def __init__(self, tf = [0.1], orders = [1], dx = 0.01, xlim=1, scheme=2, equation=Advection()):
self.tf = tf
self.orders = orders
self.dx = dx
self.CFL = {1:0.8, 2:0.6, 3:0.5, 4:0.4, 5:0.4, 7:0.4, 9:0.4}
self.scheme = scheme
self.xlim = xlim
self.N = int(2*self.xlim/self.dx)
self.equation = equation
self.ifunc = Complex()
self.shift = True
self.legend = []
class CompareOrders(Test):
def __init__(self, tf = [0.1], orders = [1], dx = 0.01, xlim=1, scheme=2, equation=Advection()):
self.tf = tf
self.orders = orders
self.dx = dx
self.CFL = {1:0.8, 2:0.6, 3:0.5, 4:0.4, 5:0.4, 7:0.4, 9:0.4}
self.scheme = scheme
self.xlim = xlim
self.N = int(2*self.xlim/self.dx)
self.equation = equation
self.ifunc = Complex()
self.shift = True
self.legend = []
def plotanalytical(self, t):
s = Solver(f = self.equation, xlim=self.xlim, N=self.N, CFL=0.8, order=1, ifunc=self.ifunc, scheme=self.scheme)
u_actual = self.ifunc.init(s.xc, t)
plot(s.xc, u_actual, 'x-')
self.legend.append("Analytical Time: %s" %(t))
def test(self, t, order):
self.s = Solver(f = self.equation, xlim=self.xlim, N=self.N, CFL=self.CFL[order], order=order, ifunc=self.ifunc, scheme=self.scheme)
I = RK2(solver=self.s, tf=t, shift=self.shift)
I.run()
#u_actual = self.ifunc.init(self.s.xc, t)
#error = abs((u_actual - self.s.u))
#print max(error)
plot(self.s.xc, self.s.u, 'x-')
self.legend.append("Order: %s, Time: %s"%(self.s.scheme_map[order].__name__, t))
def run(self):
for t in self.tf:
figure()
self.legend = []
self.plotanalytical(t)
for order in self.orders:
self.test(t, order)
print "Testing Complete......tf: %s, Order: %s %s"%(t, order, self.s.scheme_map[order].__name__)
legend(self.legend)
grid()
savefig("./png/time%s.png"%(t))
#show()
def multiplot(self, tf = [1.0]):
for t in tf:
#figure()
filename = "./data/%s_%s_%s_%s_%s.npz"%(self.equation.__name__, 1, self.scheme, self.N, t)
data = np.load(filename)
x = data['x']
uactual = data['uactual']
pyplot.plot(x, uactual, 'x-', label='analytical')
for order in self.orders:
self.plot(t, order)
legend()
grid(True)
show()
def plot(self, t, order):
filename = "./data/%s_%s_%s_%s_%s.npz"%(self.equation.__name__, order, self.scheme, self.N, t)
data = np.load(filename)
x = data['x']
u = data['u']
plot(x, u, 'x-', label='Order %s Time %s'%(order, t))
# for i in range(self.N - self.order-1, self.N):
# res[i] = res[self.N - self.order-2]
# for i in range(self.order):
# res[i] = res[self.N-1]
return res
def calc_dt(self):
umax = max(abs(self.f.cspeed(self.u)))
self.dt = self.CFL*(self.x[1]-self.x[0])/umax
return self.CFL*(self.x[1]-self.x[0])/umax
if __name__ == "__main__":
f = Advection()
ifunc = Complex()
N = 1000
tf = 1.0
scheme = 2
xlim = 10
shift = True
s = Solver(f = f, xlim=xlim, N=N, CFL=0.8, order=1, ifunc=ifunc, scheme=scheme)
u_actual = ifunc.init(s.x, tf)
plot(s.x, u_actual, 'x-')
I = RK2(solver=s, tf=tf, shift=shift)
I.run()
plot(s.xc, s.u, 'x-')
s = Solver(f = f, xlim=xlim, N=N, CFL=0.2, order=2, ifunc=ifunc, scheme=scheme)
I = RK2(solver=s, tf=tf, shift=shift)
I.run()
