演講訊息 TALKS

Abstract: In this work, we propose a simple and novel prediction-correction direct-forcing immersed boundary method, which is combined with the projection methods, for simulating the dynamics of fluid-solid interaction problems. The immersed solid object can be stationary or moving in the fluid with a prescribed velocity. As usual, an Eulerian description is used for the fluid dynamics, while the Lagrangian representation is employed for the immersed solid boundary. The proposed approach can be categorized as a discrete forcing method with a prediction-correction strategy, in which a virtual force of discrete type distributed on the whole solid body is introduced and added to the fluid momentum equations to accommodate the no-slip boundary condition at the immersed solid boundary. More precisely, based on the rate of moment changes of the solid body, the virtual force at the grid points can be first predicted by using the difference between the prescribed solid velocities and the computed velocities which are obtained by the projection method for the incompressible Navier-Stokes equations without adding any virtual forcing term. Such predicted virtual force is then put into the momentum equations for the correction step to update the velocity field, pressure and virtual force. This prediction-correction process can be iterated to generate a more general method, if necessary. Numerical experiments of several benchmark problems are performed to illustrate the simplicity and high performance of the proposed prediction-correction approach. We find that our numerical results are in very good agreement with the previous works in the literature and in most cases, one correction step is good enough. This is joint work with Tzyy-Leng Horng, Po-Wen Hsieh and Suh-Yuh Yang.