  We introduce new second-order adaptive low-dissipation central-upwind (LDCU)
schemes for the one- and two-dimensional hyperbolic systems of conservation
laws. The new adaptive LDCU schemes employ the LDCU numerical fluxes (recently
proposed in [{\sc A. Kurganov and R. Xin}, J. Sci. Comput., 96 (2023), Paper
No. 56]) computed using the point values reconstructed with the help of
adaptively selected nonlinear limiters. To this end, we use a smoothness
indicator to detect ``rough'' parts of the computed solution, where the
piecewise linear reconstruction is performed using an overcompressive limiter,
which leads to extremely sharp resolution of shock and contact waves. In the
``smooth'' areas, we use a more dissipative limiter to prevent the appearance
of artificial kinks and staircase-like structures there. In order to avoid
oscillations, we perform the reconstruction in the local characteristic
variables obtained using the local characteristic decomposition. We test two
different smoothness indicators and apply the developed schemes to the one- and
two-dimensional Euler equations of gas dynamics. The obtained numerical results
clearly demonstrate that the new adaptive LDCU schemes outperform the original
ones.
