Positivity-preserving and entropy-bounded discontinuous Galerkin method for the chemically reacting, compressible Navier-Stokes equations

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

Shock Tube and Gas Dynamic Design Considerations and Implementation for Extended Test Times

A new shock tube test section has been designed and manufactured for the purpose of increasing the test time and expanding the applications of the shock tube for a multitude of ongoing and future projects. One purpose for the test section extension is to allow for flow visualization of droplets impacted by a shock wave for the interaction of hypersonic vehicles and atmospheric disturbances. Another purpose is to measure behind the incident shock to capture the chemical kinetics for a high-altitude environment and low-pressure, high-temperature space applications. This new test section contains 24 round optical ports for laser spectroscopy for multiple measurement locations in addition to 3 rectangular ports upstream for introducing and imaging droplets in the tube. StanShock was used to simulate the expected test time for the desired temperatures and pressures. This was compared against theoretical calculations of test time as a function of distance and velocity of the shock. The optimal length of the extension of 5 feet was then determined based on minimum required test time and limitations of the physical lab space