def evolve(gr, a, C, num, nolimit=1):
#-------------------------------------------------------------------------
# first frame -- the original cell-averages
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, gr.ng + nzones / 2, r"$i$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 - 1, r"$i-1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 + 1, r"$i+1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 - 2, r"$i-2$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 + 2, r"$i+2$", fontsize="medium")
# draw cell averages
n = gr.ilo
while (n <= gr.ihi):
gpu.drawCellAvg(gr, n, a[n], color="r")
n += 1
pylab.axis([gr.xmin - 0.5 * gr.dx, gr.xmax + 0.5 * gr.dx, -1.25, 2.0])
pylab.axis("off")
print gr.xmin - 0.5 * gr.dx, gr.xmax + 0.5 * gr.dx
pylab.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
ax = pylab.gca()
pylab.text(0.5,
0.75,
"initial state (cell averages)",
horizontalalignment="center",
fontsize=16,
color="b",
transform=ax.transAxes)
pylab.text(0.5,
0.95,
"Piecewise Linear Method for Linear Advection",
horizontalalignment="center",
fontsize=20,
color="k",
transform=ax.transAxes)
f = pylab.gcf()
f.set_size_inches(12.8, 7.2)
if (nolimit):
pylab.savefig("rea-nolimit-start_%3.3d.png" % (num))
pylab.savefig("rea-nolimit-start_%3.3d.eps" % (num))
else:
pylab.savefig("rea-start_%3.3d.png" % (num))
pylab.savefig("rea-start_%3.3d.eps" % (num))
#-------------------------------------------------------------------------
# second frame -- reconstruction
# compute the slopes
lda = gpu.lslopes(a, nolimit=nolimit)
# draw
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, gr.ng + nzones / 2, r"$i$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 - 1, r"$i-1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 + 1, r"$i+1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 - 2, r"$i-2$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 + 2, r"$i+2$", fontsize="medium")
# draw cell averages
n = gr.ilo
while (n <= gr.ihi):
gpu.drawCellAvg(gr, n, a[n], color="0.5", ls=":")
n += 1
n = gr.ilo
while (n <= gr.ihi):
gpu.drawSlope(gr, n, lda[n], a[n], color="r")
n += 1
pylab.axis([gr.xmin - 0.5 * gr.dx, gr.xmax + 0.5 * gr.dx, -1.25, 2.0])
pylab.axis("off")
pylab.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
pylab.text(0.5,
0.75,
"reconstructed slopes",
horizontalalignment="center",
fontsize=16,
color="b",
transform=ax.transAxes)
pylab.text(0.5,
0.95,
"Piecewise Linear Method for Linear Advection",
horizontalalignment="center",
fontsize=20,
color="k",
transform=ax.transAxes)
f = pylab.gcf()
f.set_size_inches(12.8, 7.2)
if (nolimit):
pylab.savefig("rea-nolimit-reconstruction_%3.3d.png" % (num))
pylab.savefig("rea-nolimit-reconstruction_%3.3d.eps" % (num))
else:
pylab.savefig("rea-reconstruction_%3.3d.png" % (num))
pylab.savefig("rea-reconstruction_%3.3d.eps" % (num))
#-------------------------------------------------------------------------
# third frame -- evolve
# draw
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, gr.ng + nzones / 2, r"$i$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 - 1, r"$i-1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 + 1, r"$i+1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 - 2, r"$i-2$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 + 2, r"$i+2$", fontsize="medium")
# draw cell slopes
n = gr.ilo
while (n <= gr.ihi):
gpu.drawSlope(gr, n, lda[n], a[n], color="0.75", ls=":")
n += 1
# evolve
n = gr.ilo
while (n <= gr.ihi):
gpu.evolveToRight(gr, n, lda, a, C, color="r")
n += 1
pylab.axis([gr.xmin - 0.5 * gr.dx, gr.xmax + 0.5 * gr.dx, -1.25, 2.0])
pylab.axis("off")
print gr.xmin - 0.5 * gr.dx, gr.xmax + 0.5 * gr.dx
pylab.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
pylab.text(0.5,
0.75,
"evolved with C = {}".format(C),
horizontalalignment="center",
fontsize=16,
color="b",
transform=ax.transAxes)
pylab.text(0.5,
0.95,
"Piecewise Linear Method for Linear Advection",
horizontalalignment="center",
fontsize=20,
color="k",
transform=ax.transAxes)
f = pylab.gcf()
f.set_size_inches(12.8, 7.2)
if (nolimit):
pylab.savefig("rea-nolimit-evolve_%3.3d.png" % (num))
pylab.savefig("rea-nolimit-evolve_%3.3d.eps" % (num))
else:
pylab.savefig("rea-evolve_%3.3d.png" % (num))
pylab.savefig("rea-evolve_%3.3d.eps" % (num))
#-------------------------------------------------------------------------
# fourth frame -- re-average
# left states (we don't need the right state when u > 0)
al = numpy.zeros(2 * gr.ng + gr.nx, dtype=numpy.float64)
n = gr.ilo
while (n <= gr.ihi + 1):
al[n] = a[n - 1] + 0.5 * (1 - C) * lda[n - 1]
n += 1
# the Riemann problem just picks the left state. Do a conservative
# update
anew = numpy.zeros(2 * gr.ng + gr.nx, dtype=numpy.float64)
anew[gr.ilo:gr.ihi+1] = a[gr.ilo:gr.ihi+1] + \
C*(al[gr.ilo:gr.ihi+1] - al[gr.ilo+1:gr.ihi+2])
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, gr.ng + nzones / 2, r"$i$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 - 1, r"$i-1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 + 1, r"$i+1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 - 2, r"$i-2$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones / 2 + 2, r"$i+2$", fontsize="medium")
# show the evolved profiles from the old time
n = gr.ilo
while (n <= gr.ihi):
gpu.evolveToRight(gr, n, lda, a, C, color="0.5", ls=":")
n += 1
# draw new averages
n = gr.ilo
while (n <= gr.ihi):
gpu.drawCellAvg(gr, n, anew[n], color="red")
n += 1
pylab.axis([gr.xmin - 0.5 * gr.dx, gr.xmax + 0.5 * gr.dx, -1.25, 2.0])
pylab.axis("off")
print gr.xmin - 0.5 * gr.dx, gr.xmax + 0.5 * gr.dx
pylab.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
pylab.text(0.5,
0.75,
"averaged profile (final state)",
horizontalalignment="center",
fontsize=16,
color="b",
transform=ax.transAxes)
pylab.text(0.5,
0.95,
"Piecewise Linear Method for Linear Advection",
horizontalalignment="center",
fontsize=20,
color="k",
transform=ax.transAxes)
f = pylab.gcf()
f.set_size_inches(12.8, 7.2)
if (nolimit):
pylab.savefig("rea-nolimit-final_%3.3d.png" % (num))
pylab.savefig("rea-nolimit-final_%3.3d.eps" % (num))
else:
pylab.savefig("rea-final_%3.3d.png" % (num))
pylab.savefig("rea-final_%3.3d.eps" % (num))
return anew
gpu.labelCenter(gr, gr.ng + nzones/2+1, r"$i+1$")
gpu.labelCenter(gr, gr.ng + nzones/2-2, r"$i-2$")
gpu.labelCenter(gr, gr.ng + nzones/2+2, r"$i+2$")
# draw cell slopes
n = gr.ilo
while (n <= gr.ihi):
gpu.drawSlope(gr, n, lda[n], a[n], color="0.75", ls=":")
n += 1
# evolve
n = gr.ilo
while (n <= gr.ihi):
gpu.evolveToRight(gr, n, lda, a, C, color="r")
n += 1
pylab.axis([gr.xmin-0.5*gr.dx,gr.xmax+0.5*gr.dx, -0.25, 1.2])
pylab.axis("off")
print gr.xmin-0.5*gr.dx, gr.xmax+0.5*gr.dx
pylab.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.95)
f = pylab.gcf()
f.set_size_inches(8.0,2.0)
def evolve(gr, a, C, num, nolimit=1):
#-------------------------------------------------------------------------
# first frame -- the original cell-averages
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, gr.ng + nzones/2, r"$i$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2-1, r"$i-1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2+1, r"$i+1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2-2, r"$i-2$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2+2, r"$i+2$", fontsize="medium")
# draw cell averages
n = gr.ilo
while (n <= gr.ihi):
gpu.drawCellAvg(gr, n, a[n], color="r")
n += 1
pylab.axis([gr.xmin-0.5*gr.dx,gr.xmax+0.5*gr.dx, -0.25, 1.2])
pylab.axis("off")
print gr.xmin-0.5*gr.dx, gr.xmax+0.5*gr.dx
pylab.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.95)
f = pylab.gcf()
f.set_size_inches(8.0,2.0)
if (nolimit):
pylab.savefig("rea-nolimit-start_%3.3d.png" % (num))
pylab.savefig("rea-nolimit-start_%3.3d.eps" % (num))
else:
pylab.savefig("rea-start_%3.3d.png" % (num))
pylab.savefig("rea-start_%3.3d.eps" % (num))
#-------------------------------------------------------------------------
# second frame -- reconstruction
# compute the slopes
lda = gpu.lslopes(a, nolimit=nolimit)
# draw
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, gr.ng + nzones/2, r"$i$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2-1, r"$i-1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2+1, r"$i+1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2-2, r"$i-2$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2+2, r"$i+2$", fontsize="medium")
# draw cell averages
n = gr.ilo
while (n <= gr.ihi):
gpu.drawCellAvg(gr, n, a[n], color="0.5", ls=":")
n += 1
n = gr.ilo
while (n <= gr.ihi):
gpu.drawSlope(gr, n, lda[n], a[n], color="r")
n += 1
pylab.axis([gr.xmin-0.5*gr.dx,gr.xmax+0.5*gr.dx, -0.25, 1.2])
pylab.axis("off")
pylab.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.95)
f = pylab.gcf()
f.set_size_inches(8.0,2.0)
if (nolimit):
pylab.savefig("rea-nolimit-reconstruction_%3.3d.png" % (num))
pylab.savefig("rea-nolimit-reconstruction_%3.3d.eps" % (num))
else:
pylab.savefig("rea-reconstruction_%3.3d.png" % (num))
pylab.savefig("rea-reconstruction_%3.3d.eps" % (num))
#-------------------------------------------------------------------------
# third frame -- evolve
# draw
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, gr.ng + nzones/2, r"$i$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2-1, r"$i-1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2+1, r"$i+1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2-2, r"$i-2$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2+2, r"$i+2$", fontsize="medium")
# draw cell slopes
n = gr.ilo
while (n <= gr.ihi):
gpu.drawSlope(gr, n, lda[n], a[n], color="0.75", ls=":")
n += 1
# evolve
n = gr.ilo
while (n <= gr.ihi):
gpu.evolveToRight(gr, n, lda, a, C, color="r")
n += 1
pylab.axis([gr.xmin-0.5*gr.dx,gr.xmax+0.5*gr.dx, -0.25, 1.2])
pylab.axis("off")
print gr.xmin-0.5*gr.dx, gr.xmax+0.5*gr.dx
pylab.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.95)
f = pylab.gcf()
f.set_size_inches(8.0,2.0)
if (nolimit):
pylab.savefig("rea-nolimit-evolve_%3.3d.png" % (num))
pylab.savefig("rea-nolimit-evolve_%3.3d.eps" % (num))
else:
pylab.savefig("rea-evolve_%3.3d.png" % (num))
pylab.savefig("rea-evolve_%3.3d.eps" % (num))
#-------------------------------------------------------------------------
# fourth frame -- re-average
# left states (we don't need the right state when u > 0)
al = numpy.zeros(2*gr.ng + gr.nx, dtype=numpy.float64)
n = gr.ilo
while (n <= gr.ihi+1):
al[n] = a[n-1] + 0.5*(1 - C)*lda[n-1]
n += 1
# the Riemann problem just picks the left state. Do a conservative
# update
anew = numpy.zeros(2*gr.ng + gr.nx, dtype=numpy.float64)
anew[gr.ilo:gr.ihi+1] = a[gr.ilo:gr.ihi+1] + \
C*(al[gr.ilo:gr.ihi+1] - al[gr.ilo+1:gr.ihi+2])
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, gr.ng + nzones/2, r"$i$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2-1, r"$i-1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2+1, r"$i+1$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2-2, r"$i-2$", fontsize="medium")
gpu.labelCenter(gr, gr.ng + nzones/2+2, r"$i+2$", fontsize="medium")
# show the evolved profiles from the old time
n = gr.ilo
while (n <= gr.ihi):
gpu.evolveToRight(gr, n, lda, a, C, color="0.5", ls=":")
n += 1
# draw new averages
n = gr.ilo
while (n <= gr.ihi):
gpu.drawCellAvg(gr, n, anew[n], color="red")
n += 1
pylab.axis([gr.xmin-0.5*gr.dx,gr.xmax+0.5*gr.dx, -0.25, 1.2])
pylab.axis("off")
print gr.xmin-0.5*gr.dx, gr.xmax+0.5*gr.dx
pylab.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.95)
f = pylab.gcf()
f.set_size_inches(8.0,2.0)
if (nolimit):
pylab.savefig("rea-nolimit-final_%3.3d.png" % (num))
pylab.savefig("rea-nolimit-final_%3.3d.eps" % (num))
else:
pylab.savefig("rea-final_%3.3d.png" % (num))
pylab.savefig("rea-final_%3.3d.eps" % (num))
return anew
