Differential Operators¶

discretize.DiffOperators.
checkBC
(bc)[source]¶ Checks if boundary condition ‘bc’ is valid.
Each bc must be either ‘dirichlet’ or ‘neumann’

discretize.DiffOperators.
ddxCellGrad
(n, bc)[source]¶ Create 1D derivative operator from cellcenters to nodes this means we go from n to n+1
For CellCentered Dirichlet, use a ghost point:
(u_1  u_g)/hf = grad u_g u_1 u_2 *  *  * ... ^ 0 u_g =  u_1 grad = 2*u1/dx negitive on the other side.
For CellCentered Neumann, use a ghost point:
(u_1  u_g)/hf = 0 u_g u_1 u_2 *  *  * ... u_g = u_1 grad = 0; put a zero in.

discretize.DiffOperators.
ddxCellGradBC
(n, bc)[source]¶ Create 1D derivative operator from cellcenters to nodes this means we go from n to n+1
For CellCentered Dirichlet, use a ghost point:
(u_1  u_g)/hf = grad u_g u_1 u_2 *  *  * ... ^ u_b
We know the value at the boundary (u_b):
(u_g+u_1)/2 = u_b (the average) u_g = 2*u_b  u_1 So plug in to gradient: (u_1  (2*u_b  u_1))/hf = grad 2*(u_1u_b)/hf = grad
Separate, because BC are known (and can move to RHS later):
( 2/hf )*u_1 + ( 2/hf )*u_b = grad ( ^ ) JUST RETURN THIS

class
discretize.DiffOperators.
DiffOperators
[source]¶ Class creates the differential operators that you need!

faceDiv
¶ Construct divergence operator (facestg to cellcentres).

faceDivx
¶ Construct divergence operator in the x component (facestg to cellcentres).

faceDivy
¶

faceDivz
¶ Construct divergence operator in the z component (facestg to cellcenters).

nodalGrad
¶ Construct gradient operator (nodes to edges).

nodalLaplacian
¶ Construct laplacian operator (nodes to edges).

setCellGradBC
(BC)[source]¶ Function that sets the boundary conditions for cellcentred derivative operators.
 Examples::
# Neumann in all directions BC = ‘neumann’
# 3D, Dirichlet in y Neumann else BC = [‘neumann’, ‘dirichlet’, ‘neumann’]
# 3D, Neumann in x on bottom of domain, Dirichlet else BC = [[‘neumann’, ‘dirichlet’], ‘dirichlet’, ‘dirichlet’]

cellGrad
¶ The cell centered Gradient, takes you to cell faces.

cellGradBC
¶ The cell centered Gradient boundary condition matrix

cellGradx
¶ Cell centered Gradient in the x dimension. Has neumann boundary conditions.

cellGrady
¶

cellGradz
¶ Cell centered Gradient in the x dimension. Has neumann boundary conditions.

edgeCurl
¶ Construct the 3D curl operator.

getBCProjWF
(BC, discretization='CC')[source]¶ The weak form boundary condition projection matrices.
 Examples::
# Neumann in all directions BC = ‘neumann’
# 3D, Dirichlet in y Neumann else BC = [‘neumann’, ‘dirichlet’, ‘neumann’]
# 3D, Neumann in x on bottom of domain, Dirichlet else BC = [[‘neumann’, ‘dirichlet’], ‘dirichlet’, ‘dirichlet’]

getBCProjWF_simple
(discretization='CC')[source]¶ The weak form boundary condition projection matrices when mixed boundary condition is used

aveF2CC
¶ Construct the averaging operator on cell faces to cell centers.

aveF2CCV
¶ Construct the averaging operator on cell faces to cell centers.

aveFx2CC
¶ Construct the averaging operator on cell faces in the x direction to cell centers.

aveFy2CC
¶ Construct the averaging operator on cell faces in the y direction to cell centers.

aveFz2CC
¶ Construct the averaging operator on cell faces in the z direction to cell centers.

aveCC2F
¶ Construct the averaging operator on cell centers to faces.

aveCCV2F
¶ Construct the averaging operator on cell centers to faces as a vector.

aveE2CC
¶ Construct the averaging operator on cell edges to cell centers.

aveE2CCV
¶ Construct the averaging operator on cell edges to cell centers.

aveEx2CC
¶ Construct the averaging operator on cell edges in the x direction to cell centers.

aveEy2CC
¶ Construct the averaging operator on cell edges in the y direction to cell centers.

aveEz2CC
¶ Construct the averaging operator on cell edges in the z direction to cell centers.

aveN2CC
¶ Construct the averaging operator on cell nodes to cell centers.

aveN2E
¶ Construct the averaging operator on cell nodes to cell edges, keeping each dimension separate.

aveN2F
¶ Construct the averaging operator on cell nodes to cell faces, keeping each dimension separate.
