def riemann():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 1
ng = 0
gr = gpu.grid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gpu.drawGrid(gr)
gpu.labelCenter(gr, 0, r"$i$")
gpu.labelCellCenter(gr, 0, r"$q_i$")
gpu.markCellLeftState(gr, 0, r"$q_{i-1/2,R}^{n+1/2}$", color="r")
gpu.markCellRightState(gr, 0, r"$q_{i+1/2,L}^{n+1/2}$", color="r")
pylab.arrow(gr.xc[0]-0.05*gr.dx, 0.5, -0.13*gr.dx, 0,
shape='full', head_width=0.075, head_length=0.05,
lw=1, width=0.01,
edgecolor="none", facecolor="r",
length_includes_head=True, zorder=100)
pylab.arrow(gr.xc[0]+0.05*gr.dx, 0.5, 0.13*gr.dx, 0,
shape='full', head_width=0.075, head_length=0.05,
lw=1, width=0.01,
edgecolor="none", facecolor="r",
length_includes_head=True, zorder=100)
pylab.xlim(gr.xl[0]-0.25*gr.dx,gr.xr[2*ng+nzones-1]+0.25*gr.dx)
# pylab.ylim(-0.25, 0.75)
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(4.0,2.5)
pylab.savefig("states.png")
pylab.savefig("states.eps")
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")
def riemann():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 1
ng = 0
gr = gpu.grid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gpu.drawGrid(gr)
gpu.labelCenter(gr, 0, r"$i$")
gpu.labelCellCenter(gr, 0, r"$q_i$")
gpu.markCellLeftState(gr, 0, r"$q_{i-1/2,R}^{n+1/2}$", color="r")
gpu.markCellRightState(gr, 0, r"$q_{i+1/2,L}^{n+1/2}$", color="r")
pylab.arrow(gr.xc[0] - 0.05 * gr.dx,
0.5,
-0.13 * gr.dx,
0,
shape='full',
head_width=0.075,
head_length=0.05,
lw=1,
width=0.01,
edgecolor="none",
facecolor="r",
length_includes_head=True,
zorder=100)
pylab.arrow(gr.xc[0] + 0.05 * gr.dx,
0.5,
0.13 * gr.dx,
0,
shape='full',
head_width=0.075,
head_length=0.05,
lw=1,
width=0.01,
edgecolor="none",
facecolor="r",
length_includes_head=True,
zorder=100)
pylab.xlim(gr.xl[0] - 0.25 * gr.dx,
gr.xr[2 * ng + nzones - 1] + 0.25 * gr.dx)
# pylab.ylim(-0.25, 0.75)
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(4.0, 2.5)
pylab.savefig("states.png")
pylab.savefig("states.eps")
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")
