From c313e71c9a1911a9138e2d81dda9900d4aff3a8f Mon Sep 17 00:00:00 2001
From: Joe Pater <02joepater06@gmail.com>
Date: Mon, 3 Mar 2025 12:11:49 +0000
Subject: [PATCH] Partially done shock calculation
---
flood.py | 56 ++++++++++++++++++++++++++++++--------------------------
1 file changed, 30 insertions(+), 26 deletions(-)
diff --git a/flood.py b/flood.py
index c79f6db..ff0541a 100644
--- a/flood.py
+++ b/flood.py
@@ -3,32 +3,6 @@ from matplotlib import pyplot as plt
from scipy import integrate as sp_int
import numpy as np
-# def wrt_w():
-# A_sym = Symbol("A")
-# l = Function("l")(A_sym)
-
-# w_sym = w = Symbol("w", positive=True)
-# x = Symbol("x")
-
-# a = Symbol("a", positive=True)
-# large = 100000
-# h = Piecewise((large*(a-x), x<-a), (0, x<=a), (large*(x-a), True))
-# w_of_A = a
-
-# dh_dx = diff(h, x)
-# dl_dx = sqrt(dh_dx**2 + 1)
-# l = integrate(dl_dx, (x, -w/2, w/2))
-
-# A = w*h.subs(x, w/2) - integrate(dh_dx, (x, -w/2, w/2))
-
-# if w_of_A is None:
-# w_of_A = solve(A_sym - A, w)[0]
-
-# w = w_of_A.subs("A", A)
-
-# print(simplify(l))
-# print(simplify(l.subs(w_sym, w)))
-
def plot_expr(f, x_sym, lim, N):
F = lambdify(x_sym, f)
x = []
@@ -86,6 +60,36 @@ def derive_wetted_perim(w, y, A_sym, debug=False):
return l_of_A
+def shock_step(y, t, vs, vc, dvc_dc, dc_dx0):
+ x = y[0]
+ c_L = y[1]
+ c_R = y[2]
+
+ dx_dt = vs(c_L, c_R)
+
+ vc_L = vc(c_L)
+ vc_R = vc(c_R)
+ x0L = x - t*vc_L
+ x0R = x - t*vc_R
+ dcL_dx0 = dc_dx0(x0L)
+ dcR_dx0 = dc_dx0(x0R)
+
+ dcL_dt = dcL_dx0 * (vc_L - dx_dt) / (1 - t*dvc_dc(c_L)*dcL_dx0)
+ dcR_dt = dcR_dx0 * (vc_R - dx_dt) / (1 - t*dvc_dc(c_R)*dcR_dx0)
+
+ return [dx_dt, dcL_dt, dcR_dt]
+
+def solve_shock(Q, c_init, x0, t0):
+ pass
+
+def solve_characteristics(Q, c_init, delta_x, delta_t, T):
+ ch = [{"pts":[],"x":c} for c in c_init]
+
+ for i in range(int(T/delta_t)):
+ t = delta_t * i
+ for char in ch:
+ char["pts"].append()
+
def godunov_solve(Q, c_init, c_inflow, delta, t):
gstep = lambda c, t: godunov_step(Q, delta, c, c_inflow)
return sp_int.odeint(gstep, c_init, t)
--
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