Positivity‐Preserving and Shock‐Capturing via Adaptive Filtering Direct Flux Reconstruction Scheme for Solving Multi‐Component Euler Equations

ABSTRACT An extension of the direct flux reconstruction scheme for simulating compressible multi‐component flows using the Euler equations is presented via adaptive filtering and positivity preservation. It is not an unknown fact that high‐order schemes are not robust in the vicinity of shocks and other flow discontinuities. Thus, in the presented work, an adaptive filtering procedure for shock capturing, which dissipates Gibbs oscillations around shocks, has been used. While shock capturing dissipates spurious oscillations associated with shocks, it doesn't guarantee that the physical quantities will not attain unphysical states. These unphysical states are not just due to high‐order interpolations, but also when these physical values are already near zero. Thus, in the present work, we also use a simple positivity‐preserving scheme that can be applied when solving the multi‐component Euler equations. The developed flow solver is then validated using problems for both 1‐dimensional and 2‐dimensional flows.