def FourthOrderDamping(U, DampCoeff):
    """Return fourth-order damping term.

    Calculated using Equation 6-77 in CFD Vol. 1 by Hoffmann.

    Call signature:

        FourthOrderDamping(U, DampCoeff)

    Parameters
    ----------
    U : 1D or 2D array

        The dependent variable from time level (n) within the domain.

    DampCoeff : float

        Damping coefficient. The value must be selected in the range of
        0 to 0.125 for a stable solution.

    Returns
    -------
    D : 1D or 2D array

        The fourth-order damping term within the entire domain.
    """
    D = U.copy()  # Initialize D
    D[2:-2] = (
        -DampCoeff*(U[0:-4] - 4.0*U[1:-3] + 6.0*U[2:-2]
                    - 4.0*U[3:-1] + U[4:])
        )
    return D