Exploratory research on application Multi-Level Multi-Fidelity Monte Carlo in fluid dynamics topics: study on flow past a porous cylinder

Abstract

In offshore engineering complex simulation models are constructed for design optimization using Monte Carlo methods. These models incur large computational costs. Multi-Level Multi-Fidelity Monte Carlo is proposed as a method to reduce the computational cost of these simulations. In addition, research is conducted on the use of porous media as passive damping systems. Hence, an analysis on the effect of porosity on the vortex shedding frequency is conducted. This thesis is an exploratory investigation on the application of Multi-Level Multi-Fidelity Monte Carlo in fluid dynamics topics and its particular use for analysis of the effect of porosity on the vortex shedding frequency on a porous circular cylinder. Three case studies are conducted. Firstly, applying Multi-Level Multi-Fidelity Monte Carlo on a solid circular cylinder case, which is deemed as a successful application, based on the estimated quantity of interest, variance reduction and computational cost reduction. Furthermore, two parametric studies are conducted: 1) to discover empirical relationships (low-fidelity models) and 2) forward uncertainty propagation with Multi-Level Multi-Fidelity Monte Carlo using a uniform input distribution. Both parametric studies consist of a number of equally distributed points of porosity on a case setup of flow past a porous circular cylinder. The parametric studies use a frequency detection algorithm, which approximates the vortex shedding frequency using the frequency of lift force oscillation. The results of the first parametric study indicate there is a drop in vortex shedding frequency as experienced by the cylinder for increasing porosity. The hypothesis is that for increasing porosity the formation length of vortex shedding increases. Two empirical relationships are derived from the results by curve fitting the Strouhal number (dimensionless form of the vortex shedding frequency) versus porosity. These empirical relationships are incorporated in the Multi-Level Multi-Fidelity Monte Carlo method and applied to a similar parametric study on the effect of porosity on the vortex shedding frequency. The results indicate the presence of systemic errors in the high-fidelity model. The conjecture is that the major influence on these errors is due to the resolution of the frequency detection algorithm being too low. For this reason, no clear conclusion on the validity of the empirical relationships is obtained and further research is required.