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JohnLeM
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Navier Stokes and Finance ?

December 23rd, 2019, 9:56 am

I would like to share this post. It is simply a Navier Stokes equation, AKA CFD (Computational Fluid Dynamic), but the numerical simulation is done with ... a finance oriented framework.
Maybe it could be a warm-up to discuss Navier Stokes type modeling for Finance equations ? For instance, we could have fun trying to model market turbulences mixing CFD and Fokker Planck equations !
 
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Cuchulainn
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Re: Navier Stokes and Finance ?

December 23rd, 2019, 4:33 pm

These links look broken..
(reproduced from this link) In this preprint, we prese
??
 
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FaridMoussaoui
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Re: Navier Stokes and Finance ?

December 23rd, 2019, 6:53 pm

You can benchmark your code with exact solutions or NS equations: "Exact Fully 3D Navier Stokes Solutions For Benchmarking". IJNMF, vol 19, 1994. More challenging example is the driven cavity.

Just google the article title, you find it free of charge.
 
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FaridMoussaoui
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Re: Navier Stokes and Finance ?

December 23rd, 2019, 6:59 pm

These links look broken..
(reproduced from this link) In this preprint, we prese
??
I am getting a message in chinese when I click on one of those links:

Image
 
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Cuchulainn
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Re: Navier Stokes and Finance ?

December 23rd, 2019, 7:39 pm

Indeed. De udder one gives '404'.
 
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JohnLeM
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Re: Navier Stokes and Finance ?

December 23rd, 2019, 8:50 pm

Indeed. De udder one gives '404'.
Fixed. Thank you for pointing this out to me.
 
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JohnLeM
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Re: Navier Stokes and Finance ?

December 23rd, 2019, 8:55 pm

You can benchmark your code with exact solutions or NS equations: "Exact Fully 3D Navier Stokes Solutions For Benchmarking". IJNMF, vol 19, 1994. More challenging example is the driven cavity.

Just google the article title, you find it free of charge.
Thx, I will benchmark it, although I only implemented at present time 2D solutions, just to see how this method is behaving for NS.
 
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FaridMoussaoui
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Re: Navier Stokes and Finance ?

December 23rd, 2019, 11:45 pm

In the introduction, Taylor's exact 2D solution is given (1923 paper).

Image
 
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FaridMoussaoui
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Re: Navier Stokes and Finance ?

December 24th, 2019, 9:25 am

Indeed. De udder one gives '404'.
Fixed. Thank you for pointing this out to me.
What is fixed? The first link is not working (the website was redesigned and articles before 2018 are gone). For the second link, it sems that you didn't renew your domain name and it was taken by "others".
 
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JohnLeM
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Re: Navier Stokes and Finance ?

December 24th, 2019, 10:11 am

Indeed. De udder one gives '404'.
Fixed. Thank you for pointing this out to me.
What is fixed? The first link is not working (the website was redesigned and articles before 2018 are gone). For the second link, it sems that you didn't renew your domain name and it was taken by "others".
Links are fixed where Cuchullain noticed it, that is here. And yes, I did not renew my domain, that's why links are broken.
 
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Cuchulainn
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Re: Navier Stokes and Finance ?

January 27th, 2020, 4:10 pm

Hi JohnLeM,
Somewhere you mentioned Godounov scheme but couldn't find it. A related scheme for the pde 
[$]\frac{\partial u}{\partial t} +a\frac{\partial u}{\partial x}  = 0 [$] on the interval [$](0,1)[$] (1)

is 
[$](u_i^{n+1} - u_i^{n})/k + a(u_i^{n+1}  - u_{i-1}^{n})/h = 0[$]

here

[$] a > 0 [$] constant
[$]h,k[$] step sizes in [$]x[$] and [$]t[$] directions, respectively.

Its symbol < 1 and it works for my examples (e.g. Asian style). 

My question is; have you or one of your colleagues seen this, maybe for NS pde? By Godounov's theorem I am 95% sure it is monotonicity preserving.