  We introduce an explicit invariant-region-preserving limiter applied to DG
methods for compressible Euler equations. The invariant region considered
consists of positivity of density and pressure and a maximum principle of a
specific entropy. The modified polynomial by the limiter preserves the cell
average, lies entirely within the invariant region and does not destroy the
high order of accuracy for smooth solutions. Numerical tests are presented to
illustrate the properties of the limiter. In particular, the tests on Riemann
problems show that the limiter helps to damp the oscillations near
discontinuities.
