  A phenomenological momentum-independent (MID) model is constructed to
describe the equation of state (EOS) for isospin asymmetric nuclear matter,
especially the density dependence of the nuclear symmetry energy
$E_{\text{\textrm{sym}}}(\rho)$. This model can reasonably describe the general
properties of the EOS for symmetric nuclear matter and the symmetry energy
predicted by both the sophisticated isospin and momentum dependent MDI model
and the Skyrme-Hartree-Fock approach. We find that there exists a nicely linear
correlation between $K_{\mathrm{sym}}$ and $L$ as well as between $J_{0}/K_{0}
$ and $K_{0}$, where $L$ and $K_{\mathrm{sym}}$ represent, respectively, the
slope and curvature parameters of the symmetry energy at the normal nuclear
density $\rho_{0}$ while $K_{0}$ and $J_{0}$ are, respectively, the
incompressibility and the third-order derivative parameter of symmetric nuclear
matter at $\rho_{0}$. These correlations together with the empirical
constraints on $K_{0}$, $L$ and $E_{\text{\textrm{sym}}}(\rho_{0}) $ lead to an
estimation of -477 MeV $\leq K_{\mathrm{sat,2}}\leq -241 $ MeV for the
second-order isospin asymmetry expansion coefficient for the incompressibility
of asymmetric nuclear matter at the saturation point.
