Date of Award
Master of Science
Department of Aeronautics and Astronautics
Richard J. McMullan, PhD
A global fourth-order solution method that incorporates compact differencing with Roe's approximate Riemann solver was investigated. This method was incorporated into a one-dimensional numerical simulation of the compressible Euler equations, and applied to a one-dimensional shock tube problem. The method was also extended to two dimensions, and applied to a two-dimensional shock tube problem and an advecting vortical structure problem on both rectilinear and curvilinear meshes. The results were compared to a third-order Roe scheme and a fourth-order compact difference scheme. An order of accuracy determination showed that it has an order of accuracy somewhere near fourth order, with absolute error comparable to that of the standard compact difference scheme. With proper selection of solution parameters, the scheme was also shown to accurately capture a discontinuous solution where unfiltered compact schemes would become unstable.
DTIC Accession Number
Croker, Barry A., "Development of a Higher-Order Upwind Algorithm for Compressible Fluid Flow" (2005). Theses and Dissertations. 3666.