high fidelity" CFD-CSM coupling, describing the latest experimental research to validate the numerical fluid-structure interaction analysis methodologies resulting from the EU-funded RBF4AERO and RIBES projects.

"Hydrothermal and Supercritical Water Processes" presents an overview on the properties and applications of water at elevated temperatures and pressures. It combines fundamentals with production process aspects. Water is an extraordinary substance. At elevated temperatures (and pressures)its properties change dramatically due to the modifications of the molecular structure of bulk water that varies from a stable three-dimensional network, formed by hydrogen bonds at low and moderate temperatures, to an assembly of separated polar water molecules at high and supercritical temperatures. With varying pressure and temperature, water is turned from a solvent for ionic species to a solvent for polar and non-polar substances. This variability and an enhanced reactivity of water have led to many practical applications and to even more research activities, related to such areas as energy transfer, extraction of functional molecules, unique chemical reactions, biomass conversion and fuel materials processing, destruction of dangerous compounds and recycling of useful ones, growth of monolithic crystals, and preparation of metallic nanoparticles.

This book provides an introduction into the wide range of activities that are possible in aqueous mixtures. It is organized to facilitate understanding of the main features, outlines the main applications, and gives access to further information
Summarizes fundamental properties of water for engineering applicationsCompares process and reactor designs Evaluates processes from thermodynamic, economic, and social impact viewpoints"

This book offers a compact primer on advanced numerical flux functions in computational fluid dynamics (CFD). It comprehensively introduces readers to methods used at the forefront of compressible flow simulation research. Further, it provides a comparative evaluation of the methods discussed, helping readers select the best numerical flux function for their specific needs. The first two chapters of the book reviews finite volume methods and numerical functions, before discussing issues commonly encountered in connection with each. The third and fourth chapter, respectively, address numerical flux functions for ideal gases and more complex fluid flow cases- multiphase flows, supercritical fluids and magnetohydrodynamics. In closing, the book highlights methods that provide high levels of accuracy. The concise content provides an overview of recent advances in CFD methods for shockwaves. Further, it presents the author's insights into the advantages and disadvantages of each method, helping readers implement the numerical methods in their own research.