#%% vertical spacing
class Grid:
    def __init__(self, kmax, dz0):
        self.kmax = kmax
        self.dz0  = dz0
        self.z = np.zeros(kmax)
        self.dz = np.zeros(kmax)
        self.zsize = None
class Grid_linear_stretched(Grid):
    def __init__(self, kmax, dz0, alpha):
        Grid.__init__(self, kmax, dz0)
        self.dz[:] = dz0 * (1 + alpha)**np.arange(kmax)
        zh         = np.zeros(kmax+1)
        zh[1:]     = np.cumsum(self.dz)
        self.z[:]  = 0.5 * (zh[1:] + zh[:-1])
        self.zsize = zh[-1]

grid = Grid_linear_stretched(kmax=150, dz0=20, alpha=0.012)