Error estimation and mesh adaptation paradigm for unstructured mesh finite volume methods

Error quantification for industrial CFD requires a new paradigm in which a robust flow solver with error quantification capabilities reliably produces solutions with known error bounds. Error quantification hinges on the ability to accurately estimate and efficiently exploit the local truncation error. The goal of this thesis is to develop a reliable truncation error estimator for finite-volume schemes and to use this truncation error estimate to improve flow solutions through defect correction, to correct the output functional, and to adapt the mesh. We use a higher-order flux integral based on lower order solution as an estimation of the truncation error which includes the leading term in the truncation error. Our results show that using this original truncation error estimate is dominated by rough modes and fails to provide the desired convergence for the applications of defect correction, output error estimation and mesh adaptation. So, we tried to obtain an estimate of the truncation error based on the continuous interpolated solution to improve their performance. Two different methods for interpolating were proposed: CGM's 3D surfaces and C¹ interpolation of the solution. We compared the effectiveness of these two interpolating schemes for defect correction and using C¹ interpolation of the solution for interpolating is more helpful compared to CGM, so we continued using C¹ interpolation for other purposes. For defect correction, although using the modified truncation error does not improve the order of accuracy, significant quantitative improvements are obtained. Output functional correction is based on the truncation error and the adjoint solution. Both discrete and continuous adjoint solutions can be used for functional correction. Our results for a variety of governing equations suggest that the interpolating scheme can improve the correction process significantly and improve accuracy asymptotically. Different adaptation indicators were considered for mesh adaptation and our results show that the estimate of the truncation error based on the interpolated solution is a more accurate indicator compared to the original truncation error. Adjoint-based mesh adaptation combined with modified truncation error provides even faster convergence of the output functional.Applied Science, Faculty ofMechanical Engineering, Department ofGraduat