A numerical solution of the NS equations based on the mean value theorem with applications to aerothermodynamics

An innovative and robust algorithm capable of solving a variety of complex fluid dynamics problems is developed. This so-called, Integra-Differential Scheme (IDS) is designed to overcome known limitations of well-established schemes. The IDS implements a smart approach in transforming 3-D computational flowfields of fluid dynamic problems into their 2-D counterparts, while preserving their physical attributes. The strength of IDS rests on the implementation of the mean value theorem to the integral form of the conservation laws. This process transforms the integral equations into a finite difference scheme that lends itself to efficient numerical implementation. Preliminary solutions generated by IDS demonstrated its accuracy in terms of its ability to capture complex flowfield behaviours. In this paper, the results obtained from the application of the IDS to two problems; namely, the hypersonic flat plate problem, and the shock/boundary layer interaction problem, are documented and discussed. In both cases, the results showed very good agreement with the physical expectation of these problems. In an effort to this new algorithm, IDS solution to the shock/boundary layer interaction problem was compared to the experimental findings described in NASA Mem., No., 2-18-59W, March, 1959. The results obtained by IDS show excellent agreement with the experimental data.