def simplegrid():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 2
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid(draw_end=False, edge_ticks=False)
gr.label_center(0, r"$i$")
gr.label_center(1, r"$i+1$")
gr.label_edge(1, r"$q_{i+\myhalf,R}^{n+\myhalf}$")
# draw waves
# u - c
plt.plot([gr.xr[0], gr.xr[0] - 0.75 * gr.dx], [0, 1.0],
color="0.5",
ls="-")
plt.text(gr.xr[0] - 0.75 * gr.dx,
1.0 + 0.05,
"$\lambda^{(-)} =\, u - c$",
horizontalalignment="center")
# u
plt.plot([gr.xr[0], gr.xr[0] - 0.2 * gr.dx], [0, 1.0], color="0.5", ls="-")
plt.text(gr.xr[0] - 0.2 * gr.dx,
1.0 + 0.05,
"$\lambda^{(\circ)} =\, u$",
horizontalalignment="center")
# u + c
plt.plot([gr.xr[0], gr.xr[0] + 0.4 * gr.dx], [0, 1.0], color="0.5", ls="-")
plt.text(gr.xr[0] + 0.4 * gr.dx,
1.0 + 0.05,
"$\lambda^{(+)} =\, u + c$",
horizontalalignment="center")
# label regions
plt.text(gr.xr[0] - 0.5 * gr.dx, 0.2, r"$L$", color="r")
plt.text(gr.xr[0] - 0.33 * gr.dx, 0.6, r"$L^*$", color="r")
plt.text(gr.xr[0] + 0.05 * gr.dx, 0.6, r"$R^*$", color="r")
plt.text(gr.xr[0] + 0.3 * gr.dx, 0.2, r"$R$", color="r")
gr.clean_axes(padding=False)
plt.ylim(-0.2, 1.2)
plt.tight_layout()
f = plt.gcf()
f.set_size_inches(5, 2.5)
plt.savefig("riemann-waves.pdf")
def simplegrid():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 2
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid(draw_end=False, edge_ticks=False)
gr.label_center(0, r"$i$")
gr.label_center(1, r"$i+1$")
gr.label_edge(1, r"$q_{i+\myhalf}$")
# draw waves
# u - c
plt.plot([gr.xr[0], gr.xr[0] - 0.75 * gr.dx], [0, 1.0], color="C0", ls="-")
plt.text(gr.xr[0] - 0.75 * gr.dx,
1.0 + 0.05,
"$\lambda^{(-)} =\, u - c$",
horizontalalignment="center")
# u
plt.plot([gr.xr[0], gr.xr[0] - 0.2 * gr.dx], [0, 1.0], color="C0", ls="-")
plt.text(gr.xr[0] - 0.2 * gr.dx,
1.0 + 0.05,
"$\lambda^{(\circ)} =\, u$",
horizontalalignment="center")
# u + c
plt.plot([gr.xr[0], gr.xr[0] + 0.4 * gr.dx], [0, 1.0], color="C0", ls="-")
plt.text(gr.xr[0] + 0.4 * gr.dx,
1.0 + 0.05,
"$\lambda^{(+)} =\, u + c$",
horizontalalignment="center")
plt.plot([gr.xl[0], gr.xr[0]], [0.3, 0.3], color="C1", linewidth=2)
plt.text(gr.xc[0], 0.33, r"$\langle q \rangle_i$", color="C1")
plt.plot([gr.xl[1], gr.xr[1]], [0.6, 0.6], color="C1", linewidth=2)
plt.text(gr.xc[1], 0.63, r"$\langle q \rangle_{i+1}$", color="C1")
gr.clean_axes(padding=False)
plt.ylim(-0.2, 1.2)
plt.tight_layout()
f = plt.gcf()
f.set_size_inches(6, 3.5)
plt.savefig("riemann-waves-jump.png", dpi=150)
def riemann():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 2
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid(emphasize_end=True)
# label a few
gr.label_center(0, r"$i$", fontsize="medium")
gr.label_center(1, r"$i+1$", fontsize="medium")
gr.label_edge(1, r"$i+1/2$", fontsize="medium")
gr.mark_cell_left_state(1, r"$q_{i+1/2,R}^{n+1/2}$", fontsize="large",
color="b")
gr.mark_cell_right_state(0, r"$q_{i+1/2,L}^{n+1/2}$", fontsize="large",
color="b")
gr.label_cell_center(0, r"$q_i$")
gr.label_cell_center(1, r"$q_{i+1}$")
# flux
plt.arrow(gr.xl[ng+nzones/2]-0.25*gr.dx, 1.05, 0.5*gr.dx, 0,
shape='full', head_width=0.075, head_length=0.05,
lw=1, width=0.03,
edgecolor="none", facecolor="red",
length_includes_head=True, zorder=100)
plt.text(gr.xl[ng+nzones/2], 1.15, r"$F(U(q_{i+1/2}^{n+1/2}))$", color="red",
horizontalalignment="center")
gr.clean_axes(padding=False)
plt.ylim(-0.25, 1.25)
plt.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.95)
f = plt.gcf()
f.set_size_inches(6.0,2.25)
plt.tight_layout()
plt.savefig("riemann_comp_q.pdf")
plt.savefig("riemann_comp_q.png")
def simplegrid():
# grid info
nzones = 7
ng = 1
gr = gp.FVGrid(nzones, ng, xmin=0.0, xmax=1.0)
gr.draw_grid(emphasize_end=1, edge_ticks=0, draw_ghost=1)
# label a few
gr.label_center(ng + nzones / 2, r"$i$", fontsize="medium")
gr.label_center(ng + nzones / 2 - 1, r"$i-1$", fontsize="medium")
gr.label_center(ng + nzones / 2 + 1, r"$i+1$", fontsize="medium")
gr.label_center(ng - 1, r"$\mathrm{lo}-1$", fontsize="medium")
gr.label_center(ng, r"$\mathrm{lo}$", fontsize="medium")
gr.label_center(ng + nzones - 1, r"$\mathrm{hi}$", fontsize="medium")
gr.label_center(ng + nzones, r"$\mathrm{hi+1}$", fontsize="medium")
# label dx
plt.plot([gr.xl[ng + nzones / 2 - 2], gr.xl[ng + nzones / 2 - 2]],
[-0.35, -0.25],
color="k")
plt.plot([gr.xr[ng + nzones / 2 - 2], gr.xr[ng + nzones / 2 - 2]],
[-0.35, -0.25],
color="k")
plt.plot([gr.xl[ng + nzones / 2 - 2], gr.xr[ng + nzones / 2 - 2]],
[-0.3, -0.3],
color="k")
plt.text(gr.xc[ng + nzones / 2 - 2],
-0.5,
r"$\Delta x$",
horizontalalignment="center")
plt.xlim(gr.xl[0] - 0.05 * gr.dx,
gr.xr[2 * ng + nzones - 1] + 0.25 * gr.dx)
plt.ylim(-0.5, 1.5)
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(10.0, 2.5)
plt.tight_layout()
plt.savefig("simplegrid_gc.png")
plt.savefig("simplegrid_gc.pdf", bbox_inches="tight")
def riemann(with_time=True):
# grid info
xmin = 0.0
xmax = 1.0
nzones = 1
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
plt.clf()
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid()
gr.label_center(0, r"$i$", fontsize="medium")
gr.label_edge(0, r"$i-\myhalf$", fontsize="medium")
gr.label_edge(0, r"$i+\myhalf$", fontsize="medium", right_edge=True)
plt.arrow(gr.xc[0]+0.05*gr.dx, 0.5, 0.12*gr.dx, 0,
shape='full', head_width=0.05, head_length=0.025,
lw=1, width=0.02,
edgecolor="none", facecolor="r",
length_includes_head=True, zorder=100)
plt.arrow(gr.xc[0]-0.05*gr.dx, 0.5, -0.12*gr.dx, 0,
shape='full', head_width=0.05, head_length=0.025,
lw=1, width=0.02,
edgecolor="none", facecolor="r",
length_includes_head=True, zorder=100)
gr.mark_cell_left_state(0, r"$a_{i-\myhalf,R}$", fontsize="large",
color="b")
gr.mark_cell_right_state(0, r"$a_{i+\myhalf,L}$", fontsize="large",
color="b")
gr.label_cell_center(0, r"$a_i$")
gr.clean_axes(pad_fac=0.125, ylim=(-0.25, 1.0))
f = plt.gcf()
f.set_size_inches(5.0,2.0)
plt.tight_layout()
plt.savefig("advection-states.png")
def riemann():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 1
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid()
gr.label_center(0, r"$i$")
gr.label_cell_center(0, r"$q_i$")
gr.mark_cell_left_state(0, r"$q_{i-1/2,R}^{n+1/2}$", color="r")
gr.mark_cell_right_state(0, r"$q_{i+1/2,L}^{n+1/2}$", color="r")
plt.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)
plt.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)
plt.xlim(gr.xl[0]-0.25*gr.dx,gr.xr[2*ng+nzones-1]+0.25*gr.dx)
# plt.ylim(-0.25, 0.75)
plt.axis("off")
plt.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.95)
f = plt.gcf()
f.set_size_inches(4.0,2.5)
plt.savefig("states.png")
plt.savefig("states.pdf")
def laplace():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 3
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid(emphasize_end=True)
# label a few
gr.label_center(0, r"$i-1$", fontsize="medium")
gr.label_center(1, r"$i$", fontsize="medium")
gr.label_center(2, r"$i+1$", fontsize="medium")
gr.label_edge(1, r"$i-\myhalf$", fontsize="medium")
gr.label_edge(2, r"$i+\myhalf$", fontsize="medium")
gr.label_cell_center(0, r"$\phi_{i-1}$")
gr.label_cell_center(1, r"$\phi_{i}$", value=0.7)
gr.label_cell_center(2, r"$\phi_{i+1}$")
gr.mark_cell_edge(1, r"$\left .\frac{d\phi}{dx} \right |_{i-\myhalf}$", color="C0")
gr.mark_cell_edge(2, r"$\left .\frac{d\phi}{dx} \right |_{i+\myhalf}$", color="C0")
gr.label_cell_center(1, r"$\left .\frac{d^2\phi}{dx^2} \right |_{i}$",
value=0.3, color="C1")
gr.clean_axes(padding=False)
plt.ylim(-0.25, 1.25)
plt.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.95)
f = plt.gcf()
f.set_size_inches(6.0,2.25)
plt.tight_layout()
plt.savefig("laplacian.pdf")
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 simplegrid():
# grid info
nzones = 7
ng = 1
gr = gp.FVGrid(nzones, ng, xmin=0.0, xmax=1.0)
gr.draw_grid(emphasize_end=1, edge_ticks=0, draw_ghost=1)
# label a few
gr.label_center(ng + nzones // 2, r"$i$", fontsize="medium")
gr.label_center(ng + nzones // 2 - 1, r"$i-1$", fontsize="medium")
gr.label_center(ng + nzones // 2 + 1, r"$i+1$", fontsize="medium")
gr.label_center(ng - 1, r"$\mathrm{lo}-1$", fontsize="medium")
gr.label_center(ng, r"$\mathrm{lo}$", fontsize="medium")
gr.label_center(ng + nzones - 1, r"$\mathrm{hi}$", fontsize="medium")
gr.label_center(ng + nzones, r"$\mathrm{hi+1}$", fontsize="medium")
# label dx
gr.label_dx(ng + nzones // 2 - 2)
gr.clean_axes(show_ghost=True,
ylim=(-0.5, 1.5),
padding=True,
pad_fac=0.05)
#plt.xlim(gr.xl[0]-0.05*gr.dx,gr.xr[2*ng+nzones-1]+0.25*gr.dx)
#plt.ylim(-0.5, 1.5)
#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(10.0, 2.5)
plt.tight_layout()
plt.savefig("simplegrid_gc.pdf", bbox_inches="tight")
def simplegrid():
nzones = 7
gr = gp.FVGrid(nzones, xmin=0, xmax=1)
gr.draw_grid(edge_ticks=0)
# label a few cell-centers
gr.label_center(nzones / 2, r"$i$")
gr.label_center(nzones / 2 - 1, r"$i-1$")
gr.label_center(nzones / 2 + 1, r"$i+1$")
# label a few edges
gr.label_edge(nzones / 2, r"$i-1/2$")
gr.label_edge(nzones / 2 + 1, r"$i+1/2$")
# sample data
A = 0.4
a = A * np.ones(nzones, dtype=np.float64)
pc = gp.PiecewiseConstant(gr, a)
# draw an average quantity
pc.draw_cell_avg(nzones / 2, color="r")
pc.label_cell_avg(nzones / 2, r"$\,\langle a \rangle_i$", color="r")
gr.clean_axes()
plt.ylim(-0.25, 1.5)
plt.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
f = plt.gcf()
f.set_size_inches(10.0, 2.5)
plt.savefig("simplegrid2.png")
plt.savefig("simplegrid2.pdf")
import numpy as np
import matplotlib.pyplot as plt
import grid_plot as gp
#-----------------------------------------------------------------------------
nzones = 8
# data that lives on the grid
#a = np.array([0.3, 1.0, 0.9, 0.8, 0.25, 0.15, 0.5, 0.55])
a = np.array([0.3, 1.0, 1.0, 0.8, 0.2, 0.15, 0.5, 0.55])
gr = gp.FVGrid(nzones)
plt.clf()
gr.draw_grid(center_only=1)
gr.label_center(nzones//2-1, r"$i$")
gr.label_center(nzones//2, r"$i+1$")
ppm = gp.PiecewiseParabolic(gr, a)
for n in range(gr.nx//2-1, gr.nx//2+1):
ppm.draw_parabola(n, color="r")
nn = gr.nx//2-1
sigma = 0.6
def simplegrid():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 2
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid(draw_end=False, edge_ticks=False)
gr.label_center(0, r"$i$")
gr.label_center(1, r"$i+1$")
gr.label_edge(1, r"$q_{i+\myhalf}$")
# draw waves
# u - c
plt.plot([gr.xr[0], gr.xr[0] - 0.75 * gr.dx], [0, 1.0], color="C0", ls="-")
plt.text(gr.xr[0] - 0.75 * gr.dx,
1.0 + 0.05,
"$\lambda^{(-)} =\, u - c$",
horizontalalignment="center")
# u
plt.plot([gr.xr[0], gr.xr[0] - 0.2 * gr.dx], [0, 1.0], color="C0", ls="-")
plt.text(gr.xr[0] - 0.2 * gr.dx,
1.0 + 0.05,
"$\lambda^{(\circ)} =\, u$",
horizontalalignment="center")
# u + c
plt.plot([gr.xr[0], gr.xr[0] + 0.4 * gr.dx], [0, 1.0], color="C0", ls="-")
plt.text(gr.xr[0] + 0.4 * gr.dx,
1.0 + 0.05,
"$\lambda^{(+)} =\, u + c$",
horizontalalignment="center")
# label regions
plt.text(gr.xr[0] - 0.5 * gr.dx,
0.3,
r"$L$",
horizontalalignment="center",
color="C1")
plt.text(gr.xr[0] - 0.5 * gr.dx,
0.22,
r"$(\rho_L, u_L, p_L)$",
horizontalalignment="center",
color="C1",
fontsize="small")
plt.text(gr.xr[0] - 0.33 * gr.dx,
0.75,
r"$L_*$",
horizontalalignment="center",
color="C1")
plt.text(gr.xr[0] - 0.33 * gr.dx,
0.67,
r"$(\rho_{\star L}, u_\star, p_\star)$",
horizontalalignment="center",
color="C1",
fontsize="small")
plt.text(gr.xr[0] + 0.1 * gr.dx,
0.75,
r"$R_*$",
horizontalalignment="center",
color="C1")
plt.text(gr.xr[0] + 0.1 * gr.dx,
0.67,
r"$(\rho_{\star R}, u_\star, p_\star)$",
horizontalalignment="center",
color="C1",
fontsize="small",
zorder=1000)
plt.text(gr.xr[0] + 0.3 * gr.dx,
0.3,
r"$R$",
horizontalalignment="center",
color="C1")
plt.text(gr.xr[0] + 0.3 * gr.dx,
0.22,
r"$(\rho_R, u_R, p_R)$",
horizontalalignment="center",
color="C1",
fontsize="small")
gr.clean_axes(padding=False)
plt.ylim(-0.2, 1.2)
plt.tight_layout()
f = plt.gcf()
f.set_size_inches(6, 3.5)
plt.savefig("riemann-waves.pdf")
def riemann(with_time=True):
# grid info
xmin = 0.0
xmax = 1.0
nzones = 2
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
plt.clf()
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid()
gr.label_center(0, r"$i$", fontsize="medium")
gr.label_center(0,
r"${\tt a[i]}$",
fontsize="medium",
extra_voff=-0.3,
color="r")
gr.label_center(1, r"$i+1$", fontsize="medium")
gr.label_center(1,
r"${\tt a[i+1]}$",
fontsize="medium",
extra_voff=-0.3,
color="r")
gr.label_edge(0, r"$i-\myhalf$", fontsize="medium")
gr.label_edge(0,
r"${\tt aint[i]}$",
fontsize="medium",
extra_voff=-0.3,
color="r")
gr.label_edge(1, r"$i+\myhalf$", fontsize="medium")
gr.label_edge(1,
r"${\tt aint[i+1]}$",
fontsize="medium",
extra_voff=-0.3,
color="r")
gr.label_edge(1, r"$i+\mythreehalf$", fontsize="medium", right_edge=True)
gr.label_edge(1,
r"${\tt aint[i+2]}$",
fontsize="medium",
extra_voff=-0.3,
color="r",
right_edge=True)
gr.mark_cell_edge(0, r"$a_{i-\myhalf}$", fontsize="large", color="r")
gr.mark_cell_edge(1, r"$a_{i+\myhalf}$", fontsize="large", color="r")
gr.mark_cell_edge(1,
r"$a_{i+\mythreehalf}$",
fontsize="large",
color="r",
right_edge=True)
gr.label_cell_center(0, r"$a_i$", color="r")
gr.label_cell_center(1, r"$a_{i+1}$", color="r")
gr.clean_axes(pad_fac=0.125, ylim=(-0.25, 1.0))
f = plt.gcf()
f.set_size_inches(7.0, 2.0)
plt.tight_layout()
plt.savefig("array-labels.png")
import numpy as np
import matplotlib.pyplot as plt
import grid_plot as gp
# plot two stacked fv grids of different (2x) resolution to show prolongation
#-----------------------------------------------------------------------------
nf = 4
nc = nf // 2
grf = gp.FVGrid(nf, voff=2.0)
grc = gp.FVGrid(nc)
plt.clf()
grf.draw_grid()
grc.draw_grid()
grf.label_center(nf // 2 - 2, r"$i-2$")
grf.label_center(nf // 2 - 1, r"$i-1$")
grf.label_center(nf // 2, r"$i$")
grf.label_center(nf // 2 + 1, r"$i+1$")
grc.label_center(nc // 2 - 1, r"$j-1$")
grc.label_center(nc // 2, r"$j$")
grf.label_cell_center(nf // 2 - 2, r"$\phi_{i-2}^f$")
grf.label_cell_center(nf // 2 - 1, r"$\phi_{i-1}^f$")
grf.label_cell_center(nf // 2, r"$\phi_i^f$")
grf.label_cell_center(nf // 2 + 1, r"$\phi_{i+1}^f$")
import matplotlib.pyplot as plt
import grid_plot as gp
# plot two stacked fv grids of different (2x) resolution to show prolongation
#-----------------------------------------------------------------------------
gr = []
nzones = [2, 4, 8, 16]
for nf in nzones:
gr.append(gp.FVGrid(nf, ng=1, voff=2.0 * len(gr)))
plt.clf()
for g in gr:
g.draw_grid(emphasize_end=1, draw_ghost=1, edge_ticks=0)
f = plt.gcf()
f.set_size_inches(7.0, 5.0)
grf = gr[0]
plt.xlim(grf.xmin - 1.1 * grf.dx, grf.xmax + 1.1 * grf.dx)
plt.axis("off")
plt.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
plt.savefig("mgtower.pdf")
def riemann():
# grid info
xmin = 0.0
xmax = 1.0
nzones = 2
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
#------------------------------------------------------------------------
# plot a domain without ghostcells
gr.draw_grid()
gr.label_center(0, r"$i$", fontsize="medium")
gr.label_center(1, r"$i+1$", fontsize="medium")
gr.label_edge(1, r"$i+1/2$", fontsize="medium")
plt.arrow(gr.xc[0] + 0.05 * gr.dx,
0.5,
0.12 * gr.dx,
0,
shape='full',
head_width=0.05,
head_length=0.025,
lw=1,
width=0.02,
edgecolor="none",
facecolor="r",
length_includes_head=True,
zorder=100)
plt.arrow(gr.xc[1] - 0.1 * gr.dx,
0.5,
-0.12 * gr.dx,
0,
shape='full',
head_width=0.05,
head_length=0.025,
lw=1,
width=0.02,
edgecolor="none",
facecolor="r",
length_includes_head=True,
zorder=100)
gr.mark_cell_left_state(1,
r"$a_{i+1/2,L}^{n+1/2}$",
fontsize="large",
color="b")
gr.mark_cell_right_state(0,
r"$a_{i+1/2,R}^{n+1/2}$",
fontsize="large",
color="b")
gr.label_cell_center(0, r"$a_i$")
gr.label_cell_center(1, r"$a_{i+1}$")
plt.xlim(gr.xl[0] - 0.125 * gr.dx,
gr.xr[2 * ng + nzones - 1] + 0.125 * gr.dx)
plt.ylim(-0.25, 1.0)
plt.axis("off")
plt.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
f = plt.gcf()
f.set_size_inches(7.0, 2.0)
plt.tight_layout()
plt.savefig("riemann-adv.pdf")
else:
for n in range(5):
x3 = self.x0 + self.dx * np.tan(
np.radians(self.right_pos + 2 * n))
plt.plot([self.x0, x3], [0, self.dx], color="C0", lw=1)
if __name__ == "__main__":
xmin = 0.0
xmax = 8.0
nzones = 4
ng = 0
gr = gp.FVGrid(nzones, xmin=xmin, xmax=xmax)
gr.draw_grid()
gr.label_edge(0, r"$i-\mythreehalf$", fontsize="medium")
gr.label_edge(1, r"$i-\myhalf$", fontsize="medium")
gr.label_edge(2, r"$i+\myhalf$", fontsize="medium")
gr.label_edge(3, r"$i+\mythreehalf$", fontsize="medium")
gr.label_edge(3, r"$i+\myfivehalf$", fontsize="medium", right_edge=True)
gr.label_center(0, r"$i-1$", fontsize="medium")
gr.label_center(1, r"$i$", fontsize="medium")
gr.label_center(2, r"$i+1$", fontsize="medium")
gr.label_center(3, r"$i+2$", fontsize="medium")
riemann = []
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 matplotlib.pyplot as plt
import grid_plot as gp
# plot two stacked fv grids of different (2x) resolution to show prolongation
#-----------------------------------------------------------------------------
gr = []
nf = 8
gr.append(gp.FVGrid(nf, ng=1, voff=0.0))
gr.append(gp.FVGrid(nf, ng=1, voff=0.0, xmin=0.25, xmax=0.75))
plt.clf()
gr[0].draw_grid(emphasize_end=1, draw_ghost=0, edge_ticks=0, color="0.75")
gr[1].draw_grid(emphasize_end=1, draw_ghost=0, edge_ticks=0)
f = plt.gcf()
f.set_size_inches(7.0, 1.0)
grf = gr[0]
plt.xlim(grf.xmin - 0.75 * grf.dx, grf.xmax + 0.25 * grf.dx)
plt.axis("off")
plt.subplots_adjust(left=0.05, right=0.95, bottom=0.05, top=0.95)
plt.savefig("nested1.pdf")
#-----------------------------------------------------------------------------
[-0.35 + voff, -0.25 + voff],
color="k")
plt.plot([gr.xc[gr.ng + nzones / 2 - 1], gr.xc[gr.ng + nzones / 2]],
[-0.3 + voff, -0.3 + voff],
color="k")
plt.text(0.5 * (gr.xc[gr.ng + nzones / 2 - 1] + gr.xc[gr.ng + nzones / 2]),
-0.45 + voff,
r"$\Delta x$",
horizontalalignment="center")
# finite-volume
av = 0.5 * (a[0:nzones - 1] + a[1:])
nzones = len(av)
ng = 1
gr = gp.FVGrid(nzones, ng=1)
gr.draw_grid(emphasize_end=True, draw_ghost=True)
gr.label_center(ng + nzones / 2, r"$i$", fontsize="large")
gr.label_center(ng + nzones / 2 - 1, r"$i-1$", fontsize="large")
gr.label_center(ng + nzones / 2 + 1, r"$i+1$", fontsize="large")
gr.label_center(ng + nzones - 1, r"$\mathrm{hi}$", fontsize="large")
gr.label_center(ng + nzones, r"$\mathrm{hi+1}$", fontsize="large")
gr.label_center(gr.ilo, r"$\mathrm{lo}$", fontsize="large")
gr.label_center(gr.ilo - 1, r"$\mathrm{lo-1}$", fontsize="large")
a = gr.scratch_array()
a[gr.ilo:gr.ihi + 1] = av
import matplotlib.pyplot as plt
import grid_plot as gp
# plot two stacked fv grids of different (2x) resolution to show prolongation
#-----------------------------------------------------------------------------
nf = 4
nc = nf / 2
grf = gp.FVGrid(nf)
grc = gp.FVGrid(nc, voff=2.0)
plt.clf()
grf.draw_grid()
grc.draw_grid()
grf.label_center(nf / 2 - 2, r"$i-2$")
grf.label_center(nf / 2 - 1, r"$i-1$")
grf.label_center(nf / 2, r"$i$")
grf.label_center(nf / 2 + 1, r"$i+1$")
grc.label_center(nc / 2 - 1, r"$j-1$")
grc.label_center(nc / 2, r"$j$")
grf.label_cell_center(nf / 2 - 2, r"$\phi_{i-2}^h$")
grf.label_cell_center(nf / 2 - 1, r"$\phi_{i-1}^h$")
grf.label_cell_center(nf / 2, r"$\phi_i^h$")
grf.label_cell_center(nf / 2 + 1, r"$\phi_{i+1}^h$")
