Improvement of Nested Cartesian Finite Difference Grid Solvers



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Computational Fluid Dynamics (CFD) has been a successful tool for industry applica- tions during the last decades. However, still accurate solutions involving vortex propagation, separated and turbulent flows are associated with high computing costs. LES simulations of complex geometries, such as an automobile, at high Reynolds number require several days to obtain a solution with information statistically relevant on an arbitrary high number of cores. FDFLO is a High Order Cartesian Finite Difference (FD) code, developed for industrial applications at the CFD Center at George Mason University. FDFLO is able to perform LES simulation with the aim of overnight turnarounds. A study of the capabilities of an FD solver to obtain accurate turbulent results in complex geometries and the main implementations an improvements introduced in the code are the subject of this thesis. The two central issues addressed in this thesis are: a) Proper schemes for the transition between grids of different spatial resolution, and b) Development of high order methods for the time discretization with minimal stage count. The first issue was resolved using high order interpolation post-processing interpolation schemes. The second issue was addressed by employing multivalue multistage Runge-Kutta (MMRK) schemes. The methods developed were tested on canonical analytical test cases such as the Lambvortex and the Taylor-Green vortex, as well as experimental results for the Ahmed Body. The results obtained showed the expected spatial and temporal convergence characteristics of the methods, as well as very good agreement (overall drag, location of flow structures, etc.) for the Ahmed body. The gains in computational performance for the MMRK methods used as compared to classical Runge-Kutta or Low-Storage RK schemes reached up to 25% with no loss in accuracy. An interesting empirical result observed for the Taylor-Green vortex was that for fully turbulent flows the accuracy of 8th order schemes on grids of size 2h was equivalent to 2nd order schemes on grids of size h. The resulting overall speedup of the 8th order scheme over the 2nd order scheme was more than a factor of 5:1.