Merge 2dee461 into 47a3c79

examples/euler_2d/shock_bubble_interaction.py

@@ -1,6 +1,6 @@
 #!/usr/bin/env python
 # encoding: utf-8
-"""
+r"""
 Compressible Euler flow in cylindrical symmetry
 ===============================================
 
@@ -185,6 +185,8 @@ def setup(use_petsc=False,solver_type='classic', outdir='_output', kernel_langua
         solver.step_source = step_Euler_radial
         solver.source_split = 1
         solver.limiters = [4,4,4,4,2]
+        solver.cfl_max = 0.5
+        solver.cfl_desired = 0.45
 
     x = pyclaw.Dimension('x',0.0,2.0,mx)
     y = pyclaw.Dimension('y',0.0,0.5,my)
@@ -198,9 +200,6 @@ def setup(use_petsc=False,solver_type='classic', outdir='_output', kernel_langua
     qinit(state)
     auxinit(state)
 
-    solver.cfl_max = 0.5
-    solver.cfl_desired = 0.45
-    solver.dt_initial=0.005
     solver.user_bc_lower = incoming_shock
 
     solver.bc_lower[0]=pyclaw.BC.custom

examples/euler_3d/shock_bubble.py

@@ -0,0 +1,159 @@
+#!/usr/bin/env python
+# encoding: utf-8
+r""" 
+3D shock-bubble interaction problem.
+A planar shock wave impacts a spherical region of low density.
+
+This problem involves the 3D Euler equations:
+.. math::
+    \rho_t + (\rho u)_x + (\rho v)_y + (\rho w)_z & = 0 \\
+    (\rho u)_t + (\rho u^2 + p)_x + (\rho uv)_y & = 0 \\
+    (\rho v)_t + (\rho uv)_x + (\rho v^2 + p)_y + (\rho vw)_z & = 0 \\
+    (\rho w)_t + (\rho uw)_x + (\rho vw)_y + (\rho w^2 + p)_z & = 0 \\
+    E_t + \nabla \cdot (u (E + p) ) & = 0.
+
+
+The conserved quantities are: 
+    density (rho), x-,y-, and z-momentum (rho*u,rho*v,rho*w), and energy.
+"""
+import numpy as np
+from scipy import integrate
+
+gamma = 1.4 # Ratio of Specific Heats
+gamma1 = gamma - 1.
+x0 = 0.5; y0 = 0.; z0 = 0. # Bubble location
+r_bubble = 0.2 # Bubble radius
+
+# Ambient state
+rhoout = 1.0
+pout   = 1.0
+
+# Bubble state
+rhoin  = 0.1
+pin    = 1.0
+
+xshock = 0.2 # Initial shock wave location
+
+# State behind shock wave
+p_shock = 5.0
+rho_shock = (gamma1 + p_shock*(gamma+1.))/ ((gamma+1.) + gamma1*p_shock)
+v_shock = (p_shock - 1.) / np.sqrt(0.5 * ((gamma+1.) * p_shock+gamma1))
+e_shock = 0.5*rho_shock*v_shock**2 + p_shock/gamma1
+
+
+def bubble(y, x, zdown, zup, which):
+    "Used to compute how much of each cell is in the bubble."
+    def sphere_top(y, x, which):
+        z2 = r_bubble**2 - (x-x0)**2 - (y-y0)**2
+        if z2 < 0:
+            return 0
+        else:
+            return z0 + np.sqrt(z2)
+
+    def sphere_bottom(y, x, which):
+        z2 = (r_bubble**2 - (x-x0)**2 - (y-y0)**2)
+        if z2 < 0:
+            return 0
+        else:
+            return z0 - np.sqrt(z2)
+
+    top = min(sphere_top(y,x, which), zup)
+    bottom = min(top,max(sphere_bottom(y,x, which), zdown))
+    return top-bottom
+
+def incoming_shock(state,dim,t,qbc,auxbc,num_ghost):
+    """
+    Incoming shock at x=0 boundary.
+    """
+    for i in xrange(num_ghost):
+        qbc[0,i,...] = rho_shock
+        qbc[1,i,...] = rho_shock*v_shock
+        qbc[2,i,...] = 0.
+        qbc[3,i,...] = 0.
+        qbc[4,i,...] = e_shock
+
+
+def setup(kernel_language='Fortran', solver_type='classic', use_petsc=False,
+          dimensional_split=False, outdir='_output', output_format='hdf5',
+          disable_output=False, num_cells=(256,64,64),
+          tfinal=0.6, num_output_times=10):
+
+    from clawpack import riemann
+    if use_petsc:
+        import clawpack.petclaw as pyclaw
+    else:
+        from clawpack import pyclaw
+
+    if solver_type=='classic':
+        solver = pyclaw.ClawSolver3D(riemann.euler_3D)
+        solver.dimensional_split = dimensional_split
+    else:
+        raise Exception('Unrecognized solver_type.')
+
+    x = pyclaw.Dimension('x',  0.0, 2.0, num_cells[0])
+    y = pyclaw.Dimension('y',  0.0, 0.5, num_cells[1])
+    z = pyclaw.Dimension('z',  0.0, 0.5, num_cells[2])
+    domain = pyclaw.Domain([x,y,z])
+
+    solver.all_bcs = pyclaw.BC.extrap
+    solver.bc_lower[0]  = pyclaw.BC.custom
+    solver.user_bc_lower = incoming_shock
+    solver.bc_lower[1] = pyclaw.BC.wall
+    solver.bc_lower[2] = pyclaw.BC.wall
+
+    state = pyclaw.State(domain,solver.num_eqn)
+
+    state.problem_data['gamma']  = gamma
+
+    grid = state.grid
+    X,Y,Z = grid.p_centers
+    r0 = np.sqrt((X-x0)**2 + (Y-y0)**2 + (Z-z0)**2)
+
+    state.q[0,:,:,:] = rho_shock*(X<xshock) + rhoout*(X>=xshock) # density (rho)
+    state.q[1,:,:,:] = 0. # x-momentum (rho*u)
+    state.q[2,:,:,:] = 0. # y-momentum (rho*v)
+    state.q[3,:,:,:] = 0. # z-momentum (rho*w)
+    state.q[4,:,:,:] = e_shock*(X<xshock) + pout/gamma1*(X>=xshock) # energy (e)
+
+    # Compute cell fraction inside bubble
+    dx, dy, dz = state.grid.delta
+    dx2, dy2, dz2 = [d/2. for d in state.grid.delta]
+    dmax = max(state.grid.delta)
+
+    for i in xrange(state.q.shape[1]):
+        for j in xrange(state.q.shape[2]):
+            for k in xrange(state.q.shape[3]):
+                if (r0[i,j,k] - dmax > r_bubble):
+                    continue
+                xdown = X[i,j,k] - dx2
+                xup   = X[i,j,k] + dx2
+                ydown = lambda x : Y[i,j,k] - dy2
+                yup   = lambda x : Y[i,j,k] + dy2
+                zdown = Z[i,j,k] - dz2
+                zup   = Z[i,j,k] + dz2
+
+                infrac,abserr = integrate.dblquad(bubble,xdown,xup,ydown,yup,
+                                                  args=(zdown,zup,0),
+                                                  epsabs=1.e-3,epsrel=1.e-2)
+                infrac=infrac/(dx*dy*dz)
+
+                state.q[0,i,j,k] = rhoout*(1.-infrac) + rhoin*infrac
+                state.q[4,i,j,k] = (pout*(1.-infrac) + pin*infrac)/gamma1 # energy (e)
+
+    claw = pyclaw.Controller()
+    claw.solution = pyclaw.Solution(state, domain)
+    claw.solver = solver
+    claw.output_format = output_format
+    claw.keep_copy = True
+    if disable_output:
+        claw.output_format = None
+    claw.tfinal = tfinal
+    claw.num_output_times = num_output_times
+    claw.outdir = outdir
+
+    return claw
+
+# __main__()
+if __name__=="__main__":
+    from clawpack.pyclaw.util import run_app_from_main
+    output = run_app_from_main(setup)

examples/shallow_2d/radial_dam_break.py

@@ -1,7 +1,9 @@
 #!/usr/bin/env python
 # encoding: utf-8
+r"""
+2D shallow water: radial dam break
+==================================
 
-"""
 Solve the 2D shallow water equations:
 
 .. :math:

examples/shallow_sphere/Rossby_wave.py

@@ -1,6 +1,9 @@
 #!/usr/bin/env python
 # encoding: utf-8
 """
+Shallow water flow on the sphere
+================================
+
 2D shallow water equations on a spherical surface. The approximation of the 
 three-dimensional equations is restricted to the surface of the sphere. 
 Therefore only the solution on the surface is updated.