Hi all,

I have developed the code below to solve a non-linear scalar hyperbolic conservation law (Burgers' equation). I want to advance to solving a one dimensional system of Euler equations for Gas Dynamics (which is also a hyperbolic partial differential equation) in the similar manner. Can anyone advise on how to do this? Thanks.

"""  """
from numpy import *
from scitools.std import *
import time
import glob,os
for filename in glob.glob('Burgers*.png'):

N = 1001
M = 75; 
Dx = 1.5/M    
Dt = 0.0005
a = 1.0
def Initialise():
    U = zeros(M)
    K  = linspace(0.0,1.5, M+1) 
    for i in range(M):          
        if K[i] <= 0.5:  U[i] = -0.5
        elif K[i] >= 0.5 and K[i] <= 1 : U[i] = 1
        elif K[i] >= 1: U[i]  = 0

         return U

def Evolve_in_One_Timestep (U):

#Create an array to store the new values of the solution

    U_new = zeros((M,), float32)

    for k in range (1, M-1):
        derivative = -0.25*(U[k+1]**2 - U[k-1]**2)*(Dt/Dx) + 0.5*sqrt(a)*(U[k+1] - 2*U[k] + U[k-1])*(Dt/Dx)

        U_new[k] = U[k] + derivative
        U_new[0] = -0.5
        U_new[M-1] = 0
    return  U_new

#Initialising the data array

U_data = Initialise()
counter = 0
for n in range(0,N):
    U_data = Evolve_in_One_Timestep(U_data)
    t = n*Dt

    if (n%100==0):
        plotlabel= "t = " + str(n*Dt)  #time labelling
        plot(linspace(0.0,0.75,M), U_data,'r0.3',label=plotlabel,legend='t=%4.2f' % t , hardcopy = 'Burgers%04d.png' % counter )
        counter += 1
        time.sleep(0.5) # a pause to control movie speed


Edited 4 Years Ago by mike_2000_17: Fixed formatting

Could you give it another try. Your formatting is complitly mixed up. Also variables and functions have capitalized names normally recerved for object classes. Try to change names more descriptive and follow Python PEP8 standard when possible if you want help. Otherwise the helper should recode the program to understand it. Comments like initializing data array do not help, that is obvious in next line. Goood that you have giving little effort to it but you are going wrong way.

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