def __init__(self, N, NV, NDIM, F, S=None, B=None, M=None, pars=None,
stiff=False, stiff_guess=False, newton_guess=False, tol=1e-6,
max_iter=50, max_size=1e16):
self.N = N
self.NV = NV
self.NDIM = NDIM
self.NT = N**(NDIM + 1)
self.F = F
self.S = S
self.B = B
self.M = M
self.pars = pars
self.max_iter = max_iter
self.tol = tol
self.max_size = max_size
self.stiff = stiff
if stiff_guess:
self.initial_guess = stiff_initial_guess
else:
self.initial_guess = standard_initial_guess
self.newton_guess = newton_guess
basis = Basis(N)
self.GAPS = basis.GAPS
self.DERVALS = basis.DERVALS
self.DG_W, self.DG_V, self.DG_U, self.DG_M, self.DG_D = galerkin_matrices(
N, NV, NDIM, basis)
def plot_weno(wh, var, MPs=None):
NDIM = int((wh.ndim - 1) / 2)
shape = wh.shape[:NDIM]
N = wh.shape[-2]
NV = wh.shape[-1]
basis = Basis(N)
inds = [N * s for s in shape]
x = zeros(inds)
u = zeros(inds + [NV])
for i in range(shape[0]):
ind = i * N
for j in range(N):
x[ind + j] = i + basis.NODES[j]
u[ind + j] = wh[i, j]
if var == 'density':
plot_density(u, x=x)
if var == 'energy':
plot_energy(u, x=x)
if var == 'velocity':
plot_velocity(u, x=x)
if var == 'pressure':
plot_pressure(u, MPs, x=x)
def plot_dg(qh, var, t, MPs=None):
n, _, _, N, _, NV = qh.shape
basis = Basis(N)
wh = zeros([n, 1, 1, N, NV])
for i in range(n):
for j in range(N):
for k in range(N):
wh[i, 0, 0, j] += basis.ψ[k](t) * qh[i, 0, 0, k, j]
plot_weno(wh, var, MPs)
def __init__(self, N, NV, NDIM, λc=1e5, λs=1, r=8, ε=1e-14):
self.N = N
self.NV = NV
self.NDIM = NDIM
self.Λ = [λs, λs, λc, λc]
self.fN = int(floor((N - 1) / 2))
self.cN = int(ceil((N - 1) / 2))
self.r = r
self.ε = ε
basis = Basis(N)
self.W = weno_matrices(N, basis.ψ)
self.Σ = oscillation_indicator(N, basis.dψ)
def __init__(self,
N,
NV,
NDIM,
F,
S=None,
B=None,
M=None,
max_eig=None,
pars=None,
riemann_solver='rusanov',
time_rec=True):
self.N = N
self.NV = NV
self.NDIM = NDIM
self.F = F
self.S = S
self.B = B
self.M = M
self.max_eig = max_eig
self.pars = pars
if riemann_solver == 'rusanov':
self.D_FUN = D_RUS
elif riemann_solver == 'roe':
self.D_FUN = D_ROE
elif riemann_solver == 'osher':
self.D_FUN = D_OSH
else:
raise ValueError("Choice of 'riemann_solver' not recognised.\n" +
"Choose from 'rusanov', 'roe', and 'osher'.")
self.time_rec = time_rec
basis = Basis(N)
self.NODES = basis.NODES
self.WGHTS = basis.WGHTS
self.ENDVALS = basis.ENDVALS
self.DERVALS = basis.DERVALS
self.TN, self.WGHT, self.WGHT_END = quad_weights(
N, NDIM, basis.WGHTS, time_rec)