def simplegrid():
nzones = 7
gr = gpu.grid(nzones, xmin=0, xmax=1)
gpu.drawGrid(gr, edgeTicks=0)
# label a few cell-centers
gpu.labelCenter(gr, nzones/2, r"$i$")
gpu.labelCenter(gr, nzones/2-1, r"$i-1$")
gpu.labelCenter(gr, nzones/2+1, r"$i+1$")
# label a few edges
gpu.labelEdge(gr, nzones/2, r"$i-1/2$")
gpu.labelEdge(gr, nzones/2+1, r"$i+1/2$")
# draw an average quantity
gpu.drawCellAvg(gr, nzones/2, 0.4, color="r")
gpu.labelCellAvg(gr, nzones/2, 0.4, r"$\,\langle a \rangle_i$", color="r")
pylab.axis([gr.xmin-1.5*gr.dx,gr.xmax+1.5*gr.dx, -0.25, 1.5])
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(10.0,2.5)
pylab.savefig("simplegrid2.png")
pylab.savefig("simplegrid2.eps")
a = numpy.array([0.3, 1.0, 0.9, 0.8, 0.25, 0.15, 0.5])
gr = gpu.grid(nzones)
gpu.drawGrid(gr)
gpu.labelCenter(gr, nzones/2, r"$x_i$")
gpu.labelAvg(gr, nzones/2, a[nzones/2], r"$\langle f\rangle_i$")
gpu.labelCenter(gr, nzones/2-1, r"$x_{i-1}$")
gpu.labelCenter(gr, nzones/2+1, r"$x_{i+1}$")
gpu.labelCenter(gr, nzones/2-2, r"$x_{i-2}$")
gpu.labelCenter(gr, nzones/2+2, r"$x_{i+2}$")
gpu.labelEdge(gr, nzones/2, r"$x_{i-1/2}$")
gpu.labelEdge(gr, nzones/2+1, r"$x_{i+1/2}$")
n = 0
while (n < nzones):
gpu.drawCellAvg(gr, n, a[n])
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)
def riemann():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 4
ng = 2
gr = gpu.grid(nzones, ng=ng)
# interior
atemp = numpy.array([0.8, 0.7, 0.4, 0.5])
a = numpy.zeros(2 * gr.ng + gr.nx, dtype=numpy.float64)
# fill interior and ghost cells
a[gr.ilo:gr.ihi + 1] = atemp[:]
a[0:gr.ilo] = a[gr.ihi - 1:gr.ihi + 1]
a[gr.ihi:2 * gr.ng + gr.nx] = a[gr.ihi]
#------------------------------------------------------------------------
# plot a domain without ghostcells
gpu.drawGrid(gr, emphasizeEnd=1, drawGhost=1)
gpu.labelCenter(gr, gr.ng - 2, r"$\mathrm{lo-2}$")
gpu.labelCenter(gr, gr.ng - 1, r"$\mathrm{lo-1}$")
gpu.labelCenter(gr, gr.ng, r"$\mathrm{lo}$")
gpu.labelCenter(gr, gr.ng + 1, r"$\mathrm{lo+1}$")
gpu.labelEdge(gr, gr.ng, r"$\mathrm{lo}-1/2$")
# draw cell averages
n = 0
while n < gr.ng + gr.nx:
gpu.drawCellAvg(gr, n, a[n], color="0.5", ls=":")
n += 1
# get slopes
lda = gpu.lslopes(a, nolimit=1)
n = gr.ilo - 1
while (n <= gr.ihi):
gpu.drawSlope(gr, n, lda[n], a[n], color="r")
n += 1
# 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) * lda[gr.ilo - 1]
ar = a[gr.ilo] - 0.5 * gr.dx * (1.0 + C) * lda[gr.ilo]
# L
gpu.markCellRightState(gr,
ng - 1,
r"$a_{\mathrm{lo}+1/2,L}^{n+1/2}$",
value=al,
vertical="top",
color="b")
# R
gpu.markCellLeftState(gr,
ng,
r"$a_{\mathrm{lo}+1/2,R}^{n+1/2}$",
value=ar,
vertical="top",
color="b")
pylab.xlim(gr.xl[0] - 0.15 * gr.dx, gr.xr[ng + 1] + 0.15 * gr.dx)
pylab.ylim(-0.25, 1.1)
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)
pylab.tight_layout()
pylab.savefig("riemann-bc.png")
pylab.savefig("riemann-bc.eps")
gpu.drawGrid(gr, drawGhost=1, emphasizeEnd=1)
gpu.labelCenter(gr, ng+nzones/2, r"$i$")
gpu.labelCenter(gr, ng+nzones/2-1, r"$i-1$")
gpu.labelCenter(gr, ng+nzones/2+1, r"$i+1$")
gpu.labelCenter(gr, gr.ilo, r"$\mathrm{lo}$")
gpu.labelCenter(gr, gr.ilo-1, r"$\mathrm{lo-1}$")
gpu.labelCenter(gr, gr.ilo-2, r"$\mathrm{lo-2}$")
gpu.labelCenter(gr, gr.ihi, r"$\mathrm{hi}$")
gpu.labelCenter(gr, gr.ihi+1, r"$\mathrm{hi+1}$")
gpu.labelCenter(gr, gr.ihi+2, r"$\mathrm{hi+2}$")
gpu.labelEdge(gr, ng+nzones/2, r"$i-1/2$")
gpu.labelEdge(gr, ng+nzones/2+1, r"$i+1/2$")
# draw the data
i = 0
while i < nzones:
gpu.drawCellAvg(gr, ng+i, a[i], color="r")
i += 1
gpu.labelCellAvg(gr, ng+nzones/2, a[nzones/2], r"$\langle a\rangle_i$", color="r")
# label dx
pylab.plot([gr.xr[gr.ng+nzones/2-1], gr.xr[gr.ng+nzones/2-1]], [-0.35,-0.25], color="k")
pylab.plot([gr.xr[gr.ng+nzones/2], gr.xr[gr.ng+nzones/2]], [-0.35,-0.25], color="k")
pylab.plot([gr.xr[gr.ng+nzones/2-1], gr.xr[gr.ng+nzones/2]], [-0.3,-0.3], color="k")
pylab.text(gr.xc[gr.ng+nzones/2], -0.55, r"$\Delta x$",
# data that lives on the grid
a = numpy.array([0.3, 1.0, 0.9, 0.8, 0.25, 0.15, 0.5])
gr = gpu.grid(nzones)
gpu.drawGrid(gr)
gpu.labelCenter(gr, nzones / 2, r"$x_i$")
gpu.labelAvg(gr, nzones / 2, a[nzones / 2], r"$\langle f\rangle_i$")
gpu.labelCenter(gr, nzones / 2 - 1, r"$x_{i-1}$")
gpu.labelCenter(gr, nzones / 2 + 1, r"$x_{i+1}$")
gpu.labelCenter(gr, nzones / 2 - 2, r"$x_{i-2}$")
gpu.labelCenter(gr, nzones / 2 + 2, r"$x_{i+2}$")
gpu.labelEdge(gr, nzones / 2, r"$x_{i-1/2}$")
gpu.labelEdge(gr, nzones / 2 + 1, r"$x_{i+1/2}$")
n = 0
while (n < nzones):
gpu.drawCellAvg(gr, n, a[n])
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)
a = numpy.array([0.3, 1.0, 0.9, 0.8, 0.25, 0.1, 0.5, 0.55])
gr = gpu.grid(nzones)
pylab.clf()
gpu.drawGrid(gr)
gpu.labelCenter(gr, nzones/2, r"$i$")
gpu.labelCenter(gr, nzones/2-1, r"$i-1$")
gpu.labelCenter(gr, nzones/2+1, r"$i+1$")
gpu.labelCenter(gr, nzones/2-2, r"$i-2$")
gpu.labelCenter(gr, nzones/2+2, r"$i+2$")
gpu.labelEdge(gr, nzones/2, r"$i-1/2$")
gpu.labelEdge(gr, nzones/2+1, r"$i+1/2$")
# draw the data
i = 0
while i < nzones:
gpu.drawCellAvg(gr, i, a[i], color="r")
i += 1
gpu.labelCellAvg(gr, nzones/2, a[nzones/2], r"$\langle f\rangle_i$", color="r")
# label dx
pylab.plot([gr.xr[gr.ng+nzones/2-1], gr.xr[gr.ng+nzones/2-1]], [-0.35,-0.25], color="k")
pylab.plot([gr.xr[gr.ng+nzones/2], gr.xr[gr.ng+nzones/2]], [-0.35,-0.25], color="k")
pylab.plot([gr.xr[gr.ng+nzones/2-1], gr.xr[gr.ng+nzones/2]], [-0.3,-0.3], color="k")
pylab.text(gr.xc[gr.ng+nzones/2], -0.45, r"$\Delta x$",
def riemann():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 4
ng = 2
gr = gpu.grid(nzones, ng=ng)
# interior
atemp = numpy.array([0.8, 0.7, 0.4, 0.5])
a = numpy.zeros(2*gr.ng + gr.nx, dtype=numpy.float64)
# fill interior and ghost cells
a[gr.ilo:gr.ihi+1] = atemp[:]
a[0:gr.ilo] = a[gr.ihi-1:gr.ihi+1]
a[gr.ihi:2*gr.ng+gr.nx] = a[gr.ihi]
#------------------------------------------------------------------------
# plot a domain without ghostcells
gpu.drawGrid(gr, emphasizeEnd=1, drawGhost=1)
gpu.labelCenter(gr, gr.ng-2, r"$\mathrm{lo-2}$")
gpu.labelCenter(gr, gr.ng-1, r"$\mathrm{lo-1}$")
gpu.labelCenter(gr, gr.ng, r"$\mathrm{lo}$")
gpu.labelCenter(gr, gr.ng+1, r"$\mathrm{lo+1}$")
gpu.labelEdge(gr, gr.ng, r"$\mathrm{lo}-1/2$")
# draw cell averages
n = 0
while n < gr.ng+gr.nx:
gpu.drawCellAvg(gr, n, a[n], color="0.5", ls=":")
n += 1
# get slopes
lda = gpu.lslopes(a, nolimit=1)
n = gr.ilo-1
while (n <= gr.ihi):
gpu.drawSlope(gr, n, lda[n], a[n], color="r")
n += 1
# 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)*lda[gr.ilo-1]
ar = a[gr.ilo] - 0.5*gr.dx*(1.0 + C)*lda[gr.ilo]
# L
gpu.markCellRightState(gr, ng-1, r"$a_{\mathrm{lo}+1/2,L}^{n+1/2}$",
value=al, vertical="top", color="b")
# R
gpu.markCellLeftState(gr, ng, r"$a_{\mathrm{lo}+1/2,R}^{n+1/2}$",
value=ar, vertical="top", color="b")
pylab.xlim(gr.xl[0]-0.15*gr.dx,gr.xr[ng+1]+0.15*gr.dx)
pylab.ylim(-0.25, 1.1)
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)
pylab.tight_layout()
pylab.savefig("riemann-bc.png")
pylab.savefig("riemann-bc.eps")
gpu.drawGrid(gr, emphasizeEnd=1, drawGhost=1)
gpu.labelCenter(gr, ng + ncells / 2, r"$i$")
gpu.labelCenter(gr, ng + ncells / 2 - 1, r"$i-1$")
gpu.labelCenter(gr, ng + ncells / 2 + 1, r"$i+1$")
#gpu.labelCenter(gr, ng+ncells/2-2, r"$i-2$")
#gpu.labelCenter(gr, ng+ncells/2+2, r"$i+2$")
gpu.labelCenter(gr, ng + 0, r"$\mathrm{lo}$")
gpu.labelCenter(gr, ng - 1, r"$\mathrm{lo-1}$")
gpu.labelCenter(gr, ng + gr.nx - 1, r"$\mathrm{hi}$")
gpu.labelCenter(gr, ng + gr.nx, r"$\mathrm{hi+1}$")
gpu.labelEdge(gr, ng + ncells / 2, r"$i-1/2$")
gpu.labelEdge(gr, ng + ncells / 2 + 1, r"$i+1/2$")
gpu.labelEdge(gr, ng + gr.nx, r"$b$")
gpu.labelEdge(gr, ng + 0, r"$a$")
# draw the data
i = 0
while i < ncells + 2 * ng:
gpu.drawCellAvg(gr, i, acell[i], color="r")
i += 1
gpu.labelCellAvg(gr,
ng + ncells / 2,
acell[ng + ncells / 2],
r"$\langle f\rangle_i$",