Validation Study Of The Integral-Differential Scheme For Multi-Block Grids
Abstract
This MS Thesis seeks to validate the accuracy of the Integral-Differential Scheme (IDS). In the attempts to accomplish this task, research efforts were focused on the scheme's ability to capture the physics of known flow fields, as well as the scheme's ability to predict the features of flow field quantities that may be derived from experimental measurements. The IDS was developed with the goal of being computationally efficient, from a programming perspective, as well as being numerically accurate, stable, and robust, from a mathematical perspective. The IDS is designed to solve the full Navier-Stokes equations in their integral forms. Unlike traditional control volume schemes, the IDS is built upon two sets of cells: spatial and temporal cells. For 2-D flows, the IDS considers an elementary control volume as a collection of four spatial cells and a single temporal cell. Similar to other explicit CFD schemes, the IDS relies on the use of the Taylor series expansion and other traditional CFD criteria. It is of interest to note that there are previous IDS validation studies which were conducted at North Carolina A&T State University. These past studies mainly focused on the qualitative aspects of the flow field physics. Furthermore, in all cases, they focused on flow field problems that can be represented by single-block grids. In this analysis, the validation studies are focused on multi-block grids in which the physics of the flow field is made complicated due to the presence of shock waves and flow separation zones. Of interest to this MS Thesis are two supersonic flow field problems that are supported by experimental data; namely, the supersonic flow over a rearward-facing step problem and the supersonic flow over a cavity problem. The validation studies conducted herein demonstrated that the IDS was able to predict the experimental data in both cases.