MMS Verification of LevelSetAdvection Kernel

This computes the forcing function for a known solution of the advection portion of the level set equation.

Load the necessary python libraries.



In [1]:

    
%matplotlib inline
import glob
from sympy import *
import pandas
init_printing()

Define the Manufactured solution

Define the assumed (exact) solution as a fuction of x with a non-constant velocity.



In [2]:

    
x,a,b= symbols('x a b')
v = 2 
u = a*cos(pi*x)*sin(pi*x/b)
u









    Out[2]:





$$a \sin{\left (\frac{\pi x}{b} \right )} \cos{\left (\pi x \right )}$$

Compute the forcing function.



In [3]:

    
f = v*diff(u, x)
f









    Out[3]:





$$- 2 \pi a \sin{\left (\pi x \right )} \sin{\left (\frac{\pi x}{b} \right )} + \frac{2 \pi}{b} a \cos{\left (\pi x \right )} \cos{\left (\frac{\pi x}{b} \right )}$$

Create ParsedFunction Strings

Build a string of the exact and forcing function to be copied to the input file (advection_mms.i).

The only syntax that needs to change to make this string work with MOOSE ParsedFunction is the exponent operator.



In [4]:

    
str(u).replace('**', '^')









    Out[4]:





'a*sin(pi*x/b)*cos(pi*x)'



In [5]:

    
str(f).replace('**', '^')









    Out[5]:





'-2*pi*a*sin(pi*x)*sin(pi*x/b) + 2*pi*a*cos(pi*x)*cos(pi*x/b)/b'

Convergence Plot



In [11]:

    
%run convergence.py