moving by u0

no_c_moving_boundaries.py

+import dolfin as df
+import numpy as np
+import progressbar
+
+df.set_log_level(df.LogLevel.ERROR)
+df.parameters['form_compiler']['optimize'] = True
+
+class MovingBoundaries(object):
+    def __init__(self, parameters):
+        # read in parameters
+        for key in parameters:
+            setattr(self, key, parameters[key])
+
+        # create mesh, mixed element and function space
+        self.mesh = df.IntervalMesh(self.resolution, 0.0 ,2.0 * np.pi * self.system_size_by_2PI)
+        conc_element = df.FiniteElement('P', self.mesh.ufl_cell(), 1)
+        mixed_element = df.MixedElement([conc_element, conc_element, conc_element]) # u, v, rho
+
+        # define function space with this mixed element
+        self.function_space = df.FunctionSpace(self.mesh,mixed_element)
+        self.bc = df.DirichletBC(self.function_space.sub(2), df.Constant(0.0), 'on_boundary')
+
+        # define the reqd functions on this function space
+        self.f = df.Function(self.function_space)                 # f at current time
+        self.f0 = df.Function(self.function_space)                 # f at t =0
+
+
+    def advection(self, conc, v, tconc):
+        return (df.inner((v*conc).dx(0), tconc))
+
+    def active_stress(self, rho):
+        return self.lamda * (rho/(rho + self.saturation_rho))
+
+    def passive_stress(self, u, v):
+        return (self.elasticity * u.dx(0) + self.viscosity * v.dx(0))
+
+    def stress(self, u, v, rho):
+        return self.active_stress(rho) + self.passive_stress(u, v)
+
+    def reaction_rho(self, rho, trho):
+        return self.turnover_rho * df.inner(rho - self.average_rho, trho)
+
+    def reaction_diffusion_rho(self, rho, trho):
+        return ( self.diffusion_rho * df.inner(rho.dx(0), trho.dx(0))
+                + self.reaction_rho(rho, trho)
+                )
+
+    def setup_initial_conditions(self, u0, rho0):
+        u0 = df.interpolate(u0, self.function_space.sub(0).collapse())
+        rho0 = df.interpolate(rho0, self.function_space.sub(2).collapse())
+
+        # solve for v0
+        v0_FS = df.FunctionSpace(self.mesh, 'P', 1)
+        v0  = df.Function(v0_FS)
+        tv0 = df.TestFunction(v0_FS)
+        v0form = (self.friction * df.inner(v0, tv0)
+                + df.inner(self.stress(u0, v0, rho0), tv0.dx(0))
+                ) * df.dx
+        df.solve(v0form == 0, v0)
+        df.assign(self.f0, [u0, v0, rho0])
+
+    def setup_weak_forms(self):
+        u0, v0, rho0 = df.split(self.f0)
+        u,  v, rho = df.split(self.f)
+        tu, tv, trho = df.TestFunctions(self.function_space)
+
+        uform = (df.inner((u-u0)/self.timestep, tu) - df.inner(v, tu))
+        
+        vform = (self.friction * df.inner(v, tv)
+                + df.inner(self.stress(u, v, rho), tv.dx(0))
+                )
+        
+        rhoform = (df.inner((rho-rho0)/self.timestep, trho)
+                + self.advection(rho, v, trho)
+                + self.reaction_diffusion_rho(rho, trho)
+                )
+        
+        self.form = (uform + vform + rhoform) * df.dx
+
+    def solve(self, u0, rho0):
+        times = np.arange(0,self.maxtime,self.timestep)
+        x_array = np.zeros((len(times), self.mesh.num_vertices()))
+        u_array = np.zeros_like(x_array)
+        v_array = np.zeros_like(x_array)
+        rho_array = np.zeros_like(x_array)
+
+        self.setup_initial_conditions(u0, rho0)
+        self.setup_weak_forms()
+
+        u, v, rho = self.f0.split(deepcopy=True)
+        u_array[0] = u.compute_vertex_values(self.mesh)
+        v_array[0] = v.compute_vertex_values(self.mesh) 
+        rho_array[0] = rho.compute_vertex_values(self.mesh)
+        x_array[0] = self.mesh.coordinates()[:,0]
+
+        for i in progressbar.progressbar(range(0, len(times))):
+            df.solve(self.form == 0, self.f, self.bc)
+            u, v, rho = self.f.split(deepcopy=True)
+            u_array[i] = u.compute_vertex_values(self.mesh)
+            v_array[i] = v.compute_vertex_values(self.mesh)
+            rho_array[i] = rho.compute_vertex_values(self.mesh)
+            self.f0.assign(self.f)
+            
+            u0, v0, rho0 = self.f0.split()
+
+            df.ALE.move(self.mesh, u0)
+            x_array[i] = self.mesh.coordinates()[:,0]
+            
+        return (x_array, u_array, v_array, rho_array)
+
+
+
+if __name__ == '__main__':
+    import dolfin as df
+
+    import json
+    import matplotlib.pyplot as plt
+    from matplotlib.widgets import Slider
+    
+    with open('growth_parameters.json') as jsonFile:
+        params = json.load(jsonFile)
+    assert(params['dimension']==1)
+
+    mb = MovingBoundaries(params)
+    u0 = df.Expression('cos(x[0])', degree=1)
+    rho0 = df.Expression('sin(x[0])', degree=1)
+    (x, u, v, rho) = mb.solve(u0, rho0)
+
+    times = np.arange(0, mb.maxtime, mb.timestep)    
+    fig, (axu, axv, axrho) = plt.subplots(3,1, sharex=True, figsize=(8,6))
+    axu.set_xlabel(r'$x$')
+    axu.set_ylabel(r'$u(x,t)$')
+    axv.set_ylabel(r'$v(x,t)$')
+    axrho.set_ylabel(r'$\rho(x,t)$')
+    axu.set_xlim(np.min(x), np.max(x))
+    axu.set_ylim(np.min(u), np.max(u))
+    axv.set_ylim(np.min(v), np.max(v))
+    axrho.set_ylim(np.min(rho), np.max(rho))
+    
+    uplot, = axu.plot(x[0], u[0])
+    vplot, = axv.plot(x[0], v[0])
+    rhoplot, = axrho.plot(x[0], rho[0])
+
+    def update(value):
+        ti = np.abs(times-value).argmin()
+        uplot.set_xdata(x[ti])
+        uplot.set_ydata(u[ti])
+        
+        vplot.set_xdata(x[ti])
+        vplot.set_ydata(v[ti])
+        
+        rhoplot.set_xdata(x[ti])
+        rhoplot.set_ydata(rho[ti])
+        
+        plt.draw()
+        
+    sax = plt.axes([0.1, 0.92, 0.7, 0.02])
+    slider = Slider(sax, r'$t/\tau$', min(times), max(times),
+            valinit=min(times), valfmt='%3.1f',
+            fc='#999999')
+    slider.drawon = False
+    slider.on_changed(update)
+    plt.show()
\ No newline at end of file