Matrix and Varialbe Definition

treima · July 12, 2012, 02:51

Hello,

is it possible to define a 5x5 matrix in OpenFoam? If yes, how?

The same question is, if there is a possibility to define a vector with 5 components? But I´ve to make this definition in "createFields.H"

I would like to solve the equation

$\frac{d}{dt} v + A \frac{d}{dx} v + B \frac{d}{dy} v + C \frac{d}{dz} v = 0$

where A,B,C are 5x5 matrices and v a 5x1 vector.

Best regards

treima

kathrin_kissling · July 13, 2012, 02:27

Is it just the equation or are you going to solve that on a finite-volume grid?

In Version 1.6-ext there is support for NxN matrices. You might want to check this out!

Best

Kathrin

treima · July 13, 2012, 02:49

Thanks.

I´d like to solve that one the grid for v, yes. I´ve tried to divied this into three equations like the density, momentum and energy equation like the "normal" way, but they are coupled.

Have you ever tried this with OpenFoam 2.1.0, too? Or have you any experience if there is support, too?

And the last question

. Do you know how it is done in 1.6-ext?

Best

treima

treima · August 10, 2012, 03:23

Hello,

I didn´t work on this for a while, but now I´ve found some possiblities and, of course, new problems.

Here ist my partial differential equation system, which i like to solve:

$\frac{\partial}{\partial t} \begin{pmatrix} \Lambda_1 \\ \Lambda_2 \\ \Lambda_3 \\ \Lambda_ 4 \\ \Lambda_5 \end{pmatrix} + \begin{pmatrix} 0 & a_{21} & a_{31} & a_{41} & a_{51} \\ 1 & a_{22} & a_{32} & a_{42} & a_{52} \\ 0 & a_{23} & a_{33} & 0 & a_{53} \\ 0 & a_{24} & 0 & a_{44} & a_{54} \\ 0 & a_{25} & 0 & 0 & a_{55} \end{pmatrix} \frac{\partial}{\partial x} \begin{pmatrix} \Lambda_1 \\ \Lambda_2 \\ \Lambda_3 \\ \Lambda_ 4 \\ \Lambda_5 \end{pmatrix} +$
$+ \begin{pmatrix} 0 & b_{21} & b_{31} & b_{41} & b_{51} \\ 0 & b_{22} & b_{32} & 0 & b_{52} \\ 1 & b_{23} & b_{33} & b_{43} & b_{53} \\ 0 & 0 & b_{34} & b_{44} & b_{54} \\ 0 & 0 & b_{35} & 0 & b_{55} \end{pmatrix} \frac{\partial}{\partial y} \begin{pmatrix} \Lambda_1 \\ \Lambda_2 \\ \Lambda_3 \\ \Lambda_4 \\ \Lambda_5 \end{pmatrix} +$
$+ \begin{pmatrix} 0 & c_{21} & c_{31} & c_{41} & c_{51} \\ 0 & c_{22} & 0 & c_{42} & c_{52} \\ 0 & 0 & c_{33} & c_{43} & c_{53} \\ 1 & c_{24} & c_{34} & c_{44} & c_{54} \\ 0 & 0 & 0 & c_{45} & c_{55} \end{pmatrix} \frac{\partial}{\partial z} \begin{pmatrix} \Lambda_1 \\ \Lambda_2 \\ \Lambda_3 \\ \Lambda_4 \\ \Lambda_5 \end{pmatrix} = 0 \,.$

I´ve defined the matrices via
Matrix<volScalarField,scalarField> jacobi_f(5,5), jacobi_g(5,5), jacobi_h(5,5);
and assigned the elements via
jacobi_f[i][j] = functions;
and so on.

My problem is now, how to deal with vectors of dimension five. It´s not possible to define a five-dimensional volVectorField and to combine this with my matrices.
Is it possible to solve the five dimensional coupled system with OpenFoam? If yes, how can this be done? Do you have any ideas?

regards,
treima

kathrin_kissling · August 10, 2012, 03:32

Check out the VectorN class in 1.6-ext.

There is no such thing in the vanilla version.

Sorry

Best

Kathrin

treima · August 10, 2012, 05:05

Thanks a lot for this quick reply!

I´ve to make some changes in my solver for using it with 1.6-ext.

But do you know an existing solver where VectorN is used?

kathrin_kissling · August 10, 2012, 05:14

Hey treima,

in 1.6-ext there is blockCoupledScalarTransportFoam

documentation and application of the tecnique can be found in Ivor Cliffords work (6th OFW training material) and in my work (see this years OFW presentation slides)

Best

Kathrin

Hisham · August 11, 2012, 07:36

Hello

I think you can go around your problem in OF 2.x by dividing your equation into 5 scalar equations and solve each separately.

I mean the interaction-terms can be treated explicitly and you iterate to converge (the segregated way)

Regards,
Hisham

treima · August 14, 2012, 02:30

Hello,

I´ve thought about this, too. But the five equations are coupled with each other, so that it isn´t possible to extract parts with less then four variables and I think. In OpenFOAM you can´t solve equations with more than one variable, right? Perhaps I didn´t understand this solution, but at the moment I can´t see your point

Thanks Kathrin for hints, I´ll have a closer look at the blockCoupled-solver and try to extend this one for five equations!

Regards
treima

treima · August 24, 2012, 09:34

Hello,

I´ve tried to sperate these equations, like Hisham suggested, in scalar equations. Now I´m solving this problem (for demonstration, I take the first row)

$\frac{\partial}{\partial t} \Lambda_1 + a_{21} \frac{\partial}{\partial x} \Lambda_2 + a_{31} \frac{\partial}{\partial x} \Lambda_3 + a_{41} \frac{\partial}{\partial x} \Lambda_4 + a_{51} \frac{\partial}{\partial x} + b_{21} \frac{\partial}{\partial y} \Lambda_2 + b_{31} \frac{\partial}{\partial y} \Lambda_3 + b_{41} \frac{\partial}{\partial y} \Lambda_4 + b_{51} \frac{\partial}{\partial y} +$
$c_{21} \frac{\partial}{\partial z} \Lambda_2 + c_{31} \frac{\partial}{\partial z} \Lambda_3 + c_{41} \frac{\partial}{\partial z} \Lambda_4 + c_{51} \frac{\partial}{\partial z} = 0$

+ the four other equations.

In OpenFOAM I´ve Implemented this:

solve
(
fvm::ddt(Lambda_1) + a21*gradXLambda2 + 1./tcoeff*a31*gradXLambda3 +
1./tcoeff*a41*gradXLambda4 + 1./pow(tcoeff,2)*a51*gradXLambda5 +
1./tcoeff*b21*gradYLambda2 + 1./tcoeff*b31*gradYLambda3 +
1./tcoeff*b41*gradYLambda4 + 1./pow(tcoeff,2)*b51*gradYLambda5 +
1./tcoeff*c21*gradZLambda2 + 1./tcoeff*c31*gradZLambda3 +
1./tcoeff*c41*gradZLambda4 + 1./pow(tcoeff,2)*c51*gradZLambda5
);

solve
(
equation2
);

solve
(
equation3
);

solve
(
equation4
);

solve
(
equation5
);

where tcoeff is a cofactor to get the right dimensions (at the end, dimensions doesn´t matter) and gradXLambda2, gradXLambda3 are defined as followed:

volScalarField gradXLambda2 (unitVector_x & fvc::grad(Lambda_2));

Is this the right way to do this? The results are a little bit confusing. Perhaps the mistake is in my implementation, in my derivation of the equations, in my boundary conditions or somewhere else.

Do anyone have any experience or suggestions concerning my problem?

Thanks,
treima

July 12, 2012, 02:51	Matrix and Varialbe Definition	#1
treima Member Join Date: Mar 2012 Location: Munich, Germany Posts: 67 Rep Power: 14	Hello, is it possible to define a 5x5 matrix in OpenFoam? If yes, how? The same question is, if there is a possibility to define a vector with 5 components? But I´ve to make this definition in "createFields.H" I would like to solve the equation $\frac{d}{dt} v + A \frac{d}{dx} v + B \frac{d}{dy} v + C \frac{d}{dz} v = 0$ where A,B,C are 5x5 matrices and v a 5x1 vector. Best regards treima

July 13, 2012, 02:27		#2
kathrin_kissling Senior Member Kathrin Kissling Join Date: Mar 2009 Location: Besigheim, Germany Posts: 134 Rep Power: 17	Is it just the equation or are you going to solve that on a finite-volume grid? In Version 1.6-ext there is support for NxN matrices. You might want to check this out! Best Kathrin

July 13, 2012, 02:49		#3
treima Member Join Date: Mar 2012 Location: Munich, Germany Posts: 67 Rep Power: 14	Thanks. I´d like to solve that one the grid for v, yes. I´ve tried to divied this into three equations like the density, momentum and energy equation like the "normal" way, but they are coupled. Have you ever tried this with OpenFoam 2.1.0, too? Or have you any experience if there is support, too? And the last question . Do you know how it is done in 1.6-ext? Best treima

August 10, 2012, 03:23		#4
treima Member Join Date: Mar 2012 Location: Munich, Germany Posts: 67 Rep Power: 14	Hello, I didn´t work on this for a while, but now I´ve found some possiblities and, of course, new problems. Here ist my partial differential equation system, which i like to solve: $\frac{\partial}{\partial t} \begin{pmatrix} \Lambda_1 \\ \Lambda_2 \\ \Lambda_3 \\ \Lambda_ 4 \\ \Lambda_5 \end{pmatrix} + \begin{pmatrix} 0 & a_{21} & a_{31} & a_{41} & a_{51} \\ 1 & a_{22} & a_{32} & a_{42} & a_{52} \\ 0 & a_{23} & a_{33} & 0 & a_{53} \\ 0 & a_{24} & 0 & a_{44} & a_{54} \\ 0 & a_{25} & 0 & 0 & a_{55} \end{pmatrix} \frac{\partial}{\partial x} \begin{pmatrix} \Lambda_1 \\ \Lambda_2 \\ \Lambda_3 \\ \Lambda_ 4 \\ \Lambda_5 \end{pmatrix} +$ $+ \begin{pmatrix} 0 & b_{21} & b_{31} & b_{41} & b_{51} \\ 0 & b_{22} & b_{32} & 0 & b_{52} \\ 1 & b_{23} & b_{33} & b_{43} & b_{53} \\ 0 & 0 & b_{34} & b_{44} & b_{54} \\ 0 & 0 & b_{35} & 0 & b_{55} \end{pmatrix} \frac{\partial}{\partial y} \begin{pmatrix} \Lambda_1 \\ \Lambda_2 \\ \Lambda_3 \\ \Lambda_4 \\ \Lambda_5 \end{pmatrix} +$ $+ \begin{pmatrix} 0 & c_{21} & c_{31} & c_{41} & c_{51} \\ 0 & c_{22} & 0 & c_{42} & c_{52} \\ 0 & 0 & c_{33} & c_{43} & c_{53} \\ 1 & c_{24} & c_{34} & c_{44} & c_{54} \\ 0 & 0 & 0 & c_{45} & c_{55} \end{pmatrix} \frac{\partial}{\partial z} \begin{pmatrix} \Lambda_1 \\ \Lambda_2 \\ \Lambda_3 \\ \Lambda_4 \\ \Lambda_5 \end{pmatrix} = 0 \,.$ I´ve defined the matrices via Matrix<volScalarField,scalarField> jacobi_f(5,5), jacobi_g(5,5), jacobi_h(5,5); and assigned the elements via jacobi_f[i][j] = functions; and so on. My problem is now, how to deal with vectors of dimension five. It´s not possible to define a five-dimensional volVectorField and to combine this with my matrices. Is it possible to solve the five dimensional coupled system with OpenFoam? If yes, how can this be done? Do you have any ideas? regards, treima

August 10, 2012, 03:32		#5
kathrin_kissling Senior Member Kathrin Kissling Join Date: Mar 2009 Location: Besigheim, Germany Posts: 134 Rep Power: 17	Check out the VectorN class in 1.6-ext. There is no such thing in the vanilla version. Sorry Best Kathrin

August 10, 2012, 05:05		#6
treima Member Join Date: Mar 2012 Location: Munich, Germany Posts: 67 Rep Power: 14	Thanks a lot for this quick reply! I´ve to make some changes in my solver for using it with 1.6-ext. But do you know an existing solver where VectorN is used?

August 10, 2012, 05:14		#7
kathrin_kissling Senior Member Kathrin Kissling Join Date: Mar 2009 Location: Besigheim, Germany Posts: 134 Rep Power: 17	Hey treima, in 1.6-ext there is blockCoupledScalarTransportFoam documentation and application of the tecnique can be found in Ivor Cliffords work (6th OFW training material) and in my work (see this years OFW presentation slides) Best Kathrin

August 11, 2012, 07:36		#8
Hisham Senior Member Hisham Elsafti Join Date: Apr 2011 Location: Braunschweig, Germany Posts: 257 Blog Entries: 10 Rep Power: 17	Hello I think you can go around your problem in OF 2.x by dividing your equation into 5 scalar equations and solve each separately. I mean the interaction-terms can be treated explicitly and you iterate to converge (the segregated way) Regards, Hisham

August 14, 2012, 02:30		#9
treima Member Join Date: Mar 2012 Location: Munich, Germany Posts: 67 Rep Power: 14	Hello, I´ve thought about this, too. But the five equations are coupled with each other, so that it isn´t possible to extract parts with less then four variables and I think. In OpenFOAM you can´t solve equations with more than one variable, right? Perhaps I didn´t understand this solution, but at the moment I can´t see your point Thanks Kathrin for hints, I´ll have a closer look at the blockCoupled-solver and try to extend this one for five equations! Regards treima

August 24, 2012, 09:34		#10
treima Member Join Date: Mar 2012 Location: Munich, Germany Posts: 67 Rep Power: 14	Hello, I´ve tried to sperate these equations, like Hisham suggested, in scalar equations. Now I´m solving this problem (for demonstration, I take the first row) $\frac{\partial}{\partial t} \Lambda_1 + a_{21} \frac{\partial}{\partial x} \Lambda_2 + a_{31} \frac{\partial}{\partial x} \Lambda_3 + a_{41} \frac{\partial}{\partial x} \Lambda_4 + a_{51} \frac{\partial}{\partial x} + b_{21} \frac{\partial}{\partial y} \Lambda_2 + b_{31} \frac{\partial}{\partial y} \Lambda_3 + b_{41} \frac{\partial}{\partial y} \Lambda_4 + b_{51} \frac{\partial}{\partial y} +$ $c_{21} \frac{\partial}{\partial z} \Lambda_2 + c_{31} \frac{\partial}{\partial z} \Lambda_3 + c_{41} \frac{\partial}{\partial z} \Lambda_4 + c_{51} \frac{\partial}{\partial z} = 0$ + the four other equations. In OpenFOAM I´ve Implemented this: solve ( fvm::ddt(Lambda_1) + a21gradXLambda2 + 1./tcoeffa31gradXLambda3 + 1./tcoeffa41gradXLambda4 + 1./pow(tcoeff,2)a51gradXLambda5 + 1./tcoeffb21gradYLambda2 + 1./tcoeffb31gradYLambda3 + 1./tcoeffb41gradYLambda4 + 1./pow(tcoeff,2)b51gradYLambda5 + 1./tcoeffc21gradZLambda2 + 1./tcoeffc31gradZLambda3 + 1./tcoeffc41gradZLambda4 + 1./pow(tcoeff,2)c51*gradZLambda5 ); solve ( equation2 ); solve ( equation3 ); solve ( equation4 ); solve ( equation5 ); where tcoeff is a cofactor to get the right dimensions (at the end, dimensions doesn´t matter) and gradXLambda2, gradXLambda3 are defined as followed: volScalarField gradXLambda2 (unitVector_x & fvc::grad(Lambda_2)); Is this the right way to do this? The results are a little bit confusing. Perhaps the mistake is in my implementation, in my derivation of the equations, in my boundary conditions or somewhere else. Do anyone have any experience or suggestions concerning my problem? Thanks, treima