can OpenFOAM calculate definite integral?

sharonyue · April 7, 2014, 23:05

Hi guys,

I wanna implant this equation into OpenFOAM. But I dont know how to deal with this definite integral. Any ideas?

Code:

    fvScalarMatrix nEqn
    (
	 fvm::ddt(n)   
       + fvm::div(phi1,n)
       ==
	  ????
    );

$\frac{{\partial \left( {{\rho _d}{N_d}} \right)}}{{\partial t}} + \nabla \cdot \left( {{\rho _d}{u_d}{N_d}} \right) = \int\limits_{0.5}^1 {f\left( \varepsilon \right)d\varepsilon }$

chrisb2244 · April 7, 2014, 23:15

What sort of object is f(e)?

I mean, for example, if phi is a surfaceScalarField and U is a volVectorField etc.

sharonyue · April 7, 2014, 23:21

Quote:

Originally Posted by chrisb2244

What sort of object is f(e)?

I mean, for example, if phi is a surfaceScalarField and U is a volVectorField etc.

Actually I made this very simple to make it clear. The complete edition is

$f\left( \xi \right) = {\xi ^{0.55}} \cdot {e^{\left( {surfacetension \bullet rho \bullet epsilon \bullet \xi } \right)}}$

So I think its volScalarField. rite?

chrisb2244 · April 8, 2014, 00:03

So I took a few swings at this but I think you're going to wind up with a Gamma function in your integrated quantity here.

http://reference.wolfram.com/mathematica/ref/Gamma.html

https://www.wolframalpha.com/input/?...8a%20x%29&lk=2

I'm not sure how you'd want to implement that in OpenFOAM :/

You can presumably get somewhere by just summing up over a set of values of $\xi$ but I don't know how horribly inaccurate that will become.

You have all of the fields you're going to need reasonably easily accessible, but I'm not sure how to get a better answer than writing out some sort of for loop, or a functor - which would require you to write a class afaict.

chrisb2244 · April 8, 2014, 00:05

In terms of a for loop, what I mean is something conceptually like

Code:

for (double x = 0.5; x <= 1; x = x+0.01)
{
     sum += ( pow(x, 0.55)  * exp(a * x));
}

where a is a volScalarField equal to the product of your $\rho \epsilon \sigma$

sharonyue · April 8, 2014, 00:17

Quote:

Originally Posted by chrisb2244

In terms of a for loop, what I mean is something conceptually like

Code:

for (double x = 0.5; x <= 1; x = x+0.01)
{
     sum += ( pow(x, 0.55)  * exp(a * x));
}

where a is a volScalarField equal to the product of your $\rho \epsilon \sigma$

This method is feasible. But I think if OpenFOAM can deal with definite integral directly, that would be perfect. And the Gamma function you'd mentioned Im not familar with that, maybe it will take me a while to dig into it.

Actually Im tring to implant PBM into Foam, the RHS of the equation is luo breakage kernel~. Right now Im stuck here. I will try your loop method and keep this thread update. However, I dont know if it would be accurate, but its a good start I think. Thanks very much.

April 7, 2014, 23:05	can OpenFOAM calculate definite integral?	#1
sharonyue Senior Member Dongyue Li Join Date: Jun 2012 Location: Beijing, China Posts: 848 Rep Power: 18	Hi guys, I wanna implant this equation into OpenFOAM. But I dont know how to deal with this definite integral. Any ideas? Code: fvScalarMatrix nEqn ( fvm::ddt(n) + fvm::div(phi1,n) == ???? ); $\frac{{\partial \left( {{\rho _d}{N_d}} \right)}}{{\partial t}} + \nabla \cdot \left( {{\rho _d}{u_d}{N_d}} \right) = \int\limits_{0.5}^1 {f\left( \varepsilon \right)d\varepsilon }$

April 8, 2014, 00:05		#5
chrisb2244 Member Christian Butcher Join Date: Jul 2013 Location: Japan Posts: 85 Rep Power: 13	In terms of a for loop, what I mean is something conceptually like Code: for (double x = 0.5; x <= 1; x = x+0.01) { sum += ( pow(x, 0.55) * exp(a * x)); } where a is a volScalarField equal to the product of your $\rho \epsilon \sigma$ randolph likes this.

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April 7, 2014, 23:15		#2
chrisb2244 Member Christian Butcher Join Date: Jul 2013 Location: Japan Posts: 85 Rep Power: 13	What sort of object is f(e)? I mean, for example, if phi is a surfaceScalarField and U is a volVectorField etc.

April 8, 2014, 00:03		#4
chrisb2244 Member Christian Butcher Join Date: Jul 2013 Location: Japan Posts: 85 Rep Power: 13	So I took a few swings at this but I think you're going to wind up with a Gamma function in your integrated quantity here. http://reference.wolfram.com/mathematica/ref/Gamma.html https://www.wolframalpha.com/input/?...8a%20x%29&lk=2 I'm not sure how you'd want to implement that in OpenFOAM :/ You can presumably get somewhere by just summing up over a set of values of $\xi$ but I don't know how horribly inaccurate that will become. You have all of the fields you're going to need reasonably easily accessible, but I'm not sure how to get a better answer than writing out some sort of for loop, or a functor - which would require you to write a class afaict.