Colloquium


DATE2017-05-25 15:10-16:00

PLACE數學館3174教室

SPEAKER楊肅煜 教授(中央大學數學系

TITLEA 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.