  In this paper, we develop bound-preserving discontinuous Galerkin (DG)
methods for the coupled system of compressible miscible displacement problems.
We consider the problem with two components and the (volumetric) concentration
of the $i$th component of the fluid mixture, $c_i$, should be between $0$ and
$1$. However, $c_i$ does not satisfy the maximum principle. Therefore, the
numerical techniques introduced in (X. Zhang and C.-W. Shu, Journal of
Computational Physics, 229 (2010), 3091-3120) cannot be applied directly. The
main idea is to apply the positivity-preserving techniques to both $c_1$ and
$c_2$, respectively and enforce $c_1+c_2=1$ simultaneously to obtain physically
relevant approximations. By doing so, we have to treat the time derivative of
the pressure $dp/dt$ as a source in the concentration equation. Moreover,
$c_i's$ are not the conservative variables, as a result, the classical
bound-preserving limiter in (X. Zhang and C.-W. Shu, Journal of Computational
Physics, 229 (2010), 3091-3120) cannot be applied. Therefore, another limiter
will be introduced. Numerical experiments will be given to demonstrate the
accuracy in $L^\infty$-norm and good performance of the numerical technique.
