Double Inner Product of Two Second Rank Tensors

idrees khan · December 8, 2020, 09:50

Hello,
sorry to say i post so many times but no one is going to answer my question.

I'm going to add Temperature equation to viscoelasticFluidFoam solver(screenshort is attached).

fvScalarMatrix TEqn
(
fvm::ddt(T)
+ fvm::div(phi,T)
- fvm::laplacian(DT,T)
- 1.0/rho/Cv * (gamma*visco.tau() && Foam::symm(fvc::grad(U))+ (Foam::exp( -C11*(T - To) / (C21 + T - To) )*etaS*Foam::symm(fvc::grad(U)))&& Foam:

fvc::grad(U)))
);

TEqn.relax();
TEqn.solve();

when i add and compile with "wmake" getting error's(screenshort is attached)

after this i removed the term "&& Foam:

fvc::grad(U)))" and compile with wmake it work.
kindly any one who know guide me that i may fix this problem.
regards
idrees

Tobermory · December 8, 2020, 13:06

Well, the error message is telling you that you are trying to do the double inner product of a double (ie scalar) and a tensor. Unsurprisingly it can't do this.

Also not surprising is that the code compiles when you remove the part that follows the &&, since that just leaves the left hand side of the && which is a scalar.

The question you need to ask yourself now is: why is the left hand side a scalar and not a tensor?

It's impossible to debug from your partial listing - but here are a few pieces of advice. Start by stripping back the equation and feed terms in from the right hand side. E.g. start with the symm(grad(U))&&grad(U) term, and note that one is a symm tensor, the other isn't. Get that to work, then start adding the other terms. Look for examples of similar coding in the library applications - do a grep on symm(grad(U)) for example to find these. Read the error messages carefully and think about what it's telling you - I know there's a lot of text there ... but within the text often hides the solution.

Good luck.

idrees khan · December 9, 2020, 04:04

Quote:

Originally Posted by Tobermory

Well, the error message is telling you that you are trying to do the double inner product of a double (ie scalar) and a tensor. Unsurprisingly it can't do this.

Also not surprising is that the code compiles when you remove the part that follows the &&, since that just leaves the left hand side of the && which is a scalar.

The question you need to ask yourself now is: why is the left hand side a scalar and not a tensor?

It's impossible to debug from your partial listing - but here are a few pieces of advice. Start by stripping back the equation and feed terms in from the right hand side. E.g. start with the symm(grad(U))&&grad(U) term, and note that one is a symm tensor, the other isn't. Get that to work, then start adding the other terms. Look for examples of similar coding in the library applications - do a grep on symm(grad(U)) for example to find these. Read the error messages carefully and think about what it's telling you - I know there's a lot of text there ... but within the text often hides the solution.

Good luck.

Dear Tobermory,
Bundle thanks for your reply.
Actually I'm going to review the paper (link for the paper doi:10.1016/j.cnsns.2010.07.006

Author: T. Chinyoka at University of Cape Town ).
here solvent viscosity etaS(T) = Foam::exp( -C11*(T - To) / (C21 + T - To) )*etaS,which is basically a scalar, polymeric viscosity etaP(T) and relaxation Time Lambda(T) for the simplicity instead of Arrhenius law i"m going to use WLF to update parameters like viscosity and relaxation time.

(Foam::exp( -C11*(T - To) / (C21 + T - To) )*etaS*Foam::symm(fvc::grad(U)))&& Foam:

fvc::grad(U)))
it is basically given in the paper like so (please have a look the temperature equation in paper)
but what i know that the value of etaS(T) is scalar and Foam::symm(fvc::grad(U)) tensor of rank 2 when i multiply it should be tensor again.but i don't why its scalar.
Also I'll try what you suggest me.

regards
Idrees

Tobermory · December 12, 2020, 11:01

Dear Idrees

I am running on the foundation version of OpenFOAM and so don't have direct access to viscoelasticFluidFoam, so I added the following coding to pisoFoam. As a result, I have had to hard code in some of the variables like tau etc. Regardless, this compiles fine and should show you how to modify your code. Note the way that I started testing syntax with variables tgradU, tmp1, tmp2 etc. This is a good, methodical debugging approach that is worth you copying.

Code:

	//define some dimensioned variables first
	dimensionedScalar DT("DT", dimensionSet(0, 2, -1, 0, 0, 0, 0), 0.002);
	dimensionedScalar rho("rho", dimensionSet(1, -3, 0, 0, 0, 0, 0), 1.0);
	dimensionedScalar Cp("Cp", dimensionSet(0, 2, -2, -1, 0, 0, 0), 1000);
	dimensionedScalar muS("muS", dimensionSet(1, -1, -1, 0, 0, 0, 0), 0.00001);
	dimensionedScalar muP("muP", dimensionSet(1, -1, -1, 0, 0, 0, 0), 0.00001);
	scalar gamma(1.0);

       //test syntax
	volTensorField tgradU = fvc::grad(U);
	volSymmTensorField tmp1 = symm(tgradU);
	volScalarField tmp2 = tmp1 && tgradU;
	volScalarField tmp3 = symm(tgradU) && tgradU;
	volScalarField tmp4 = symm(fvc::grad(U)) && fvc::grad(U);

        //define main quantities
	volSymmTensorField S = symm(fvc::grad(U));
	volSymmTensorField tau = muP*symm(fvc::grad(U));
	volScalarField Q = gamma*(tau && S) + muS*(S && fvc::grad(U));

       //attempt at T equation, using above variables
	fvScalarMatrix TEqn
	(
	    fvm::ddt(T)
	  + fvm::div(phi,T)
	  - fvm::laplacian(DT,T)
	  - (1.0/rho/Cp) * Q
	);

       //alternate T equation, without unnecessary additional variables (storage)
	fvScalarMatrix TEqn2
	(
	    fvm::ddt(T)
	  + fvm::div(phi,T)
	  - fvm::laplacian(DT,T)
	  - (1.0/rho/Cp) * (gamma*(muP*symm(fvc::grad(U)) && symm(fvc::grad(U))) + muS*(symm(fvc::grad(U)) && fvc::grad(U)))
	);

I hope this helps. Good luck.

rtyme06 · December 14, 2020, 08:20

Tobermory you are awsome. Every advice you gave are pure gold. I hope young CFD people will learn a lot from this.

Tobermory · December 14, 2020, 09:20

That's very kind - thank you; I am glad you appreciate my posts. This forum is a fantastic collection of people and their experiences, and I get out as much as I put in!

idrees khan · December 15, 2020, 10:19

Quote:

Originally Posted by Tobermory

Dear Idrees

I am running on the foundation version of OpenFOAM and so don't have direct access to viscoelasticFluidFoam, so I added the following coding to pisoFoam. As a result, I have had to hard code in some of the variables like tau etc. Regardless, this compiles fine and should show you how to modify your code. Note the way that I started testing syntax with variables tgradU, tmp1, tmp2 etc. This is a good, methodical debugging approach that is worth you copying.

Code:

    //define some dimensioned variables first
    dimensionedScalar DT("DT", dimensionSet(0, 2, -1, 0, 0, 0, 0), 0.002);
    dimensionedScalar rho("rho", dimensionSet(1, -3, 0, 0, 0, 0, 0), 1.0);
    dimensionedScalar Cp("Cp", dimensionSet(0, 2, -2, -1, 0, 0, 0), 1000);
    dimensionedScalar muS("muS", dimensionSet(1, -1, -1, 0, 0, 0, 0), 0.00001);
    dimensionedScalar muP("muP", dimensionSet(1, -1, -1, 0, 0, 0, 0), 0.00001);
    scalar gamma(1.0);

       //test syntax
    volTensorField tgradU = fvc::grad(U);
    volSymmTensorField tmp1 = symm(tgradU);
    volScalarField tmp2 = tmp1 && tgradU;
    volScalarField tmp3 = symm(tgradU) && tgradU;
    volScalarField tmp4 = symm(fvc::grad(U)) && fvc::grad(U);

        //define main quantities
    volSymmTensorField S = symm(fvc::grad(U));
    volSymmTensorField tau = muP*symm(fvc::grad(U));
    volScalarField Q = gamma*(tau && S) + muS*(S && fvc::grad(U));

       //attempt at T equation, using above variables
    fvScalarMatrix TEqn
    (
        fvm::ddt(T)
      + fvm::div(phi,T)
      - fvm::laplacian(DT,T)
      - (1.0/rho/Cp) * Q
    );

       //alternate T equation, without unnecessary additional variables (storage)
    fvScalarMatrix TEqn2
    (
        fvm::ddt(T)
      + fvm::div(phi,T)
      - fvm::laplacian(DT,T)
      - (1.0/rho/Cp) * (gamma*(muP*symm(fvc::grad(U)) && symm(fvc::grad(U))) + muS*(symm(fvc::grad(U)) && fvc::grad(U)))
    );

I hope this helps. Good luck.

Dear Tobermory
Thank so much i add your techniques and compile it with "wmake"
now i added some other terms in temperature equation according to paper ( screenshort is attached) and compile it it work's.
but when i run solver (name viscoelasticFluidFoamUser) it gives me an error(screenshort is attached.) please have a look the paper which i send it to you.
regards
idrees khan

Tobermory · December 15, 2020, 10:31

Good news Idrees - it looks like you are pretty close. The error message

Code:

Argument of trancendental function not dimensionless

is basically telling you that you are trying to calculate a trancendental function (i.e. a log, exp or trig function) with a parameter that is not dimensionless.

Looking at your snapshot of your code, you have

Code:

exp(-E/(R*T)

, so this is perhaps where the error is occurring. I would suggest checking that the units of E and R are correct. Good luck.

idrees khan · December 17, 2020, 10:16

Quote:

Originally Posted by Tobermory

Good news Idrees - it looks like you are pretty close. The error message

Code:

Argument of trancendental function not dimensionless

is basically telling you that you are trying to calculate a trancendental function (i.e. a log, exp or trig function) with a parameter that is not dimensionless.

Looking at your snapshot of your code, you have

Code:

exp(-E/(R*T)

, so this is perhaps where the error is occurring. I would suggest checking that the units of E and R are correct. Good luck.

Dear Tobermory
Thank you

I check that and exactly the problem was in exp(-E/(R*T) means in dimensions.
but now when i run it gives me the problem which seems that still some terms are not
dimensionally correct.

regards
Idrees

idrees khan · December 17, 2020, 10:19

Sorry i did't attached the screenshort here is screenshort of the erorr.

idrees khan · February 23, 2021, 02:59

Dear Tobermory,
kindly if you could guide me about the last term (have a look the screenshot please)

Code:

(delU.delmuS(T))/rho_

where muS is solvent viscosity just like etaP(T)(polymer viscosity ) define by

Code:

volScalarField muS   = Foam::exp( -C11_*(T - To_) / (C21_ + T - To_) )*etaS_;

how to write it

should i write it like

Code:

 fvc:: laplacian(muS /rho_, U, "laplacian(muS ,U)")

regards
idrees khan

Tobermory · February 23, 2021, 04:15

Which "last" term are you trying to write, buddy? The Laplacian
$\nabla \cdot (\eta \nabla U)$ or the "last" term in the equation $\nabla U \cdot \nabla\eta$ ?

From your post:

Code:

 fvc:: laplacian(muS /rho_, U, "laplacian(muS ,U)")

it looks like you are writing the Laplacian, in explicit (fvc) formulation. If it's the last term you want, then you'll need something like

Code:

fvc::grad(U) & fvc::grad(mu)

Whichever, try it and see what the compiler says. Best way to learn, my friend. Good luck.

idrees khan · February 23, 2021, 05:13

Dear Tobermory,
Thank you,

I was talking about this
$\nabla U \cdot \nabla\eta$ ?

Code:

fvc::grad(U) & fvc::grad(mu)

where

Code:

volScalarField muS   = Foam::exp( -C11_*(T - To_) / (C21_ + T - To_) )*etaS_;

but my question if i want to write it implicitly/explicitly how i'll write it?
we know with fvm,sp,suSp(depends upon the sign) respectively will write implicitly and fvc explicitly,

if I write it like

Code:

fvc::grad(U) & fvc::grad(mu)

it will write explicitly.
kindly correct me if I'm wrong.

regards
idrees khan

December 8, 2020, 13:06		#2
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 666 Rep Power: 14	Well, the error message is telling you that you are trying to do the double inner product of a double (ie scalar) and a tensor. Unsurprisingly it can't do this. Also not surprising is that the code compiles when you remove the part that follows the &&, since that just leaves the left hand side of the && which is a scalar. The question you need to ask yourself now is: why is the left hand side a scalar and not a tensor? It's impossible to debug from your partial listing - but here are a few pieces of advice. Start by stripping back the equation and feed terms in from the right hand side. E.g. start with the symm(grad(U))&&grad(U) term, and note that one is a symm tensor, the other isn't. Get that to work, then start adding the other terms. Look for examples of similar coding in the library applications - do a grep on symm(grad(U)) for example to find these. Read the error messages carefully and think about what it's telling you - I know there's a lot of text there ... but within the text often hides the solution. Good luck. idrees khan likes this.

December 14, 2020, 08:20		#5
rtyme06 New Member raihan Join Date: Feb 2015 Posts: 9 Rep Power: 11	Tobermory you are awsome. Every advice you gave are pure gold. I hope young CFD people will learn a lot from this. Tobermory likes this.

December 15, 2020, 10:31		#8
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 666 Rep Power: 14	Good news Idrees - it looks like you are pretty close. The error message Code: Argument of trancendental function not dimensionless is basically telling you that you are trying to calculate a trancendental function (i.e. a log, exp or trig function) with a parameter that is not dimensionless. Looking at your snapshot of your code, you have Code: exp(-E/(R*T) , so this is perhaps where the error is occurring. I would suggest checking that the units of E and R are correct. Good luck.

February 23, 2021, 04:15		#12
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 666 Rep Power: 14	Which "last" term are you trying to write, buddy? The Laplacian $\nabla \cdot (\eta \nabla U)$ or the "last" term in the equation $\nabla U \cdot \nabla\eta$ ? From your post: Code: fvc:: laplacian(muS /rho_, U, "laplacian(muS ,U)") it looks like you are writing the Laplacian, in explicit (fvc) formulation. If it's the last term you want, then you'll need something like Code: fvc::grad(U) & fvc::grad(mu) Whichever, try it and see what the compiler says. Best way to learn, my friend. Good luck.

February 23, 2021, 05:13		#13
idrees khan Member idrees khan Join Date: Jun 2019 Posts: 36 Rep Power: 6	Dear Tobermory, Thank you, I was talking about this $\nabla U \cdot \nabla\eta$ ? Code: fvc::grad(U) & fvc::grad(mu) where Code: volScalarField muS = Foam::exp( -C11_(T - To_) / (C21_ + T - To_) )etaS_; but my question if i want to write it implicitly/explicitly how i'll write it? we know with fvm,sp,suSp(depends upon the sign) respectively will write implicitly and fvc explicitly, if I write it like Code: fvc::grad(U) & fvc::grad(mu) it will write explicitly. kindly correct me if I'm wrong. regards idrees khan

December 14, 2020, 09:20		#6
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 666 Rep Power: 14	That's very kind - thank you; I am glad you appreciate my posts. This forum is a fantastic collection of people and their experiences, and I get out as much as I put in!

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