added a scalar test case (transport)

pydemo/scalar/scalar.py

+from ufl import *
+from dune.ufl import Space
+class Transport1D:
+    name = 'transport'
+
+    def F_c(U):
+        return [ [U[0], 0] ]
+
+    def outflowValue(u):
+        return u
+    boundaryValue = {1: outflowValue}
+
+    def maxLambda(U,n):
+        return abs(n[0])
+    def velocity(U):
+        return as_vector( [1,0] )
+    def physical(U):
+        return 1
+    def jump(U,V):
+        return U[0]-V[0]
+
+space = Space(2,1)
+def RiemanProblem(UL,UR):
+    x = SpatialCoordinate(space.cell())
+    return conditional(x[0]<-0.5,as_vector(UL),as_vector(UR))
+def Constant():
+    return as_vector( [0.1] )

pydemo/scalar/shock_tube.py

+import time
+from dune.grid import structuredGrid, cartesianDomain
+from dune.fem import parameter
+import dune.create as create
+from dune.models.elliptic.formfiles import loadModels
+from dune.femdg import createFemDGSolver
+
+from scalar import RiemanProblem
+from scalar import Transport1D as Model
+
+parameter.append("parameter")
+parameter.append({"fem.verboserank": -1})
+
+x0,x1,N = [-1, 0], [1, 0.1], [20, 5]
+grid = structuredGrid(x0,x1,N)
+# grid = create.grid("ALUSimplex", cartesianDomain(x0,x1,N))
+dimR     = 1
+t        = 0
+saveStep = 0.01
+saveTime = saveStep
+count    = 0
+endTime  = 1.
+
+def useODESolver():
+    global count, t, saveTime
+    initial = RiemanProblem( [1], [0] )
+
+    spaceName = "dgonb"
+    polOrder = 2
+    space = create.space(spaceName, grid, order=polOrder, dimrange=dimR)
+    u_h   = space.interpolate(initial, name='u_h')
+    u_h_n = u_h.copy(name="previous")
+    operator = createFemDGSolver( Model, space )
+
+    start = time.time()
+    grid.writeVTK(Model.name, celldata=[u_h], number=count)
+    while t < endTime:
+        u_h_n.assign(u_h)
+        operator(u_h_n, u_h)
+        dt = operator.deltaT()
+        t += dt
+        if t > saveTime:
+            print('dt = ', dt, 'time = ',t, 'count = ',count )
+            count += 1
+            grid.writeVTK(Model.name, celldata=[u_h], number=count)
+            saveTime += saveStep
+    grid.writeVTK(Model.name, celldata=[u_h], number=count)
+    print("time loop:",time.time()-start)
+
+useODESolver()