A comparison of higher-order shock capturing schemes within the LAVA CFD solver

The effciency of large-eddy type simulations can be greatly increased by employing higher-order accurate numerical schemes which provide superior accuracy for a given cost. For unsteady turbulent flow simulations including shocks, contacts, and/or material discontinuities, various numerical higher-order shock capturing schemes are available in the literature. The desired numerical scheme should be free of spurious numerical oscillations across discontinuities and obtain higher-order accuracy in smooth flow regions in an effcient manner. Suffcient robustness is absolutely necessary for effectively utilizing these numerical methods in engineering and science applications. Three types of numerical higher-order schemes are dis- cussed in this paper, i.e., central finite-difference schemes with explicit artificial dissipation, a compact centered finite-difference scheme with localized artificial diffusivity and weighted essentially non-oscillatory schemes in explicit and compact finite difference forms. Variations of these numerical schemes were implemented and tested in the Launch Ascent and Vehicle Aerodynamics (LAVA) solver, using a block-structured Cartesian mesh. The current paper provides a detailed discussion and comparison of these numerical schemes. The variety of test cases ranges from 1D shock problems to homogeneous isotropic turbulence at a turbulent Mach number of 0.5 where shocklets form.