Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

MODULARITY BASED FUZZY COMMUNITY DETECTION IN SOCIAL NETWORKS

Fuzzy community detection is to identify fuzzy communities in a network, which are groups of vertices in the network such that the membership of a vertex in one community is in [0,1] and that the sum of memberships of vertices in all communities equals to 1. Fuzzy communities are pervasive in social networks, but only a few works have been done for fuzzy community detection. Recently, a one-step forward extension of Newman’s Modularity, the most popular quality function for disjoint community detection, results into the Generalized Modularity (GM) that demonstrates good performance in finding well-known fuzzy communities. Thus, GMis chosen as the quality function in our research. We first propose a generalized fuzzy t-norm modularity to investigate the effect of different fuzzy intersection operators on fuzzy community detection, since the introduction of a fuzzy intersection operation is made feasible by GM. The experimental results show that the Yager operator with a proper parameter value performs better than the product operator in revealing community structure. Then, we focus on how to find optimal fuzzy communities in a network by directly maximizing GM, which we call it Fuzzy Modularity Maximization (FMM) problem. The effort on FMM problem results into the major contribution of this thesis, an efficient and effective GM-based fuzzy community detection method that could automatically discover a fuzzy partition of a network when it is appropriate, which is much better than fuzzy partitions found by existing fuzzy community detection methods, and a crisp partition of a network when appropriate, which is competitive with partitions resulted from the best disjoint community detections up to now. We address FMM problem by iteratively solving a sub-problem called One-Step Modularity Maximization (OSMM). We present two approaches for solving this iterative procedure: a tree-based global optimizer called Find Best Leaf Node (FBLN) and a heuristic-based local optimizer. The OSMM problem is based on a simplified quadratic knapsack problem that can be solved in linear time; thus, a solution of OSMM can be found in linear time. Since the OSMM algorithm is called within FBLN recursively and the structure of the search tree is non-deterministic, we can see that the FMM/FBLN algorithm runs in a time complexity of at least O (n2). So, we also propose several highly efficient and very effective heuristic algorithms namely FMM/H algorithms. We compared our proposed FMM/H algorithms with two state-of-the-art community detection methods, modified MULTICUT Spectral Fuzzy c-Means (MSFCM) and Genetic Algorithm with a Local Search strategy (GALS), on 10 real-world data sets. The experimental results suggest that the H2 variant of FMM/H is the best performing version. The H2 algorithm is very competitive with GALS in producing maximum modularity partitions and performs much better than MSFCM. On all the 10 data sets, H2 is also 2-3 orders of magnitude faster than GALS. Furthermore, by adopting a simply modified version of the H2 algorithm as a mutation operator, we designed a genetic algorithm for fuzzy community detection, namely GAFCD, where elite selection and early termination are applied. The crossover operator is designed to make GAFCD converge fast and to enhance GAFCD’s ability of jumping out of local minimums. Experimental results on all the data sets show that GAFCD uncovers better community structure than GALS.

TANK SIZING AND OPTIMIZING LOOP PLACEMENT IN A BRANCHED WATER DISTRIBUTION SYSTEM

More than eighteen percent of the world’s population lives without reliable access to clean water, forced to walk long distances to get small amounts of contaminated surface water. Carrying heavy loads of water long distances and ingesting contaminated water can lead to long-term health problems and even death. These problems affect the most vulnerable populations, women, children, and the elderly, more than anyone else. Water access is one of the most pressing issues in development today. Boajibu, a small village in Sierra Leone, where the author served in Peace Corps for two years, lacks access to clean water. Construction of a water distribution system was halted when a civil war broke out in 1992 and has not been continued since. The community currently relies on hand-dug and borehole wells that can become dirty during the dry season, which forces people to drink contaminated water or to travel a far distance to collect clean water. This report is intended to provide a design the system as it was meant to be built. The water system design was completed based on the taps present, interviews with local community leaders, local surveying, and points taken with a GPS. The design is a gravity-fed branched water system, supplied by a natural spring on a hill adjacent to Boajibu. The system’s source is a natural spring on a hill above Boajibu, but the flow rate of the spring is unknown. There has to be enough flow from the spring over a 24-hour period to meet the demands of the users on a daily basis, or what is called providing continuous flow. If the spring has less than this amount of flow, the system must provide intermittent flow, flow that is restricted to a few hours a day. A minimum flow rate of 2.1 liters per second was found to be necessary to provide continuous flow to the users of Boajibu. If this flow is not met, intermittent flow can be provided to the users. In order to aid the construction of a distribution system in the absence of someone with formal engineering training, a table was created detailing water storage tank sizing based on possible source flow rates. A builder can interpolate using the source flow rate found to get the tank size from the table. However, any flow rate below 2.1 liters per second cannot be used in the table. In this case, the builder should size the tank such that it can take in the water that will be supplied overnight, as all the water will be drained during the day because the users will demand more than the spring can supply through the night. In the developing world, there is often a problem collecting enough money to fund large infrastructure projects, such as a water distribution system. Often there is only enough money to add only one or two loops to a water distribution system. It is helpful to know where these one or two loops can be most effectively placed in the system. Various possible loops were designated for the Boajibu water distribution system and the Adaptive Greedy Heuristic Loop Addition Selection Algorithm (AGHLASA) was used to rank the effectiveness of the possible loops to construct. Loop 1 which was furthest upstream was selected because it benefitted the most people for the least cost. While loops which were further downstream were found to be less effective because they would benefit fewer people. Further studies should be conducted on the water use habits of the people of Boajibu to more accurately predict the demands that will be placed on the system. Further population surveying should also be conducted to predict population change over time so that the appropriate capacity can be built into the system to accommodate future growth. The flow at the spring should be measured using a V-notch weir and the system adjusted accordingly. Future studies can be completed adjusting the loop ranking method so that two users who may be using the water system for different lengths of time are not counted the same and vulnerable users are weighted more heavily than more robust users.

Control design and genetic algorithm optimization for electrostatic MEMS

This dissertation discusses structural-electrostatic modeling techniques, genetic algorithm based optimization and control design for electrostatic micro devices. First, an alternative modeling technique, the interpolated force model, for electrostatic micro devices is discussed. The method provides improved computational efficiency relative to a benchmark model, as well as improved accuracy for irregular electrode configurations relative to a common approximate model, the parallel plate approximation model. For the configuration most similar to two parallel plates, expected to be the best case scenario for the approximate model, both the parallel plate approximation model and the interpolated force model maintained less than 2.2% error in static deflection compared to the benchmark model. For the configuration expected to be the worst case scenario for the parallel plate approximation model, the interpolated force model maintained less than 2.9% error in static deflection while the parallel plate approximation model is incapable of handling the configuration. Second, genetic algorithm based optimization is shown to improve the design of an electrostatic micro sensor. The design space is enlarged from published design spaces to include the configuration of both sensing and actuation electrodes, material distribution, actuation voltage and other geometric dimensions. For a small population, the design was improved by approximately a factor of 6 over 15 generations to a fitness value of 3.2 fF. For a larger population seeded with the best configurations of the previous optimization, the design was improved by another 7% in 5 generations to a fitness value of 3.0 fF. Third, a learning control algorithm is presented that reduces the closing time of a radiofrequency microelectromechanical systems switch by minimizing bounce while maintaining robustness to fabrication variability. Electrostatic actuation of the plate causes pull-in with high impact velocities, which are difficult to control due to parameter variations from part to part. A single degree-of-freedom model was utilized to design a learning control algorithm that shapes the actuation voltage based on the open/closed state of the switch. Experiments on 3 test switches show that after 5-10 iterations, the learning algorithm lands the switch with an impact velocity not exceeding 0.2 m/s, eliminating bounce.