Development of an adaptive multigrid scheme for computational fluid dynamics

Lack of variety of adaptive multigrid schemes were spotted and motivated the thesis. Main objective was to develop a new adaptive multigrid scheme while keeping robustness and performance as possible. In order to justify a fair numerical experimentation setup, authentic code generation effort was given that implements basic finite volume methods, intergrid operations and iterative solvers. A fundamental reference case was selected in order to get proper validation which had analytical Laplace solution. Fixed and adaptive multigrid schemes and algorithms were also implemented. All methods were presented with both theory and practice in a harmonized manner. All procedures and algorithms were validated regarding the reference case. Reference work unit was defined and was suggested as a new non-dimensional unit of computational cost measurement. Results were compiled and presented in an increasingly complex order. Explorations varying grid resolutions, boundary conditions and fixed multigrid schemes revealed key factors regarding reference case and multigrid methods. Exploration of adaptive multigrid schemes revealed key aspects regarding cost and performance while enabling selection of best parameter sets for the reference case. Explorations established the basis of comparison metrics. Innovative aspect of the thesis was carried out by developing a new and an alternative adaptive multigrid scheme. Comparative performances of multigrid schemes revealed that newly developed adaptive multigrid scheme is robust and is performing as well as the other ones. The new adaptive multigrid scheme was called PID driven and was shown to have 18% lower cost compared to flexible scheme while preserving performance with same effectivity.