Date of Graduation
Statler College of Engineering and Mineral Resources
Mechanical and Aerospace Engineering
Since its conception, computational fluid dynamics (CFD) has had a role to play in both the industrial and the academic realm. Due to the availability of relatively cheap computer resources, CFD is now playing an increasingly critical role in the industry compared to experiments. It is also becoming increasingly important for the CFD analyst to have an in-depth understanding of the error inherently present in numeric and mathematical models. At a minimum, CFD simulation results should be accompanied by some analysis of the error including some type of grid convergence study and an estimation of the corresponding numerical uncertainty.;Error estimation is commonly done using a method known as Richardson Extrapolation (RE). While RE does produce good error predictions, the requirements for appropriate application of RE are often cumbersome and even prohibitive. In order to achieve an accurate estimate of the discretization error using RE, solutions on at least three grids are required. To obtain satisfactory results, all of these solutions must be in the asymptotic regime, which often requires solutions on more than three grids to verify. Solutions of practical interest in the industry are often quite complex and require a large number of grid points. In this situation, it is not always desirable to produce solutions on three significantly different grids.;This study focuses on an approach to quantify the discretization error associated with numerical solutions by solving an error transport equation (ETE). The goal is to develop a method that can be used to adequately predict the discretization error using the numerical solution on only one grid/mesh. The primary problem associated with solving the ETE is the development of the error source term which is required for the solution of the problem. In this study, a novel approach is considered which involves fitting the numerical solution with a series of locally smooth curve fits and then blending them together with a weighted spline approach. The result is a continuously differentiable analytic expression that can be used to determine the error source term. Once the source term has been developed, the ETE can easily be solved using the same solver that is used to obtain the original numerical solution.;The new methodology is applied to increasingly complex problems to quantify the discretization error. The method is first validated with the simplistic 1-D and 2-D convection diffusion problem. For both cases the results were very promising. However, in order for this method to be of practical use in the industry, the method must be applicable to the Navier-Stokes equations which are used to solve complete flow fields. The method is extended to solution of the Navier-Stokes equations with increasing complexity. The obtained results indicate that there is much promise going forward with the newly developed source evaluation technique and the ETE.
Parsons III, Don Roscoe, "Prediction of discretization error using the error transport equation" (2015). Graduate Theses, Dissertations, and Problem Reports. 6382.