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2週內演講

Colloquium, 中央大學數學系 楊肅煜教授
Thursday, May 25, 15:10—16:00 數學系3174
Title: HA Direct-Forcing Immersed Boundary Projection Method for Fluid-Solid Interaction Problems
Abstract: In this talk, we will introduce a simple and novel direct-forcing immersed boundary projection method in conjunction with a prediction-correction process for simulating the dynamics of fluid-solid interaction problems, in which each immersed solid object can be stationary or moving in the fluid. The method is mainly based on the introduction of a virtual force, which is distributed only on the immersed solid bodies and appended to the fluid momentum equations to accommodate the boundary conditions at the immersed solid boundaries. Although this method is a two-stage approach, the computational cost of the correction stage is rather cheap, since the associated discrete linear systems need to be solved in the correction stage are same with that in the prediction stage, except the right-hand side data terms. Such a prediction-correction procedure can be iterated to form a more general method, if necessary. Numerical experiments of several benchmark problems are performed to illustrate the simplicity and efficient performance of the proposed method. Convergence tests show that the accuracy of the velocity field is super-linear in space in all the 1-norm, 2-norm, and maximum norm. We also find that our numerical results are in very good agreement with the previous works in the literature and one correction at each time step seems good enough. This is joint work with Tzyy-Leng Horng, Po-Wen Hsieh and Cheng-Shu You.

Colloquium, 中央大學數學系 洪盟凱教授
Friday, June 2, 16:10—17:00 數學系3174
Title: Keller-Segel Equations with Nonlinear Interactions and Small Diffusions
Abstract: In this talk, we consider the one-dimensional Keller-Segel equations with small diffusion and nonlinear interaction between cells and chemical signals. We study the existence of the traveling pulses by the geometric singular perturbations and the trapping region. We show such traveling pulse is unstable by the spectral analysis.

   
 


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國立成功大學數學系
70101 台南市大學路一號
電話︰(06) 2757575 轉 65100   傳真︰(06) 2743191
em65100[at]email.ncku.edu.tw