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Commit 23ba624a authored by Jan Habscheid's avatar Jan Habscheid
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Adding examplery code for my problem of problem 2.3

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Project2/src/Figures/MyProblem_0.png 0 → 100644
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Project2/src/Figures/MyProblem_0.png

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Project2/src/Figures/MyProblem_1.png 0 → 100644
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Project2/src/Figures/MyProblem_1.png

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Project2/src/Figures/MyProblem_2.png

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Project2/src/Figures/MyProblem_3.png

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Project2/src/Figures/MyProblem_4.png

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Project2/src/Figures/MyProblem_numerical.png 0 → 100644
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Project2/src/Figures/MyProblem_numerical.png

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Project2/src/GPT.py
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......@@ -46,7 +46,7 @@ x = np.linspace(xmin + dx/2, xmax - dx/2, nx)
# -------------------------------------------------
# Time parameters
# -------------------------------------------------
T = 0.45 # Final time (choose T small enough that waves have not interacted too much)
T = 0.2 # Final time (choose T small enough that waves have not interacted too much)
CFL = 0.5 # CFL number; for f'(u) we know |f'| is at most 2
dt = CFL * dx / 2.0
nt = int(T / dt) + 1
......@@ -138,12 +138,13 @@ u_exact = analytic_solution(x, T)
# Plot all three solutions
# -------------------------------------------------
plt.figure(figsize=(10, 6))
plt.plot(x, u_exact, 'k--', lw=2, label='Analytic')
plt.plot(x, u_lf, 'b-', lw=2, label='Lax-Friedrichs')
plt.plot(x, u_god, 'r-', lw=2, label='Godunov')
# plt.plot(x, u_exact, 'k--', lw=2, label='Analytic')
plt.plot(x, u_lf, 'b-', lw=2)#, label='Lax-Friedrichs')
# plt.plot(x, u_god, 'r-', lw=2, label='Godunov')
plt.xlabel('x')
plt.ylabel('u')
plt.title(f'Solution at time T = {T:.3f}')
plt.legend()
plt.grid(True)
plt.savefig('Figures/MyProblem_numerical.png')
plt.show()
Project2/src/MyProblem.ipynb 0 → 100644
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%% Cell type:code id: tags:
``` python
import numpy as np
import matplotlib.pyplot as plt
```
%% Cell type:code id: tags:
``` python
x = np.linspace(-2, 3, 101)
```
%% Cell type:code id: tags:
``` python
def u0_1(x, t):
u0_1 = np.zeros_like(x)
u0_1 = np.where(
x <= 1/2 * t,
0,
np.where(
x < 1-t,
3/4,
np.where(
x <= 1 + 2*t,
(2 - x/t)/4,
0
)
)
)
return u0_1
def u0_2(x, t):
u0_2 = np.zeros_like(x)
u0_2 = np.where(
x <= -t,
0,
np.where(
x < 2*t,
(2 - x/t) / 4,
np.where(
x <= 1 + t/2,
3/4,
0
)
)
)
return u0_2
```
%% Cell type:code id: tags:
``` python
t = np.linspace(0, .2, 5)
for i in range(5):
plt.figure()
plt.title(f'Time: {t[i]}')
plt.plot(x, u0_1(x, t[i]), label=f"Solution 1")
plt.plot(x, u0_2(x, t[i]), label=f"Solution 2")
plt.legend()
plt.grid()
plt.savefig(f'Figures/MyProblem_{i}.png')
plt.show()
```
%% Output
/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_69457/2027164159.py:11: RuntimeWarning: divide by zero encountered in divide
(2 - x/t)/4,
/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_69457/2027164159.py:11: RuntimeWarning: invalid value encountered in divide
(2 - x/t)/4,
/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_69457/2027164159.py:25: RuntimeWarning: divide by zero encountered in divide
(2 - x/t) / 4,
/var/folders/v_/5q1gkdc53z34pdsfnpkx2t340000gn/T/ipykernel_69457/2027164159.py:25: RuntimeWarning: invalid value encountered in divide
(2 - x/t) / 4,
%% Cell type:code id: tags:
``` python
```
Project2/src/Problem_2_3.ipynb
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