  This article concerns the development of a fully conservative,
positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for
the multicomponent, chemically reacting, compressible Navier-Stokes equations
with complex thermodynamics. In particular, we extend to viscous flows the
fully conservative, positivity-preserving, and entropy-bounded discontinuous
Galerkin method for the chemically reacting Euler equations that we previously
introduced. An important component of the formulation is the
positivity-preserving Lax-Friedrichs-type viscous flux function devised by
Zhang [J. Comput. Phys., 328 (2017), pp. 301-343], which was adapted to
multicomponent flows by Du and Yang [J. Comput. Phys., 469 (2022), pp. 111548]
in a manner that treats the inviscid and viscous fluxes as a single flux. Here,
we similarly extend the aforementioned flux function to multicomponent flows
but separate the inviscid and viscous fluxes, resulting in a different
dissipation coefficient. This separation of the fluxes allows for use of other
inviscid flux functions, as well as enforcement of entropy boundedness on only
the convective contribution to the evolved state, as motivated by physical and
mathematical principles. We also detail how to account for boundary conditions
and incorporate previously developed techniques to reduce spurious pressure
oscillations into the positivity-preserving framework. Furthermore, potential
issues associated with the Lax-Friedrichs-type viscous flux function in the
case of zero species concentrations are discussed and addressed. The resulting
formulation is compatible with curved, multidimensional elements and general
quadrature rules with positive weights. A variety of multicomponent, viscous
flows is computed, ranging from a one-dimensional shock tube problem to
multidimensional detonation waves and shock/mixing-layer interaction.
