A set of high-order spatial and temporal finite difference stencils is developed. They are derived using an optimization procedure designed to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. In doing so, they guarantee that the numerical scheme preserves the dispersion relation of the analytic equations when the wave modes are in the long wave range. Consequently, the acoustic, entropy and vorticity waves propagate with the correct wave speeds and exhibit their appropriate properties. Waves that are short compared to the grid mesh size (waves with wavelength less than 5 mesh spacings) generally have totally different wave propagation characteristics. These waves are contaminants of the numerical solution. A method designed to eliminate such waves without significantly affecting the long waves is developed. A set of radiation and outflow boundary conditions is also constructed. These conditions are derived from the asymptotic solutions of the linearized Euler equations. A numerical simulation designed to test the effectiveness of the finite difference schemes and the boundary conditions is performed. The computed solutions agree very favorably with the exact solutions. These methods are applied then to a simulation of a 2-D supersonic Mach 1.7 jet. Initial conditions and a mapping based upon empirical data are derived. The mapping concentrates grid points in the mixing layer of the jet. In this region, very small time steps are required. A method which allows different regions of the grid to have different time steps is developed. This greatly improves the efficiency of the code. The steady state solution is computed. / Source: Dissertation Abstracts International, Volume: 54-07, Section: B, page: 3667. / Major Professor: Christopher K. W. Tam. / Thesis (Ph.D.)--The Florida State University, 1993.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_76986 |
| Contributors | Webb, Jay Christopher., Florida State University |
| Source Sets | Florida State University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | 210 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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