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Fall 2019 Colloquium: Graduate Portfolio in Scientific Computation






Sudesh Agrawal Friday, Dec. 6 12-12:30pm GDC 7.402

"Simulation Analysis of Virus Dection Problem"

Chunlin Wu Tuesday, Dec. 10 1:30-2pm GDC 7.514 "A Viscous Vorticity Equation Method for Incompressible Flow"

Sudesh Agrawal

Title: "Simulation Analysis of Virus Dection Problem"

Abstract: This research uses simulation to determine the probability of detection for stochastic models developed in literature to represent the dynamics of a virus spreading in a communication network. In the basic problem, the decision maker places a limited number of perfectly reliable detectors on a subset of nodes in the network. The objective is to determine the placement of these detectors so as to maximize the probability of detection within a given time period.  This research extends the problem to when detectors can have false negatives. We compare the results of a mixed integer program and a greedy heuristic in terms of the solution quality and the computational effort.


Chunlin Wu

Title: "A Viscous Vorticity Equation Method for Incompressible Flow"

Abstract: A fluid is a kind of substance that continually deforms under the applied force, such as water, air, and honey. The viscosity of fluids is a measure of resistance to this deformation. Due to the effect of viscosity, the fluids cannot have relative motions on the boundary. By boundary, it is always referred to as an interface with another substance, such as a solid wall. The boundary layer is the thin layer of fluids in the immediate vicinity of a boundary where the effects of viscosity are significant. In real life, the viscosity of fluids can be neglected in some cases. For example, the flow outside the boundary layer. We call this kind of inviscid flow as potential flow.

Computational Fluid Dynamics (CFD) is a branch of fluid mechanics that uses numerical methods to solve and analyze problems that involve fluid dynamics. The fundamental equations that describe the dynamics of almost all CFD problems are the Navier-Stokes (N-S) equations. Since solving the N-S equations numerically requires unperturbed far-field boundary conditions, it is always time-consuming due to a large number of cells in the computational domain and the nonlinearity of the equation. However, by neglecting the viscous related terms, the potential equations are handy to solve.

Here comes my research. A novel numerical method that solves the VIScous Vorticity Equation (VISVE) in 3D in order to model the interactions between the fluids and solid walls is presented. Since the viscous effect only appears inside the boundary layer, this method, which is designed to be spatially compact and numerically efficient, models only the small fraction of domain near the solid walls. Although this method is a lot faster than the traditional tool, we still want to gain as much efficiency as we can. So, parallelization of the code is needed. Both Open-MP and MPI will be used to parallel the code. The major goals of this project are listed below:

1. validations of the method in both 2-D and 3-D applications.
2. validations of the method under both inertial and non-inertial frame.
3. parallelization of the code to facilitate the performance.