Engineering Commons^™

Development Of A Higher-Order Upwind Algorithm For Compressible Fluid Flow, Barry A. Croker

Theses and Dissertations

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 …