This article concerns the development of a fully conservative,
positivity-preserving, and entropy-bounded discontinuous Galerkin scheme for
simulating 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. 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 discuss in detail
how to account for boundary conditions and incorporate previously developed
pressure-equilibrium-preserving techniques into the positivity-preserving
framework. Comparisons between the Lax-Friedrichs-type viscous flux function
and more conventional flux functions are provided, the results of which
motivate an adaptive solution procedure that employs the former only when the
element-local solution average has negative species concentrations, nonpositive
density, or nonpositive pressure. 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