def main():
ainit = np.array([1.0, 1.0, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
nzones = len(ainit)
nolimit = 1
# CFL number
C = 0.7
gr = gp.FVGrid(nzones, ng=4)
a = gr.scratch_array()
a[gr.ilo:gr.ihi + 1] = ainit[:]
pl = gp.PiecewiseLinear(gr, a, nolimit=nolimit)
# loop
for i in range(1, 9):
pl.fill_zero_gradient()
evolve(gr, pl, C, i, nolimit=nolimit)
def riemann():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 4
ng = 2
gr = gp.FVGrid(nzones, ng=ng, xmin=xmin, xmax=xmax)
# interior and ghost cell initialization
a = gr.scratch_array()
a[gr.ilo:gr.ihi + 1] = np.array([0.8, 0.7, 0.4, 0.5])
a[0:gr.ilo] = a[gr.ihi - 1:gr.ihi + 1]
a[gr.ihi:2 * gr.ng + gr.nx] = a[gr.ihi]
pc = gp.PiecewiseConstant(gr, a)
pl = gp.PiecewiseLinear(gr, a, nolimit=1)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid(draw_ghost=1, emphasize_end=1)
gr.label_center(gr.ng - 2, r"$\mathrm{lo-2}$", fontsize="medium")
gr.label_center(gr.ng - 1, r"$\mathrm{lo-1}$", fontsize="medium")
gr.label_center(gr.ng, r"$\mathrm{lo}$", fontsize="medium")
gr.label_center(gr.ng + 1, r"$\mathrm{lo+1}$", fontsize="medium")
gr.label_edge(gr.ng, r"$\mathrm{lo}-\myhalf$", fontsize="medium")
# draw cell averages
for n in range(0, gr.ng + gr.nx - 1):
pc.draw_cell_avg(n, color="0.5", ls=":")
# draw slopes
for n in range(gr.ilo - 1, gr.ihi):
pl.draw_slope(n, color="r")
# compute the states to the left and right of lo-1/2
C = 0.7 # CFL
al = a[gr.ilo - 1] + 0.5 * gr.dx * (1.0 - C) * pl.slope[gr.ilo - 1]
ar = a[gr.ilo] - 0.5 * gr.dx * (1.0 + C) * pl.slope[gr.ilo]
# L
gr.mark_cell_right_state(ng - 1,
r"$a_{\mathrm{lo}+\myhalf,L}^{n+\myhalf}$",
value=al,
vertical="top",
color="b")
# R
gr.mark_cell_left_state(ng,
r"$a_{\mathrm{lo}+\myhalf,R}^{n+\myhalf}$",
value=ar,
vertical="top",
color="b")
plt.xlim(gr.xl[0] - 0.025 * gr.dx, gr.xr[ng + 1] + 0.15 * gr.dx)
plt.ylim(-0.25, 1.1)
plt.axis("off")
plt.subplots_adjust(left=0.025, right=0.95, bottom=0.05, top=0.95)
f = plt.gcf()
f.set_size_inches(8.0, 2.0)
plt.tight_layout()
plt.savefig("riemann-bc.pdf")
import math
import numpy as np
import matplotlib.pyplot as plt
import grid_plot as gp
nzones = 7
# data that lives on the grid
ainit = np.array([0.3, 1.0, 0.9, 0.8, 0.25, 0.15, 0.5])
gr = gp.FVGrid(nzones)
a = gr.scratch_array()
a[gr.ilo:gr.ihi + 1] = ainit[:]
pl_nolim = gp.PiecewiseLinear(gr, a, nolimit=1)
pl = gp.PiecewiseLinear(gr, a)
gr.draw_grid()
gr.label_center(nzones / 2, r"$i$")
gr.label_center(nzones / 2 - 1, r"$i-1$")
gr.label_center(nzones / 2 + 1, r"$i+1$")
gr.label_center(nzones / 2 - 2, r"$i-2$")
gr.label_center(nzones / 2 + 2, r"$i+2$")
#labelEdge(gr, nzones/2, r"$i-1/2$")
#labelEdge(gr, nzones/2+1, r"$i+1/2$")
for n in range(nzones):
pl.draw_cell_avg(n, ls=":", color="0.5")
pl_nolim.draw_slope(n, color="0.5")
import grid_plot as gp
#-----------------------------------------------------------------------------
atemp = np.array([1.0, 1.0, 0.9, 0.8, 0.25, 0.1, 0.1, 0.1])
nzones = len(atemp)
# CFL number
C = 0.6
gr = gp.FVGrid(nzones, ng=4)
a = gr.scratch_array()
a[gr.ilo:gr.ihi + 1] = atemp[:]
pl = gp.PiecewiseLinear(gr, a)
pl.fill_zero_gradient()
#-----------------------------------------------------------------------------
# first frame -- the original cell-averages
plt.clf()
gr.draw_grid()
labels = ["$i-2$", "$i-1$", "$i$", "$i+1$", "$i+2$"]
indices = [
gr.ng + nzones / 2 - 2, gr.ng + nzones / 2 - 1, gr.ng + nzones / 2,
gr.ng + nzones / 2 + 1, gr.ng + nzones / 2 + 2
]
if nolimit:
plt.savefig("rea-nolimit-final_%3.3d.pdf" % (num))
else:
plt.savefig("rea-final_%3.3d.pdf" % (num))
return anew
#-----------------------------------------------------------------------------
ainit = np.array([1.0, 1.0, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1])
nzones = len(ainit)
# CFL number
C = 0.7
nolimit = 1
gr = gp.FVGrid(nzones, ng=4)
a = gr.scratch_array()
a[gr.ilo:gr.ihi + 1] = ainit[:]
pl = gp.PiecewiseLinear(gr, a, nolimit=nolimit)
# loop
for i in range(1, 9):
pl.fill_zero_gradient()
print i, pl.a[:]
evolve(pl, C, i, nolimit=nolimit)
plt.savefig("piecewise-constant.pdf")
plt.savefig("piecewise-constant.png")
#------------- PLM -------------
plt.clf()
gr.draw_grid()
gr.label_center(nzones // 2, r"$i$")
gr.label_center(nzones // 2 - 1, r"$i-1$")
gr.label_center(nzones // 2 + 1, r"$i+1$")
gr.label_center(nzones // 2 - 2, r"$i-2$")
gr.label_center(nzones // 2 + 2, r"$i+2$")
# not limited and limited
pl_n = gp.PiecewiseLinear(gr, a, nolimit=1)
pl_y = gp.PiecewiseLinear(gr, a)
for n in range(nzones):
pc.draw_cell_avg(n, color="0.5")
for n in range(2, nzones - 2):
pl_n.draw_slope(n, color="r", ls=":")
pl_y.draw_slope(n, color="r")
gr.clean_axes()
plt.ylim(-0.25, 1.2)
plt.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
f = plt.gcf()
