Functions, Aux Kernels, and Kernels (and materials!?)

[Bryan Eyers]

Hi all, first post. :)  I attended Derick's workshop at PSU a couple weeks ago, but it was my first exposure to MOOSE.  Also, disclaimer: this is related to a term project for Prof. Tonks.  Not that I think he'll mind me posting here; I know he reads this forum anyways.  Just thought I should mention it.

So I inherited a model that already has some multiphysics set up for a 2D axisymmetric BWR fuel pin, including heat conduction.  I added a function to implement a cosine power distribution in space and time, and dropped it into the heat transfer kernel.  I think that part's working, based on some pretty peacock pictures.  Now I want to model fission gas migrating from the fuel to the gap.  I would like to calculate buildup as proportional to Q_dot(x,t), and loss as proportional to both T(x,t) and C_gas(x,t).  Then I want to keep a running tally of all the gas lost, and use that value to drive gap conductivity.  I've tried two different approaches:

Option 1: create a new function that describes the gas rate equation in the fuel, and use a cumulative value post processor.

Reasoning: I've created functions for other things and they worked.

Problem: I don't know what "CumulativeValuePostProcessor" accumulates over.  I want to keep the spatial distribution of gas in the fuel so I can diffuse it out based on temperature at each time step.  My hunch is that CumValPP doesn't do this.

Option 2: create an aux kernel+variable that tracks gas buildup in the fuel over space and time.

Reasoning: I think aux kernels and aux variables are for spatially dependent physics that don't need to be coupled to the main solve.  Thus "aux".

Problem: I don't really know what I'm doing.  I'm not sure what type of aux kernel to use, and I have no idea of how to set up the material.

Problem: I'm also not sure how to integrate to get the cumulative gas that diffuses to the gap.

My guess is that Option 2 is the right one, and I feel like MOOSE is probably well suited to solving such a simple diff eq, if only I knew how.  Anybody willing to offer a push??  Thanks in advance. :)

Bryan

[Anil Kunwar]

Hi Bryan,
The way  we define entities in MOOSE (or FEM) in general is the structure of partial differential equation (PDE).  I believe MOOSE is very beautiful in giving such definitions.
Let's say we have an advection-diffusion-source PDE in transient description .
\partial C/\partial t = V.\nabla C +  \nabla. D.\nabla C  + S 

[Anil Kunwar]

Hi Bryan,
The way  we define entities in MOOSE (or FEM) in general is the structure of partial differential equation (PDE).  I believe MOOSE is very beautiful in giving such definitions.
Let's say we have an advection-diffusion-source PDE in transient description .

\partial C/\partial t = V.\nabla C +  \nabla. D.\nabla C  + S  ...(1)

In Eq. 1, the first term in LHS is transient term. The first, second and third term in RHS are advection, diffusion and source/sink term.
We will form residual (R) of this PDE by bringing all the terms in LHS and having 0 in the RHS.
Then, you can start to define kernel and other stuffs for the terms within this residual.
MOOSE Framework-specific definitions
Kernel: All the four terms transient term, advection terms diffusion term and source term can be sufficiently made into four  kernels in principle. Please see example 2 of moose framework (https://github.com/idaholab/moose/blob/devel/examples/ex02_kernel/ex02.i) which contains kernels only for advection and diffusion term of Eq. (1). The transient term and source term are 0 in example 2.

Materials: Materials and other blocks are the facilitators to kernel in MOOSE style or way. For an example, see the diffusion term having a material property D (diffusivity). Provided it is a scalar value, the structure of kernel will be simple. However, if we/you have to consider the temperature dependence of diffusivity or anisotropy of diffusivity, the kernel for diffusion will become very complex. In this context, you write a material block to define diffusivity (D) and this is called from the kernel with code e.g. _diffusivity(getMaterialProperty<Real>("diffusivity")) This is illustrated in e.g. 8 (https://github.com/idaholab/moose/tree/devel/examples/ex08_materials).

Auxkernelt: Let's assume that the velocity V in the advection term is the drift velocity due to electromigration [V=D*z*e*rho*j/((k_b) * T)] and we/you have defined advection kernel V.\nabla C. In the simulation run if you/we want to output the magnitudes of vector V; then as it is not the solution variable (C), we need to use the concept of Auxkernel and Auxvariable. We define V_x and V_y in 2D as auxvariables for the  calculations (auxkernels in coded form) D*z*e*rho*j_x /((k_b) * T) and D*z*e*rho*j_y/((k_b) * T) respectively. (https://github.com/idaholab/moose/tree/devel/examples/ex10_aux)

BCs: BCs have structure similar to kernel and are implemented at the boundary/boundaries (https://github.com/idaholab/moose/tree/devel/examples/ex04_bcs).


Yours Sincerely,
Anil Kunwar

[Anil Kunwar]

Hi,

Functions: If we want to apply analytical expressions (functions of time and space) from within the input file for BCs or Material Properties etc, then we use the function block. (https://github.com/idaholab/moose/tree/devel/examples/ex13_functions)

Yours Sincerely,
Anil Kunwar

On Thursday, April 20, 2017 at 11:43:31 AM UTC+8, Bryan Eyers wrote:

[Anil Kunwar]

Hi
In summary, kernels describe the physics and other blocks are used to facilitate the simple structure of MOOSE kernel block.

Yours Sincerely

Anil Kunwar

On Thursday, April 20, 2017 at 11:43:31 AM UTC+8, Bryan Eyers wrote:

[Bryan Eyers]

/Thanks, Anil!  This made the relationship between kernels and aux kernels much more clear to me. :)

One further: is there any way to integrate an aux variable over time and space from the input file?  Possibly using a function or post processor?

Thank you very much!

Bryan