bmlite.mesh#

The mesh module has functions to build pointers and meshes. Pointers are the integer indices for state variables. State variables in a model may be defined in different dimensions. For example, phi_ed is 0D in the single particle model and Li_ed is 1D in the r direction. Therefore, within any given model, it may be useful to have a combination of ptr for 0D, x_ptr for 1D in x, xr_ptr for 2D in x and r, etc.

This module also contains functions to build meshes. In finite volume methods, the mesh specifies the locations of the control volume centers as well as the interfaces between two control volumes. It makes sense to store both pointers and mesh functions in the same module because the pointers must be self consistent for any given model.

Functions#

param_weights(xm, xp)

Determine relative parameter weights between adjacent control volumes.

r_ptr(domain, keys)

Add an r pointer dictionary to the domain object.

uniform_mesh(Lx, Nx[, x0])

Determine the interface and center locations for uniformly meshed control

x_ptr(domain, keys)

Add an x pointer dictionary to the domain object.

xr_ptr(domain, keys)

Add an xr pointer dictionary to the domain object.

Module Contents#

bmlite.mesh.param_weights(xm, xp)[source]#

Determine relative parameter weights between adjacent control volumes.

In finite volume method solutions, fluxes are calculated at the boundaries between control volumes. Therefore, locally resolved parameters must be weighted between the adjacent volumes participating in the calculation. This function calculates those weights.

Parameters:

  • xm (1D array) – Locations of the “minus” interfaces in the mesh.

  • xp (1D array) – Locations of the “plus” interfaces in the mesh.

Returns:

  • wt_m (1D array) – Parameter weights for each of the “minus” half volumes.

  • wt_p (1D array) – Parameter weights for each of the “plus” half volumes.

bmlite.mesh.r_ptr(domain, keys)[source]#

Add an r pointer dictionary to the domain object.

An r pointer is a dictionary where the keys are variables and the values are 1D int arrays that specify the solution vector indices for all of the specified variable’s values in the r direction. Using this pointer removes for loops from the model DAEs and makes it easier to vectorize expressions.

Parameters:

  • domain (domain object) – A domain (anode, separator, cathode, etc.) object from one of the model domain modules. The domain should already have ptr and Nr attributes. The ptr attribute is a dictionary where the keys are variable names and the values are the indices for the first occurrence of that variable. Nr is the number of r control volumes.

  • keys (list[str]) – A list of the variable names defined in the r direction. This list should be a subset of the domain’s existing ptr keys.

bmlite.mesh.uniform_mesh(Lx, Nx, x0=0.0)[source]#

Determine the interface and center locations for uniformly meshed control volumes.

Parameters:

  • Lx (float) – The length of the domain to mesh.

  • Nx (int) – Number of control volumes that span the domain’s length.

  • x0 (int, optional) – The reference value for the start of the domain’s mesh. The default is 0.

Returns:

  • xm (1D array) – The “minus” interface locations. Note that xm[0] = x0.

  • xp (1D array) – The “plus” interface locations. Note that xp[0] = x0 + Lx.

  • x (1D array) – The locations of the control volume centers. xm[i] < x[i] < xp[i] for all control volumes i.

Notes

Although the inputs and outputs are labeled using x as the variable, this mesh is equally valid for other directions (e.g., radial).

bmlite.mesh.x_ptr(domain, keys)[source]#

Add an x pointer dictionary to the domain object.

An x pointer is a dictionary where the keys are variables and the values are 1D int arrays that specify the solution vector indices for all of the specified variable’s values in the x direction. Using this pointer removes for loops from the model DAEs and makes it easier to vectorize expressions.

Parameters:

  • domain (domain object) – A domain (anode, separator, cathode, etc.) object from one of the model domain modules. The domain should already have ptr and Nx attributes. The ptr attribute is a dictionary where the keys are variable names and the values are the indices for the first occurrence of that variable. Nx is the number of x control volumes.

  • keys (list[str]) – A list of the variable names defined in the x direction. This list should be a subset of the domain’s existing ptr keys.

bmlite.mesh.xr_ptr(domain, keys)[source]#

Add an xr pointer dictionary to the domain object.

An xr pointer is a dictionary where the keys are variables and the values are 2D int arrays that specify the solution vector indices for all of the specified variable’s values in the x (rows) and r (cols) directions. Using this pointer removes for loops from the model DAEs and makes it easier to vectorize expressions.

Parameters:

  • domain (domain object) – A domain (anode, separator, cathode, etc.) object from one of the model domain modules. The domain should already have ptr, Nx, and Nr attributes. The ptr attribute is a dictionary where the keys are variable names and the values are the indices for the first occurrence of that variable. Nx and Nr are the number of x and r control volumes, respectively.

  • keys (list[str]) – A list of the variable names defined in both the x and r directions. This list should be a subset of the domain’s existing ptr keys.