Great book. I'm a climate scientist and I run climate models which use many such numerical techniques to solve PDEs describing fluid dynamics (the flow of the atmosphere). There are many numerical "schemes" (options) to choose from which have a tradeoff between speed and accuracy. All these techniques were built due to digital computing. Now in the new generation of digital computers, neural-PDEs and their solutions are emerging as a new alternative to these classical numerical schemes.
Quantum Computers may help. I read those can already find or solve a route through a maze in a heartbeat, maybe less. So one may look to solve how a maze could be mapped, discovered.
@@johnswolterI've seen and skimmed a few papers regarding merging quantum computing and CFD, but they're all from the perspective of using QC for the linear algebra and the classical computing for the discretization. Not that that's a bad approach, but it'll take awhile before they're able to interface with each other efficiently.
I'd disagree about neural-PDEs being an alternative (at least not in what I've read). However, I think ML techniques could do a lot for modelling problems in CFD, where we're effectively just fitting the model to data anyways.
@@jameswright4732 In the brief interval since I've learnt about PINNs (Physics Informed Neural Networks), one lesson by a certain Hong Kong professor has taught me that PINNs are not nearly as data-driven as the average NNs. Although his lecture was on my field, which is Solid Mechanics, not CFD.
i understand nothing about mathematic but ive been subbed to you with notification for so long and i gotta admit i love your passion and dedication about mathematics respect to you man
@@4ctive1you can start anywhere you want and go baby steps at a time , believe me there's lot to learn even if you do know a lot it's like a deep sea that gets deeper everytime 😅 ,may Allah give you from his vast knowledge brother inchallah
For anyone interested in the modern side of Computational ("Numerical") Fluid dynamics, Anderson's Introduction to Computational Fluid Dynamics is an awesome beginner friendly introduction. Nothing else I have read cuts close
I would also mention Versteeg & Malalasekera's "An Introduction to Computational Fluid Dynamics: The Finite Volume Method". Hardly any other book can be friendlier to an absolute beginner.
@@faustobarbuto I have gone through some of it. It was an absolute joy no doubt but Anderson is still my go to. I guess it just boils down to personal taste😄
Thanks for this video! At 8:47 the intended audience is normall mechanical engineers in postgraduate studies. This topic is typically within the realm of mechanical engineering research. However, science doesn't have an owner, and it's likely that mathematicians and physicists also dedicate themselves to this area. There should be some of them who work in this field as well
I had many fluid dynamics and continuum mechanics courses in undergraduate and graduate school. This is an interesting book for 1984. The advent of powerful computers has greatly helped apply theory to engineering solutions. But, LOL, modern-day NASA has more problems putting rockets in space than the engineers did back in the 1960s.
The contrast appears overstated. Many new developments occured in the 1950s & 1960s. Most rockets then did misbehave & much was learned. Now, much more is being asked, new technologies are being added, quality standards are being taught to the aerospace industry, everything is a system, & the industry is pushing new technology into every application. Therefore failures are progress. Full speed ahead.
As a russian-speaking person, I should admit that all these excellent soviet math books are way more understandable once they are translated into English. Some terms cannot be translated without distorting the idea behind them. I believe this selective terminological lingual isolation is the reason why these books are so great. Guys had to start from the fundamentals description every time to avoid misunderstanding. My favorite example is "wavelet" which had back then at least five different translations.
Hey @mathsorcerer this is really cool, fluid mechanics is one of the most interesting subjects and the math required covers calculus, algebra, trig, numerical methods, etc. great stuff 👍
You should check out Equations of Mathematical Physics by Bitsadze. It's quite a small unique book containing essentials of PDEs, complex variables and integral equations as required by a physics major!
I took this class over 30 years ago and still literally have nightmares about it. I dream that it's the final and I haven't cracked the book or been to class all semester. Our Dept was using these methods modeling groundwater flow in 3-D.
That's what the subject is called, computational fluid dynamics. Because the differential equations that model fluid motion can't be solved by hand and have to be done by computer algorithms...
@@NewWesternFront These numerical PDEs require tens of thousands of calculations and so are impossible to do by hand. Hence a computer doing them and the word "computational..."
@@TheMathSorcerer nice! hopefully we can get a peek at your chess books in the future ;) chess folk are really passionate about their books, international master kostya kavutskiy comes to mind as someone who makes lots of chess book content on youtube!
Okay, we have a few things here.... No, not about the book... But drinking Tea with the spoon that's the highway to the danger zone.... and you know leaving the spoon in will change the taste of the tea. I've not found a Dover Book on the subject, but I'm willing to bet there is one somewhere :D
Good book but we need explen the equation in this book used for solving the fluid proplem the presantion for this book not completed plese explean mathmatics equation in book thank you
Google Translate is making any book in any language available to the world. Mathematics is a language too. Google's Translate & others will translate Mathematics language too.
The English edition was published in 1984 so it is a 40 year old anthology of computational methods in fluid dynamics. I'm not going to claim it has no value at all to current research, but the onus would be on someone who claimed it was still useful. (Computational fluid dynamics has been actively developing over the last 40 years, as have uh computers for that matter.)
I caught a glimpse of "split explicit schemes" - these are the basis of time integrators of modern day weather models - they were specifically developed for computers. I consult newer books and papers for my work but many cite old works from the 80's and 70's. I'm sure at least some of these are referenced.
![The Most Useful Curve in Mathematics [Logarithms]](/img/1.gif)
I used "Physical Fluid Dynamics" by D. J. Tritton as an Undergrad; it would be a good compliment to this book.
awesome!
Great book. I'm a climate scientist and I run climate models which use many such numerical techniques to solve PDEs describing fluid dynamics (the flow of the atmosphere). There are many numerical "schemes" (options) to choose from which have a tradeoff between speed and accuracy. All these techniques were built due to digital computing. Now in the new generation of digital computers, neural-PDEs and their solutions are emerging as a new alternative to these classical numerical schemes.
Quantum Computers may help. I read those can already find or solve a route through a maze in a heartbeat, maybe less. So one may look to solve how a maze could be mapped, discovered.
Thanks. I had no idea about the existence/emergence of Neural PDEs.
@@johnswolterI've seen and skimmed a few papers regarding merging quantum computing and CFD, but they're all from the perspective of using QC for the linear algebra and the classical computing for the discretization. Not that that's a bad approach, but it'll take awhile before they're able to interface with each other efficiently.
I'd disagree about neural-PDEs being an alternative (at least not in what I've read). However, I think ML techniques could do a lot for modelling problems in CFD, where we're effectively just fitting the model to data anyways.
@@jameswright4732 In the brief interval since I've learnt about PINNs (Physics Informed Neural Networks), one lesson by a certain Hong Kong professor has taught me that PINNs are not nearly as data-driven as the average NNs. Although his lecture was on my field, which is Solid Mechanics, not CFD.
i understand nothing about mathematic but ive been subbed to you with notification for so long and i gotta admit i love your passion and dedication about mathematics respect to you man
Awesome! Thank you!
@@TheMathSorcerer i just get it out from my heart you seem a good person so may Allah SWT guide you to Islam and i call you to embrace Islam bye
@@4ctive1you can start anywhere you want and go baby steps at a time , believe me there's lot to learn even if you do know a lot it's like a deep sea that gets deeper everytime 😅 ,may Allah give you from his vast knowledge brother inchallah
@@homamthewise6941 thnx brother i understand you
@@4ctive1 lol stealth proselytizer
For anyone interested in the modern side of Computational ("Numerical") Fluid dynamics, Anderson's Introduction to Computational Fluid Dynamics is an awesome beginner friendly introduction. Nothing else I have read cuts close
Second this
I would also mention Versteeg & Malalasekera's "An Introduction to Computational Fluid Dynamics: The Finite Volume Method". Hardly any other book can be friendlier to an absolute beginner.
@@faustobarbuto I have gone through some of it. It was an absolute joy no doubt but Anderson is still my go to. I guess it just boils down to personal taste😄
Thanks for this video! At 8:47 the intended audience is normall mechanical engineers in postgraduate studies. This topic is typically within the realm of mechanical engineering research. However, science doesn't have an owner, and it's likely that mathematicians and physicists also dedicate themselves to this area. There should be some of them who work in this field as well
Love the birds on the background
I had many fluid dynamics and continuum mechanics courses in undergraduate and graduate school. This is an interesting book for 1984. The advent of powerful computers has greatly helped apply theory to engineering solutions. But, LOL, modern-day NASA has more problems putting rockets in space than the engineers did back in the 1960s.
The contrast appears overstated. Many new developments occured in the 1950s & 1960s. Most rockets then did misbehave & much was learned.
Now, much more is being asked, new technologies are being added, quality standards are being taught to the aerospace industry, everything is a system, & the industry is pushing new technology into every application. Therefore failures are progress. Full speed ahead.
This book is one of the interesting ones from the Advances in STEM series...❤❤❤
As a russian-speaking person, I should admit that all these excellent soviet math books are way more understandable once they are translated into English. Some terms cannot be translated without distorting the idea behind them. I believe this selective terminological lingual isolation is the reason why these books are so great. Guys had to start from the fundamentals description every time to avoid misunderstanding. My favorite example is "wavelet" which had back then at least five different translations.
I'd suggest within every book review, a book's name with authors should be written near the top of all your book reviews
Hey @mathsorcerer this is really cool, fluid mechanics is one of the most interesting subjects and the math required covers calculus, algebra, trig, numerical methods, etc. great stuff 👍
Gotta love those classics and how you present them love your vids
You should check out Equations of Mathematical Physics by Bitsadze. It's quite a small unique book containing essentials of PDEs, complex variables and integral equations as required by a physics major!
Your Diff eq course with lectures on Udemy was amazing! I'm looking forward to get your writing proofs in set theory!
The CFD book by Feziger, Peric, and Street is tops!
See also Fluid Mechanics by Kundu...another cornerstone book.
1:57 I said out loud “alright just open it up bro”. And you responded.
2:36 oh the elementary theory in one or several complex variables by Cartan. Im reading through the dover reprint of it currently:)
YES!!! That's the book! Awesome!!
I took this class over 30 years ago and still literally have nightmares about it. I dream that it's the final and I haven't cracked the book or been to class all semester. Our Dept was using these methods modeling groundwater flow in 3-D.
Do you have any book reccomendations for math olympiad prep?
I see Mir Publishers, I click
I took this class but it was called Computational Fluid Dynamics.
That's what the subject is called, computational fluid dynamics. Because the differential equations that model fluid motion can't be solved by hand and have to be done by computer algorithms...
@@qsfrankfurt9513 why
@@NewWesternFront These numerical PDEs require tens of thousands of calculations and so are impossible to do by hand. Hence a computer doing them and the word "computational..."
@@qsfrankfurt9513 how cool
I have one from the same series but from 1986, and is hard cover.
awesome
I can't find a copy of this book anywhere.
you may have answered this, but do you think math is discovered-or invented?
do you have chess books in your book collection? if not you should consider it (assuming you are interested in chess).
I do have chess books:) I love chess!
@@TheMathSorcerer nice! hopefully we can get a peek at your chess books in the future ;)
chess folk are really passionate about their books, international master kostya kavutskiy comes to mind as someone who makes lots of chess book content on youtube!
Okay, we have a few things here.... No, not about the book... But drinking Tea with the spoon that's the highway to the danger zone.... and you know leaving the spoon in will change the taste of the tea. I've not found a Dover Book on the subject, but I'm willing to bet there is one somewhere :D
Good book but we need explen the equation in this book used for solving the fluid proplem the presantion for this book not completed plese explean mathmatics equation in book thank you
I prefer Ch L Mader Numerical modeling of explosives and propellants.
interested in getting a copy of the book, or at least the papers, does anyone know where to find it? Thanks
Could you make a video over Millennium Problems
Wow
C’mon @MathSorcerer. Only REAL math fans read it in its original 20th century Russian.
**Edit to highlight sarcasm**
Google Translate is making any book in any language available to the world. Mathematics is a language too. Google's Translate & others will translate Mathematics language too.
Sweet
You're so cool. :)
The English edition was published in 1984 so it is a 40 year old anthology of computational methods in fluid dynamics. I'm not going to claim it has no value at all to current research, but the onus would be on someone who claimed it was still useful. (Computational fluid dynamics has been actively developing over the last 40 years, as have uh computers for that matter.)
I caught a glimpse of "split explicit schemes" - these are the basis of time integrators of modern day weather models - they were specifically developed for computers. I consult newer books and papers for my work but many cite old works from the 80's and 70's. I'm sure at least some of these are referenced.