UQ eSpace

Abstract

The field of hypersonic direct numerical simulation (DNS) is a growing area that offers insight into the mechanisms behind turbulent transition. DNS resolves turbulence at all scales and at great computational expense, thus numerical methods are required to be both accurate and efficient. Hypersonic flow is further complicated by shocks and discontinuities, which these numerical methods must resolve without oscillations or instabilities. The choice of method is integral to the quality of results obtained from DNS studies. However, there is no clear choice within literature and due to development cost and effort, it is necessary to commit to one method before implementation in higher dimensions. This work aimed to implement different numerical schemes for hypersonic DNS to provide a recommendation of which are best suited for further development in a DNS production code. The project implemented three main schemes; a shock-fitting scheme and two shock capturing schemes-a hybrid weighted essentially non-oscillatory (WENO) scheme and a non-linear filtering (NLF) scheme, using a WENO scheme as the non-linear portion. They were implemented in 1D using the inviscid Euler equations to provide a preliminary comparison of the schemes and evaluate which, if any, should be implemented in higher dimensions. Results showed that the non-linear filter method was consistently the highest performing method across three different test cases. However, all methods exhibited oscillatory behaviour at small grid sizes, not documented in literature. It is believed that these oscillations are a result of instabilities in the methods and not due to any implementation error. Further investigation is required to determine ways to remove these oscillations for future work.