class_preso.weno_computations module¶
Helper functions for weno_computations
notebook.
Slides can be seen on nbviewer.

class_preso.weno_computations.
discontinuity_to_volume
()[source]¶ Make plots similar to introductory, but with a discontinuity.

class_preso.weno_computations.
discontinuity_to_volume_single_cell
(stopping_point=None)[source]¶ Plot a piecewise constant function w/discontinuity towards the left.
Parameters: stopping_point (int) – (Optional) The transition point to stop at when creating the plot. By passing in 0, 1, 2, … this allows us to create a short slideshow.

class_preso.weno_computations.
interp_simple_stencils
()[source]¶ Return interpolated values for \(u_{j+1/2}\) using simple stencils.
First uses three sets of interpolating values,
\[\left\{\overline{u}_{j2}, \overline{u}_{j1}, \overline{u}_j\right\}, \left\{\overline{u}_{j1}, \overline{u}_j, \overline{u}_{j+1}\right\}, \left\{\overline{u}_j, \overline{u}_{j+1}, \overline{u}_{j+2}\right\},\]to give local order three approximations.
Then uses all five points \(\left\{x_{j2}, x_{j1}, x_j, x_{j+1}, x_{j+2}\right\}\) to give an order five approximation on the whole stencil.
Return type: tuple Returns: Quadraple of LaTeX strings, one for each set of interpolating points, in the order described above.

class_preso.weno_computations.
make_intro_plots
(stopping_point=None)[source]¶ Make introductory plots.
Uses
\[\overline{u}_{2} = 0, \overline{u}_{1} = 3, \overline{u}_{0} = 2, \overline{u}_{1} = 1, \overline{u}_{2} = 2\]And plots the interpolations by quadratics (on the three contiguous subregions) and by a quartic that preserve the interval.

class_preso.weno_computations.
make_shock_plot
()[source]¶ Make plots similar to introductory, but with a discontinuity.

class_preso.weno_computations.
make_shock_plot_single_cell
()[source]¶ Plot the reconstructed polynomials that occur near a shock.

class_preso.weno_computations.
to_latex
(value, replace_dict)[source]¶ Convert an expression to LaTeX.
This method is required so we can get a specified ordering for terms that may not have the desired lexicographic ordering.
Parameters:  value (
sympy.core.expr.Expr
) – A  replace_dict (dict) – Dictionary where keys are old variable names (as strings) and values are the new variable names to replace them with.
Return type: Returns: The value as LaTeX, with all variables replaced.
 value (