Vol.4 : Computational Turbulent Incompressible Flow

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March 23, 2007, at 06:40 AM by claes -
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  • Clay Mathematics Institute Millenium Prize Problem on Navier-Stokes equations,
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  • The Clay Mathematics Institute Millenium Prize Problem on Navier-Stokes equations,
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  • flying
  • sailing
  • racing
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  • flying,
  • sailing,
  • racing,
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and and a variety of advanced applications unraveling Secrets of

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and a variety of advanced applications unraveling Secrets of

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for computational simulation and modeling of turbulence including Reynolds Averaged Navier-Stokes RANS,

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for computational simulation and modeling of turbulence including Reynolds Averaged Navier-Stokes RANS, and

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presentations

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Welcome to the homepage of the book Computational Turbulent Incompressible Flow, Volume 4 in the Springer book series of the

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Welcome to the homepage of the book Computational Turbulent Incompressible Flow, Volume 4 in the Springer book series Applied Mathematics: Body and Soul of the

March 19, 2007, at 05:33 PM by claes -
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Welcome to the homepage of the book [[http://www.springer.com/west/home/generic/search/results?SGWID=4-40109-22-173700518-0 | Computational Turbulent Incompressible Flow, Volume 4]] in the Springer book series of the

to:

Welcome to the homepage of the book Computational Turbulent Incompressible Flow, Volume 4 in the Springer book series of the

March 19, 2007, at 05:32 PM by claes -
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Welcome to the homepage of the book Computational Turbulent Incompressible Flow, Volume 4 in the Springer book series of the

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Welcome to the homepage of the book [[http://www.springer.com/west/home/generic/search/results?SGWID=4-40109-22-173700518-0 | Computational Turbulent Incompressible Flow, Volume 4]] in the Springer book series of the

March 19, 2007, at 03:50 PM by claes -
March 19, 2007, at 03:50 PM by claes -
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%The homepage is organized into

%*Forum: Mysteries, Secrets and Reception of New Ideas %*Computations Expo %*Education %*Software - FEniCS

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March 19, 2007, at 07:45 AM by claes -
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Further, the Reception by different scientific communities of the new ideas and results of the book,Fori

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Further, the Reception by different scientific communities of the new ideas and results of the book

March 19, 2007, at 07:45 AM by claes -
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classical open problems or Mysteries including

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classical open problems or Mysteries including

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and and a variety of advanced applications unraveling Secrets of

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and and a variety of advanced applications unraveling Secrets of

March 19, 2007, at 07:43 AM by claes -
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Further, the Reception by different scientific communities of the new ideas and results of the book,Fori

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Further, the Reception by different scientific communities of the new ideas and results of the book,Fori

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such as computational software including output in the form of movies, educational material,

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such as computational software including output in the form of movies, educational material,

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and a forum for debate of key issues.

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Further, the Reception by different scientific communities of the new ideas and results of the book,

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Further, the Reception by different scientific communities of the new ideas and results of the book,Fori

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The homepage is organized into

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%The homepage is organized into

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March 19, 2007, at 07:38 AM by claes -
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such as computational software including output in the form of movies, educational material,

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such as computational software including output in the form of movies, educational material,

March 18, 2007, at 09:30 AM by claes -
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is presented in referee's reviews.

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is presented on a debate forum including referee's reviews.

March 18, 2007, at 09:28 AM by claes -
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Further, the Reception by different scientific communities of the new results of the book,

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Further, the Reception by different scientific communities of the new ideas and results of the book,

March 18, 2007, at 09:27 AM by claes -
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Further, the Reception by different scientific of the new results presented

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Further, the Reception by different scientific communities of the new results of the book,

March 18, 2007, at 09:26 AM by claes -
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  • Clay Mathematics Institute Millenium Prize Problem on Navier-Stokes equations,
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Further, the official formulation of the Clay Institute Prize Problem is challenged and a new formulation and (partial) resolution is presented.

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Further, the Reception by different scientific of the new results presented is presented in referee's reviews.

March 18, 2007, at 09:15 AM by claes -
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classical open problems including

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classical open problems or Mysteries including

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and and a variety of advanced applications unraveling secrets of

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and and a variety of advanced applications unraveling Secrets of

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March 15, 2007, at 10:20 PM by claes -
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The homepage is organized into

March 15, 2007, at 10:18 PM by claes -
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Large Eddy Simulation LES and Smagorinsky turbulent viscosity. The power of G2 is demonstrated in new solutions to

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Large Eddy Simulation LES with Smagorinsky turbulent viscosity. The power of G2 is demonstrated in new solutions to

March 15, 2007, at 10:17 PM by claes -
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the Navier-Stokes equations.

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existence, uniqueness and regularity of solutions to the Navier-Stokes equations.

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turbulent and defies analytical mathematical representation. One of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

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turbulent and defies analytical mathematical representation. Accordingly, one of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

March 15, 2007, at 10:14 PM by claes -
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such as computational software including output in the form of movies

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such as computational software including output in the form of movies, educational material, presentations

March 15, 2007, at 01:14 PM by Johan Hoffman -
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March 15, 2007, at 01:12 PM by Johan Hoffman -
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Welcome to the homepage of Computational Turbulent Incompressible

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Welcome to the homepage of the book Computational Turbulent Incompressible

March 14, 2007, at 09:23 AM by claes -
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  • Loschmidt's paradox of irreversibility in reversible Hamiltonian systems.
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  • Loschmidt's paradox of irreversibility in reversible Hamiltonian systems,
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Further, the official formulation of the Clay Institute Prize Problem is challenged.

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Further, the official formulation of the Clay Institute Prize Problem is challenged and a new formulation and (partial) resolution is presented.

March 14, 2007, at 09:22 AM by claes -
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The book presents a fresh attack on the open problems based on finite element computation and a new concept of output uniqueness combined into duality-based a posteriori error estimation

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The book presents a fresh attack on the open problems of turbulent flow, based on finite element computation and a new concept of output uniqueness combined with duality-based a posteriori error estimation,

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of turbulence modeling including Reynolds Averaged Navier-Stokes RANS, Large Eddy Simulation LES and Smagorinsky viscosity. The power of G2 is demonstrated in new solutions to

to:

for computational simulation and modeling of turbulence including Reynolds Averaged Navier-Stokes RANS, Large Eddy Simulation LES and Smagorinsky turbulent viscosity. The power of G2 is demonstrated in new solutions to

March 14, 2007, at 09:19 AM by claes -
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these open problems.

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the Navier-Stokes equations.

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turbulent, which defies analytical mathematical representation. Accordingly one of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

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turbulent and defies analytical mathematical representation. One of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

March 14, 2007, at 09:12 AM by claes -
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solutions have remained without convincing anwers into our time. The reason is that slightly viscous flow always is

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solutions, have remained without convincing anwers into our time. The reason is that slightly viscous flow always is

March 14, 2007, at 09:12 AM by claes -
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Here you can find a variety of material complementing and expanding the material presented in the book such as computational software including output in the form of movies

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Here you can find a variety of material complementing and expanding the book, such as computational software including output in the form of movies

March 13, 2007, at 10:18 PM by claes -
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solutions have remained essentially open into our time. The reason is that slightly viscous flow always is turbulent.

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solutions have remained without convincing anwers into our time. The reason is that slightly viscous flow always is turbulent, which defies analytical mathematical representation.

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the open questions.

The book presents a fresh attack on the basic open problems based on finite element

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these open problems.

The book presents a fresh attack on the open problems based on finite element

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of turbulence modeling including Reynolds Averaged Navier-Stokes RANS, Large Eddy Simulation LES, Smagorinsky turbulent viscosity. The power of G2 is demonstrated in new solutions to

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of turbulence modeling including Reynolds Averaged Navier-Stokes RANS, Large Eddy Simulation LES and Smagorinsky viscosity. The power of G2 is demonstrated in new solutions to

March 13, 2007, at 10:13 PM by claes -
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The web page contains a Forum for exchange of ideas, and Expo for computational results, aspects of Education and software:

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March 13, 2007, at 10:12 PM by claes -
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The book presents a fresh attack on the basic problems based on finite element

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The book presents a fresh attack on the basic open problems based on finite element

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Smagorinsky turbulent viscosity. The power of G2 is demonsrted in new solutions to classical open problems including d'Alembert's paradox of zero drag in inviscid flow, Sommerfeld's paradox of stability of Couette flow at all Reynolds numbers, and Loschmidt's paradox of irreversibility in reversible Hamiltonian systems.

to:

Smagorinsky turbulent viscosity. The power of G2 is demonstrated in new solutions to classical open problems including

  • d'Alembert's paradox of zero drag in inviscid flow,
  • Sommerfeld's paradox of stability of Couette flow at all Reynolds numbers,
  • Loschmidt's paradox of irreversibility in reversible Hamiltonian systems.

and and a variety of advanced applications unraveling secrets of

  • flying
  • sailing
  • racing
  • ball sports.
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The material in this book in many ways goes against what is traditionally found in most text books of mathematical fluid dynamics. Since our approach is new, and may also be considered controversial by some, we here want to open for a free debate on these very important questions that are fundamental for both mathematics and fluid dynamics. At the Forum of this homepage we hope for lively discussions on these important questions.

to:

The web page contains a Forum for exchange of ideas, and Expo for computational results, aspects of Education and software:

March 13, 2007, at 10:04 PM by claes -
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Accordingly one of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns these precisely these questions.

The book presents a fresh attack on the basic problems based on a combination of finite precision computation and a new concept of output uniqueness materialized in duality-based a posteriori error estimation in stabilized Galerkin finite element methods referred to as General Galerkin or G2. The book presents a variety of new results challenging commonly accepted views. In particular, (new) solutions to d'Alembert's paradox of zero drag, Sommerfeld's paradox of stability of Couette flow nad Loschmidt's paradox of irreversibility in reversible Hamiltonian systems, are presented, together with a critical analysis of the offcial formulation of the Clay Institute Prize Problem. ies; such as the d'Alembert mystery of drag in an inviscid flow, the Sommerfeld mystery of transition to turbulence in shear flow, and the Loschmidt mystery of violation of the 2nd law of thermodynamics. We approach these mysteries using a synthesis of computational and analytical mathematics, and in the book we offer new solutions.

to:

Accordingly one of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns the open questions.

The book presents a fresh attack on the basic problems based on finite element computation and a new concept of output uniqueness combined into duality-based a posteriori error estimation referred to as General Galerkin or G2. The book presents a variety of new results on turbulent flow challenging commonly used techniques of turbulence modeling including Reynolds Averaged Navier-Stokes RANS, Large Eddy Simulation LES, Smagorinsky turbulent viscosity. The power of G2 is demonsrted in new solutions to classical open problems including d'Alembert's paradox of zero drag in inviscid flow, Sommerfeld's paradox of stability of Couette flow at all Reynolds numbers, and Loschmidt's paradox of irreversibility in reversible Hamiltonian systems. Further, the official formulation of the Clay Institute Prize Problem is challenged.

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March 13, 2007, at 08:54 PM by claes -
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solutions have remained essentially open into our time. Accordingly one of the seven

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solutions have remained essentially open into our time. The reason is that slightly viscous flow always is turbulent. Accordingly one of the seven

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these questions.

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these questions.

March 13, 2007, at 08:38 PM by claes -
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On the homepage you can find a variety of material complementing and expanding the book including computational software and movies and a forum for debate of key issues of the book.

The fundamental equations for fluid flow have been known for almost 200 years, but still today the basic mathematical question of whether there exists a solution to the equations has not been settled. In fact, this problem is one of the famous Clay Institute $1 million Prize problems. In this book we give our own critical view on the formulation of this Prize problem, and we propose a possible alternative formulation of the problem. We also address several other mysteries related to mathematical modeling of fluid flow that have haunted scientist over the centuries; such as the d'Alembert mystery of drag in

to:

Here you can find a variety of material complementing and expanding the material presented in the book such as computational software including output in the form of movies and a forum for debate of key issues.

The basic mathematical models of fluid flow, the Euler and Navier-Stokes equations, have been known for almost 200 years, but the basic mathematical questions of existence, uniqueness and stability and the related basic question of the accuracy of computational solutions have remained essentially open into our time. Accordingly one of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns these precisely these questions.

The book presents a fresh attack on the basic problems based on a combination of finite precision computation and a new concept of output uniqueness materialized in duality-based a posteriori error estimation in stabilized Galerkin finite element methods referred to as General Galerkin or G2. The book presents a variety of new results challenging commonly accepted views. In particular, (new) solutions to d'Alembert's paradox of zero drag, Sommerfeld's paradox of stability of Couette flow nad Loschmidt's paradox of irreversibility in reversible Hamiltonian systems, are presented, together with a critical analysis of the offcial formulation of the Clay Institute Prize Problem. ies; such as the d'Alembert mystery of drag in

March 13, 2007, at 08:09 PM by claes -
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Welcome to the homepage of the new book Computational Turbulent Incompressible Flow, Volume 4 of the Springer book series of the

to:

Welcome to the homepage of Computational Turbulent Incompressible Flow, Volume 4 in the Springer book series of the

March 13, 2007, at 06:29 PM by claes -
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On the homepage you can a variety of material complementing and expanding the book including computational results, software and a forum for debate of key issues of the book.

to:

On the homepage you can find a variety of material complementing and expanding the book including computational software and movies and a forum for debate of key issues of the book.

March 13, 2007, at 06:26 PM by claes -
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Flow, which is also volume 4 in the Springer book series connected to the

to:

Flow, Volume 4 of the Springer book series of the

Changed lines 9-11 from:

Here you can find useful material to complement the book, as well as participate in the open debate around subjects from the book.

to:

On the homepage you can a variety of material complementing and expanding the book including computational results, software and a forum for debate of key issues of the book.

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mathematics and fluid dynamics. At the forum of this homepage

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mathematics and fluid dynamics. At the Forum of this homepage

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Although the fundamental equations for fluid flow have been known for almost 200 years, still today the basic mathematical question of whether there exists a solution

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The fundamental equations for fluid flow have been known for almost 200 years, but still today the basic mathematical question of whether there exists a solution

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Already Leonardo da Vinci sought to capture the basic features of turbulent flow in his sketches, and later in the 18th and 19th centuries the invention of calculus opened for a mathematical description of fluid flow in the form of the viscous Navier-Stokes equations, and the inviscid Euler equations. Although the fundamental equations have been known for almost 200 years, still today the basic mathematical questions of whether there exists a classical solution to the equations have not been settled. In fact, this problem is one of the famous

to:

Although the fundamental equations for fluid flow have been known for almost 200 years, still today the basic mathematical question of whether there exists a solution to the equations has not been settled. In fact, this problem is one of the famous

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that have haunted scientist over the centuries; such as the dAlembert mystery of drag in

to:

that have haunted scientist over the centuries; such as the d'Alembert mystery of drag in

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and in the book we offer new solutions to these mysteries that we believe is more to the point than the traditional views.

to:

and in the book we offer new solutions.

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mathematics and fluid dynamics. At the forum of this homepage we have a mailinglist which we hope will host lively discussions on these important questions.

to:

mathematics and fluid dynamics. At the forum of this homepage we hope for lively discussions on these important questions.

March 11, 2007, at 06:08 PM by 130.237.224.13 -
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in the open debate around subjects from the book by joining the maillinglist.

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in the open debate around subjects from the book.

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<a href="http://www.claymath.org/millennium/Navier-Stokes_Equations/">Clay Institute $1 million Prize problems</a>.

<br>

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Clay Institute $1 million Prize problems.

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<br>

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mathematics and fluid dynamics. At <a href=wip.html>the forum of this homepage</a>

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mathematics and fluid dynamics. At the forum of this homepage

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</td> </tr>


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Already Leonardo da Vinci sought to capture the basic features of turbulent flow in his sketches, and later in the 18th and 19th centuries the invention of calculus opened for a mathematical description of fluid flow in the form of the viscous Navier-Stokes equations, and the inviscid Euler equations. Although the fundamental equations have been known for almost 200 years, still today the basic mathematical questions of whether there exists a classical solution to the equations have not been settled. In fact, this problem is one of the famous <a href="http://www.claymath.org/millennium/Navier-Stokes_Equations/">Clay Institute $1 million Prize problems</a>.

<br>

In this book we give our own critical view on the formulation of this Prize problem, and we propose a possible alternative formulation of the problem.

We also address several other mysteries related to mathematical modeling of fluid flow that have haunted scientist over the centuries; such as the dAlembert mystery of drag in an inviscid flow, the Sommerfeld mystery of transition to turbulence in shear flow, and the Loschmidt mystery of violation of the 2nd law of thermodynamics.

<br>

We approach these mysteries using a synthesis of computational and analytical mathematics, and in the book we offer new solutions to these mysteries that we believe is more to the point than the traditional views.

The material in this book in many ways goes against what is traditionally found in most text books of mathematical fluid dynamics.

Since our approach is new, and may also be considered controversial by some, we here want to open for a free debate on these very important questions that are fundamental for both mathematics and fluid dynamics. At <a href=wip.html>the forum of this homepage</a> we have a mailinglist which we hope will host lively discussions on these important questions.

</td> </tr>

March 10, 2007, at 01:59 PM by 130.237.224.13 -
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Computational Turbulent Incompressible Flow

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Computational Turbulent Incompressible Flow

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Welcome to FlowWiki!

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Computational Turbulent Incompressible Flow

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  • Software - fenics
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Welcome to the homepage of the new book Computational Turbulent Incompressible Flow, which is also volume 4 in the Springer book series connected to the mathematics education reform project Applied Mathematics Body and Soul.

Here you can find useful material to complement the book, as well as participate in the open debate around subjects from the book by joining the maillinglist.


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  • Software - fenics
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Test discussion


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Welcome to FlowWiki!

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Welcome to FlowWiki!

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Welcome to PmWiki!

A local copy of PmWiki's documentation has been installed along with the software, and is available via the documentation index.

To continue setting up PmWiki, see initial setup tasks.

The basic editing page describes how to create pages in PmWiki. You can practice editing in the wiki sandbox.

More information about PmWiki is available from http://www.pmwiki.org .

to:

Welcome to FlowWiki!