Vol.4 : Computational Turbulent Incompressible Flow

Main.HomePage History

Hide minor edits - Show changes to output

March 23, 2007, at 06:40 AM by claes -
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 by Johan Hoffman -
Changed lines 37-39 from:
*flying
*sailing
*racing
to:
*flying,
*sailing,
*racing,
March 20, 2007, at 03:45 PM by Johan Hoffman -
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 by Johan Hoffman -
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 by claes -
Changed line 11 from:
presentations
to:
[[Presentations | presentations]],
March 19, 2007, at 05:37 PM by claes -
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 by claes -
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
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 claes -
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
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 03:50 PM by claes -
March 19, 2007, at 03:50 PM by claes -
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]]
to:

March 19, 2007, at 07:45 AM by claes -
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 by claes -
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 by claes -
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 by claes -
Changed lines 10-11 from:
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]],
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]]
to:
%*[[Forum | Forum: Mysteries, Secrets and Reception of New Ideas]]
%*[[Expo | Computations Expo]]
%*[[Education | Education]]
%*[[http://www.fenics.org | Software - FEniCS]]
March 19, 2007, at 07:38 AM by claes -
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 by claes -
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 by claes -
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 claes -
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 by claes -
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.
to:
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 -
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 by claes -
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 by claes -
Added lines 43-44:

The homepage is organized into
March 15, 2007, at 10:18 PM by claes -
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 by claes -
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 by claes -
Changed lines 18-19 from:
turbulent and defies analytical mathematical representation.
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
March 15, 2007, at 10:14 PM by claes -
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
March 15, 2007, at 01:14 PM by Johan Hoffman -
Added line 47:
March 15, 2007, at 01:12 PM by Johan Hoffman -
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 by claes -
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.
March 14, 2007, at 09:22 AM by claes -
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
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,
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
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 -
Changed lines 19-20 from:
these open problems.
to:
the Navier-Stokes equations.
March 14, 2007, at 09:14 AM by claes -
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
to:
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 -
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 claes -
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
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
March 13, 2007, at 10:18 PM by claes -
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.
Changed lines 19-21 from:
the open questions.

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
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
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
March 13, 2007, at 10:13 PM by claes -
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 claes -
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.
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.
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:
March 13, 2007, at 10:04 PM by claes -
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.
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.

Deleted line 42:
March 13, 2007, at 08:54 PM by claes -
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
Changed lines 19-20 from:
these questions.
to:
these questions.
March 13, 2007, at 08:38 PM by claes -
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
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 -
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
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 -
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.
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 -
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.
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.
March 13, 2007, at 06:22 PM by claes -
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 claes -
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 claes -
Changed lines 33-34 from:
*[[Expo | Book Computations Expo]]
*[[Education | Book in Education]]
to:
*[[Expo | Computations Expo]]
*[[Education | Education]]
March 13, 2007, at 02:42 PM by claes -
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 claes -
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 claes -
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 claes -
Changed lines 32-34 from:
*[[Forum | Flow Mystery 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 claes -
Added line 34:
*[[Forumjournal | Scientific Journal Forum]]
March 12, 2007, at 12:54 PM by claes -
Changed line 33 from:
*[[Forum | Flow Secret Forum]]
to:
*[[Forumsecret | Flow Secret Forum]]
March 12, 2007, at 12:52 PM by claes -
Added line 33:
*[[Forum | Flow Secret Forum]]
March 11, 2007, at 06:30 PM by 130.237.224.13 -
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
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
Deleted line 21:
Added line 24:
March 11, 2007, at 06:28 PM by 130.237.224.13 -
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
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
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
Changed lines 24-26 from:
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.
Deleted line 26:
Changed lines 29-32 from:
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 -
March 11, 2007, at 06:07 PM by 130.237.224.13 -
Changed lines 41-43 from:
*[[ForumWiki | Flow Mystery Forum]]
*[[ExpoWiki | Book Computations Expo]]
*[[EduWiki | Book in Education]]
to:
*[[Forum | Flow Mystery Forum]]
*[[Expo | Book Computations Expo]]
*[[Education | Book in Education]]
March 11, 2007, at 06:06 PM by 130.237.224.13 -
Changed lines 41-43 from:
*[[Flow Mystery Forum]]
*[[Book Computations Expo]]
*[[Education]]
to:
*[[ForumWiki | Flow Mystery Forum]]
*[[ExpoWiki | Book Computations Expo]]
*[[EduWiki | Book in Education]]
March 11, 2007, at 06:04 PM by 130.237.224.13 -
Changed lines 44-45 from:
*[[http://www.fenics.org | Software - fenics]]
to:
*[[http://www.fenics.org | Software - FEniCS]]
March 11, 2007, at 06:02 PM by 130.237.224.13 -
Deleted line 40:
*[[Book Expo]]
Added line 42:
*[[Book Computations Expo]]
March 11, 2007, at 06:00 PM by 130.237.224.13 -
Changed lines 41-43 from:
*[[FlowExpoWiki]]
*[[FlowMysteriesWiki]]
*[[FlowEducationWiki]]
to:
*[[Book Expo]]
*[[Flow Mystery Forum]]
*[[Education]]
March 11, 2007, at 05:58 PM by 130.237.224.13 -
Deleted line 8:
March 11, 2007, at 05:58 PM by 130.237.224.13 -
Changed lines 11-13 from:
in the open debate around subjects from the book by joining the maillinglist.

to:
in the open debate around subjects from the book.
Changed lines 20-23 from:
<a href="http://www.claymath.org/millennium/Navier-Stokes_Equations/">Clay Institute $1 million Prize problems</a>.

<br>
to:
Clay Institute $1 million Prize problems.
Deleted line 23:
Deleted lines 28-29:
<br>
Changed lines 38-39 from:
mathematics and fluid dynamics. At
<a href=wip.html>the forum of this homepage</a>
to:
mathematics and fluid dynamics. At the forum of this homepage
Deleted lines 41-46:
</td>
</tr>


[[<<]]
March 11, 2007, at 05:29 PM by 130.237.224.13 -
Added lines 13-52:

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 -
Changed lines 1-2 from:
Computational Turbulent Incompressible Flow
to:
!Computational Turbulent Incompressible Flow
March 10, 2007, at 01:59 PM by 130.237.224.13 -
Changed lines 1-2 from:
!Welcome to FlowWiki!
to:
Computational Turbulent Incompressible Flow
March 10, 2007, at 01:58 PM by 130.237.224.13 -
Changed lines 3-4 from:
%lframe% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png
to:
%lfloat% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png
March 10, 2007, at 01:58 PM by 130.237.224.13 -
Changed lines 18-19 from:
*[[http://www.fenics.org | Software - fenics]]
to:
*[[http://www.fenics.org | Software - fenics]]
March 10, 2007, at 01:58 PM by 130.237.224.13 -
Added lines 5-14:
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.

[[<<]]
Changed lines 18-22 from:
*[[http://www.fenics.org | Software - fenics]]

[[<<]]

to:
*[[http://www.fenics.org | Software - fenics]]
March 10, 2007, at 01:55 PM by 130.237.224.13 -
Changed lines 3-4 from:
%lfloat% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png
to:
%lframe% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png
March 10, 2007, at 01:54 PM by 130.237.224.13 -
Changed lines 10-11 from:

to:
[[<<]]

March 10, 2007, at 01:53 PM by 130.237.224.13 -
Changed lines 3-4 from:
%lfloat% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png
to:
%lfloat% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png
March 10, 2007, at 01:53 PM by 130.237.224.13 -
Changed lines 3-4 from:
%lfloat% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png";
to:
%lfloat% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png
March 10, 2007, at 01:53 PM by 130.237.224.13 -
Changed lines 3-4 from:
http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png";
to:
%lfloat% http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png";
March 10, 2007, at 01:52 PM by 130.237.224.13 -
Changed lines 8-11 from:
*[[http://www.fenics.org | Software - fenics]]
to:
*[[http://www.fenics.org | Software - fenics]]


March 10, 2007, at 01:51 PM by 130.237.224.13 -
Added lines 3-4:
http://www.csc.kth.se/~jhoffman/graphics/coverv4-2.png";
March 10, 2007, at 01:38 PM by 130.237.224.13 -
Changed lines 6-12 from:
*[[http://www.fenics.org | Software - fenics]]

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

[[Test discussion]]

--------------
to:
*[[http://www.fenics.org | Software - fenics]]
March 10, 2007, at 01:34 PM by 130.237.224.13 -
Changed lines 6-7 from:
*[[http://www.fenics.org | Software]]
to:
*[[http://www.fenics.org | Software - fenics]]
March 10, 2007, at 01:33 PM by 130.237.224.13 -
Changed lines 6-7 from:
*[[http://www.fenics.org]]
to:
*[[http://www.fenics.org | Software]]
March 10, 2007, at 01:32 PM by 130.237.224.13 -
Changed lines 1-2 from:
Welcome to FlowWiki!
to:
!Welcome to FlowWiki!
Changed lines 6-7 from:

to:
*[[http://www.fenics.org]]
March 10, 2007, at 01:29 PM by 130.237.224.13 -
Changed lines 3-9 from:
[[*FlowExpoWiki]]

[[*FlowMysteriesWiki]]

[[*FlowEducationWiki]]

to:
*[[FlowExpoWiki]]
*[[FlowMysteriesWiki]]
*[[FlowEducationWiki]]

March 10, 2007, at 01:28 PM by 130.237.224.13 -
Added line 4:
Changed lines 6-14 from:
[[*FlowEducationWiki]]
to:

[[*FlowEducationWiki]]


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

[[Test discussion]]

--------------
March 10, 2007, at 01:26 PM by 130.237.224.13 -
Added lines 3-5:
[[*FlowExpoWiki]]
[[*FlowMysteriesWiki]]
[[*FlowEducationWiki]]
March 10, 2007, at 01:23 PM by 130.237.224.13 -
Changed lines 1-12 from:
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 .
to:
Welcome to FlowWiki!