## Main.HomePage History

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March 23, 2007, at 06:40 AM
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- Changed lines 33-34 from:

*Clay Mathematics Institute Millenium Prize Problem on Navier-Stokes equations,

to:

*The Clay Mathematics Institute Millenium Prize Problem on Navier-Stokes equations,

March 20, 2007, at 03:46 PM
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- Changed lines 37-39 from:

*flying

*sailing

*racing

*sailing

*racing

to:

*flying,

*sailing,

*racing,

*sailing,

*racing,

March 20, 2007, at 03:45 PM
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- Changed lines 35-36 from:

and and a variety of advanced applications unraveling [[forum | Secrets]] of

to:

and a variety of advanced applications unraveling [[forum | Secrets]] of

March 20, 2007, at 03:44 PM
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- Changed line 26 from:

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

to:

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

March 20, 2007, at 12:24 PM
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- Changed line 11 from:

presentations

to:

[[Presentations | presentations]],

March 19, 2007, at 05:37 PM
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- Changed line 5 from:

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 [[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 [[http://www.springer.com/west/home/generic/search/results?SGWID=4-40109-69-173623268-0 | Applied Mathematics: Body and Soul]] of the

March 19, 2007, at 05:33 PM
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- Changed lines 5-6 from:

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

Flow, Volume 4]] in the Springer book series of the

to:

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 05:32 PM
by

- Changed lines 5-6 from:

Welcome to the homepage of the book Computational Turbulent Incompressible

Flow, Volume 4 in the Springer book series of the

Flow, Volume 4 in the Springer book series of the

to:

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

Flow, Volume 4]] in the Springer book series of the

March 19, 2007, at 03:50 PM
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- March 19, 2007, at 03:50 PM
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- Changed lines 46-52 from:

%The homepage is organized into

%*[[Forum | Forum: Mysteries, Secrets and Reception of New Ideas]]

%*[[Expo | Computations Expo]]

%*[[Education | Education]]

%*[[http://www.fenics.org | Software - FEniCS]]

%*[[Forum | Forum: Mysteries, Secrets and Reception of New Ideas]]

%*[[Expo | Computations Expo]]

%*[[Education | Education]]

%*[[http://www.fenics.org | Software - FEniCS]]

to:

March 19, 2007, at 07:45 AM
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- Changed line 43 from:

Further, the [[forum | Reception]] by different scientific communities of the new ideas and results of the book,Fori

to:

Further, the [[forum | Reception]] by different scientific communities of the new ideas and results of the book

March 19, 2007, at 07:45 AM
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- Changed lines 29-30 from:

classical open problems or Mysteries including

to:

classical open problems or [[forum | Mysteries]] including

Changed lines 36-37 from:

and and a variety of advanced applications unraveling Secrets of

to:

and and a variety of advanced applications unraveling [[forum | Secrets]] of

March 19, 2007, at 07:43 AM
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- Changed line 43 from:

Further, the [[forum/reception | Reception]] by different scientific communities of the new ideas and results of the book,Fori

to:

Further, the [[forum | Reception]] by different scientific communities of the new ideas and results of the book,Fori

March 19, 2007, at 07:42 AM
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such as [[http://www.fenics.org | computational software]] including output in the form of movies, educational material,

to:

such as [[http://www.fenics.org | computational software]] including [[Expo | output in the form of movies]],

[[Education | educational material]],

[[Education | educational material]],

Changed lines 13-14 from:

and a forum for debate of key issues.

to:

and a [[Forum | forum for debate of key issues]].

Changed line 43 from:

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

to:

Further, the [[forum/reception | Reception]] by different scientific communities of the new ideas and results of the book,Fori

Changed line 46 from:

The homepage is organized into

to:

%The homepage is organized into

Changed lines 48-52 from:

*[[Forum | Forum: Mysteries, Secrets and Reception of New Ideas]]

*[[Expo | Computations Expo]]

*[[Education | Education]]

*[[http://www.fenics.org | Software - FEniCS]]

*[[Expo | Computations Expo]]

*[[Education | Education]]

*[[http://www.fenics.org | Software - FEniCS]]

to:

%*[[Forum | Forum: Mysteries, Secrets and Reception of New Ideas]]

%*[[Expo | Computations Expo]]

%*[[Education | Education]]

%*[[http://www.fenics.org | Software - FEniCS]]

%*[[Expo | Computations Expo]]

%*[[Education | Education]]

%*[[http://www.fenics.org | Software - FEniCS]]

March 19, 2007, at 07:38 AM
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- Changed line 10 from:

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

to:

such as [[http://www.fenics.org | computational software]] including output in the form of movies, educational material,

March 18, 2007, at 09:30 AM
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- Changed lines 43-44 from:

is presented in referee's reviews.

to:

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

March 18, 2007, at 09:28 AM
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- Changed line 42 from:

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

to:

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

March 18, 2007, at 09:27 AM
by

- Changed line 42 from:

Further, the Reception by different scientific of the new results presented

to:

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

March 18, 2007, at 09:26 AM
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- Changed lines 33-34 from:

to:

*Clay Mathematics Institute Millenium Prize Problem on Navier-Stokes equations,

Changed lines 42-44 from:

Further, the official formulation of the Clay Institute Prize Problem is challenged and a new formulation

and (partial) resolution is presented.

and (partial) resolution is presented.

to:

Further, the Reception by different scientific of the new results presented

is presented in referee's reviews.

is presented in referee's reviews.

March 18, 2007, at 09:15 AM
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- Changed lines 28-29 from:

classical open problems including

to:

classical open problems or Mysteries including

Changed lines 34-35 from:

and and a variety of advanced applications unraveling secrets of

to:

and and a variety of advanced applications unraveling Secrets of

March 15, 2007, at 10:20 PM
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- Changed line 46 from:

*[[Forum | Forum: Mysteries, Secrets and Reception]]

to:

*[[Forum | Forum: Mysteries, Secrets and Reception of New Ideas]]

March 15, 2007, at 10:20 PM
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- Added lines 43-44:

The homepage is organized into

March 15, 2007, at 10:18 PM
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- Changed line 27 from:

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

to:

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
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- Changed lines 20-21 from:

the Navier-Stokes equations.

to:

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

March 15, 2007, at 10:15 PM
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- Changed lines 18-19 from:

turbulent and defies analytical mathematical representation.

One of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

One of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

to:

turbulent and defies analytical mathematical representation. Accordingly,

one of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

one of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

March 15, 2007, at 10:14 PM
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- Changed lines 10-11 from:

such as computational software including output in the form of movies

to:

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

presentations

presentations

March 15, 2007, at 01:14 PM
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- Added line 47:

March 15, 2007, at 01:12 PM
by

- Changed line 5 from:

Welcome to the homepage of Computational Turbulent Incompressible

to:

Welcome to the homepage of the book Computational Turbulent Incompressible

March 14, 2007, at 09:23 AM
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- Changed lines 31-32 from:

*Loschmidt's paradox of irreversibility in reversible Hamiltonian systems.

to:

*Loschmidt's paradox of irreversibility in reversible Hamiltonian systems,

Changed lines 40-41 from:

Further, the official formulation of the Clay Institute Prize Problem is challenged.

to:

Further, the official formulation of the Clay Institute Prize Problem is challenged and a new formulation

and (partial) resolution is presented.

and (partial) resolution is presented.

March 14, 2007, at 09:22 AM
by

- Changed lines 21-22 from:

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

computation and a new concept of output uniqueness combined into duality-based a posteriori error estimation

to:

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,

computation and a new concept of output uniqueness combined with duality-based a posteriori error estimation,

Changed lines 25-26 from:

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

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

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
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- Changed lines 19-20 from:

these open problems.

to:

the Navier-Stokes equations.

March 14, 2007, at 09:14 AM
by

- Changed lines 17-18 from:

turbulent, which defies analytical mathematical representation.

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

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

to:

turbulent and defies analytical mathematical representation.

One of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

One of the seven Clay Mathematical Institute $1 million Millenium Prize problems concerns

March 14, 2007, at 09:12 AM
by

- Changed line 16 from:

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

to:

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

- Changed lines 9-10 from:

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

presented in the book such as computational software including output in the form of movies

to:

Here you can find a variety of material complementing and expanding the book,

such as computational software including output in the form of movies

such as computational software including output in the form of movies

March 13, 2007, at 10:18 PM
by

- Changed lines 16-17 from:

solutions have remained essentially open into our time. The reason is that slightly viscous flow always is turbulent.

to:

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

turbulent, which defies analytical mathematical representation.

turbulent, which defies analytical mathematical representation.

Changed lines 19-21 from:

the open questions.

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

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

to:

these open problems.

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

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

Changed lines 25-26 from:

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

Smagorinsky turbulent viscosity. The power of G2 is demonstrated in new solutions to

to:

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

Smagorinsky viscosity. The power of G2 is demonstrated in new solutions to

March 13, 2007, at 10:13 PM
by

- Changed lines 40-43 from:

The web page contains a Forum for exchange of ideas, and Expo for computational results,

aspects of Education and software:

to:

March 13, 2007, at 10:12 PM
by

- Changed line 20 from:

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

to:

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

Changed lines 25-28 from:

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.

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.

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.

Changed lines 41-48 from:

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:

aspects of Education and software:

March 13, 2007, at 10:04 PM
by

- Changed lines 17-33 from:

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.

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.

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.

Deleted line 42:

March 13, 2007, at 08:54 PM
by

- Changed lines 16-17 from:

solutions have remained essentially open into our time. Accordingly one of the seven

to:

solutions have remained essentially open into our time. The reason is that slightly viscous flow always is turbulent.

Accordingly one of the seven

Accordingly one of the seven

Changed lines 19-20 from:

these questions.

to:

these questions.

March 13, 2007, at 08:38 PM
by

- Changed lines 9-19 from:

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

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

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

- Changed lines 5-6 from:

Welcome to the homepage of the new book Computational Turbulent Incompressible

Flow, Volume 4 of the Springer book series of the

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

Flow, Volume 4 in the Springer book series of the

March 13, 2007, at 06:29 PM
by

- Changed lines 9-11 from:

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.

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.

computational software and movies and a forum for debate of key issues of the book.

March 13, 2007, at 06:26 PM
by

- Changed line 6 from:

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.

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.

computational results, software and a forum for debate of key issues of the book.

March 13, 2007, at 06:22 PM
by

- Changed line 32 from:

*[[Forum | Forum: Mysteries, Secrets and Recwption]]

to:

*[[Forum | Forum: Mysteries, Secrets and Reception]]

March 13, 2007, at 06:21 PM
by

- Changed line 32 from:

*[[Forum | Forum: Mysteries, Secrets and Rejection]]

to:

*[[Forum | Forum: Mysteries, Secrets and Recwption]]

March 13, 2007, at 02:43 PM
by

- Changed lines 33-34 from:

*[[Expo | Book Computations Expo]]

*[[Education | Book in Education]]

*[[Education | Book in Education]]

to:

*[[Expo | Computations Expo]]

*[[Education | Education]]

*[[Education | Education]]

March 13, 2007, at 02:42 PM
by

- Changed line 32 from:

*[[Forum | Forum: Mysteries, Secrets and Scientific Journals]]

to:

*[[Forum | Forum: Mysteries, Secrets and Rejection]]

March 13, 2007, at 12:05 PM
by

- Changed line 29 from:

mathematics and fluid dynamics. At the forum of this homepage

to:

mathematics and fluid dynamics. At the Forum of this homepage

Changed line 32 from:

*[[Forum | Mystery, Secret and Scientific Journal Forum]]

to:

*[[Forum | Forum: Mysteries, Secrets and Scientific Journals]]

March 13, 2007, at 12:04 PM
by

- Changed line 32 from:

*[[Forum | Forum: Mysteries, Secrets and Scientific Journals]]

to:

*[[Forum | Mystery, Secret and Scientific Journal Forum]]

March 13, 2007, at 12:03 PM
by

- Changed lines 32-34 from:

*[[Forum | Flow Mystery Forum]]

*[[Forumsecret | Flow Secret Forum]]

*[[Forumjournal | Scientific Journal Forum]]

*[[Forumsecret | Flow Secret Forum]]

*[[Forumjournal | Scientific Journal Forum]]

to:

*[[Forum | Forum: Mysteries, Secrets and Scientific Journals]]

March 12, 2007, at 12:55 PM
by

- Added line 34:

*[[Forumjournal | Scientific Journal Forum]]

March 12, 2007, at 12:54 PM
by

- Changed line 33 from:

*[[Forum | Flow Secret Forum]]

to:

*[[Forumsecret | Flow Secret Forum]]

March 12, 2007, at 12:52 PM
by

- Added line 33:

*[[Forum | Flow Secret Forum]]

March 11, 2007, at 06:30 PM
by

- Changed lines 12-13 from:

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

still today the basic mathematical question of whether there exists a solution

to:

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

but still today the basic mathematical question of whether there exists a solution

Deleted line 21:

Added line 24:

March 11, 2007, at 06:28 PM
by

- Changed lines 12-18 from:

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

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

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

Deleted line 15:

Changed line 19 from:

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.

point than the traditional views.

to:

and in the book we offer new solutions.

Deleted line 26:

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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.

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.

we hope for lively discussions on these important questions.

March 11, 2007, at 06:08 PM
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*[[ForumWiki | Flow Mystery Forum]]

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*[[EduWiki | Book in Education]]

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*[[EduWiki | Book in Education]]

to:

*[[Forum | Flow Mystery Forum]]

*[[Expo | Book Computations Expo]]

*[[Education | Book in Education]]

*[[Expo | Book Computations Expo]]

*[[Education | Book in Education]]

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*[[Education]]

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*[[Education]]

to:

*[[ForumWiki | Flow Mystery Forum]]

*[[ExpoWiki | Book Computations Expo]]

*[[EduWiki | Book in Education]]

*[[ExpoWiki | Book Computations Expo]]

*[[EduWiki | Book in Education]]

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*[[Book Expo]]

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*[[Flow Mystery Forum]]

*[[Education]]

*[[Flow Mystery Forum]]

*[[Education]]

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in the open debate around subjects from the book by joining the maillinglist.

to:

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>

<br>

to:

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>

<a href=wip.html>the forum of this homepage</a>

to:

mathematics and fluid dynamics. At the forum of this homepage

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</td>

</tr>

[[<<]]

</tr>

[[<<]]

March 11, 2007, at 05:29 PM
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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>

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Computational Turbulent Incompressible Flow

to:

!Computational Turbulent Incompressible Flow

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!Welcome to FlowWiki!

to:

Computational Turbulent Incompressible Flow

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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

[[http://www.bodysoulmath.org | 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.

[[<<]]

Flow, which is also volume 4 in the Springer book series connected to the

mathematics education reform project

[[http://www.bodysoulmath.org | 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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[[<<]]

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[[<<]]

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--------------

[[Test discussion]]

--------------

--------------

[[Test discussion]]

--------------

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*[[http://www.fenics.org | Software - fenics]]

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*[[http://www.fenics.org | Software]]

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Welcome to FlowWiki!

to:

!Welcome to FlowWiki!

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*[[http://www.fenics.org]]

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*[[FlowExpoWiki]]

*[[FlowMysteriesWiki]]

*[[FlowEducationWiki]]

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*[[FlowEducationWiki]]

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[[*FlowExpoWiki]]

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[[*FlowEducationWiki]]

[[*FlowMysteriesWiki]]

[[*FlowEducationWiki]]

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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 [[PmWiki/documentation index]].

To continue setting up PmWiki, see [[PmWiki/initial setup tasks]].

The [[PmWiki/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 .

A local copy of PmWiki's

documentation has been installed along with the software,

and is available via the [[PmWiki/documentation index]].

To continue setting up PmWiki, see [[PmWiki/initial setup tasks]].

The [[PmWiki/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!