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.

ASTAXANTHIN PRODUCTION FROM HAEMATOCOCCUS PLUVIALIS UNDER VARIOUS LIGHT INTENSITIES AND CARBON DIOXIDE CONCENTRATIONS

The microalga Haematococcus pluvialis was cultivated in MES-volvox medium at various light intensities and CO2 concentrations. It was found that CO2 concentrations of 10 and 15%, in combination with high irradiance at initial pH =6.7, accelerate astaxanthin accumulation in H. pluvialis cells but obstruct cell growth. The purpose of this research study was to devise a one-stage process consisting of the simultaneous cultivation of H. pluvialis and astaxanthin production using high light intensity and high CO2 concentration. This could be achieved at 200 µE/m2s and 15% CO2 in growth medium at initial pH = 4.3. Compared to the traditional two-stage H. pluvialis cultivation system, this one-step process can save up to 8-9 days of astaxanthin production time. The astaxanthin content in H. pluvialis cells induced with high light intensity only or with a combination of high light intensity and high CO2 concentration had comparable astaxanthin content; 94 and 97 mg/g dry biomass, respectively. However, it was extremely low in nitrate-free medium at high irradiance alone or combined with high CO2 concentration, with an average value of 4 mg/g dry biomass. Cell density was 40% less in cultures under discontinuous illumination compared to continuous illumination. This process could serve as a microalgal CO2 mitigation system after further understanding of the CO2 fixation ability of H. pluvialis has been gained.

POPLAR GENE EXPRESSION DATA ANALYSIS PIPELINES

Analyzing large-scale gene expression data is a labor-intensive and time-consuming process. To make data analysis easier, we developed a set of pipelines for rapid processing and analysis poplar gene expression data for knowledge discovery. Of all pipelines developed, differentially expressed genes (DEGs) pipeline is the one designed to identify biologically important genes that are differentially expressed in one of multiple time points for conditions. Pathway analysis pipeline was designed to identify the differentially expression metabolic pathways. Protein domain enrichment pipeline can identify the enriched protein domains present in the DEGs. Finally, Gene Ontology (GO) enrichment analysis pipeline was developed to identify the enriched GO terms in the DEGs. Our pipeline tools can analyze both microarray gene data and high-throughput gene data. These two types of data are obtained by two different technologies. A microarray technology is to measure gene expression levels via microarray chips, a collection of microscopic DNA spots attached to a solid (glass) surface, whereas high throughput sequencing, also called as the next-generation sequencing, is a new technology to measure gene expression levels by directly sequencing mRNAs, and obtaining each mRNA’s copy numbers in cells or tissues. We also developed a web portal (http://sys.bio.mtu.edu/) to make all pipelines available to public to facilitate users to analyze their gene expression data. In addition to the analyses mentioned above, it can also perform GO hierarchy analysis, i.e. construct GO trees using a list of GO terms as an input.