Study on Fluid-Structure Interaction of Flexible Membrane Structures in Wind-Induced Vibration

A strongly coupled monolithic method was previously proposed for the computation of wind-induced fluid-structure interaction of flexible membranous structures by the authors. How to obtain the accurate solution is a key issue for the strongly coupled monolithic method. Projection methods are among the commonly used methods for the coupled solution. In the work here, to impose initial pressure boundary conditions implicitly defined in the original momentum equations in classical projection methods when dealing with large-displacement of membranous structures, a modified factor is introduced in corrector step of classical projection methods and a new modified projection method is obtained. The solution procedures of the modified projection method aimed at strongly coupled monolithic equations are given, and the related equations are derived. The proposed method is applied to the computation of a two-dimensional fluid-structure interaction benchmark case and wind-induced fluid-structure interaction of a three-dimensional flexible membranous structure. The performance and efficiency of the modified projection method are evaluated. The results show that the modified projection methods are valid in the computation of wind-induced fluid-structure interaction of flexible membranous structures, with higher accuracy and efficiency compared with traditional methods. The modified value has little effects on the computation results whereas iteration times has significant effects. Computation accuracy can be improved greatly by increasing iteration times with less increase in computation time and little effects on stability with the modified projection method.

MODIFIED PROJECTION METHOD FOR GENERAL VARIATIONAL INEQUALITIES

In this paper, we suggest and analyze a modified descent-projection method for solving general variational inequalities. The method makes use of a descent direction to produce the new iterate and can be viewed as an improvement of the descent-projection method by using a new step size. We also prove the global convergence of the proposed method. An example is given to illustrate the efficiency and its comparison with other methods. Since the general variational inequalities include quasi variational inequalities and implicit complementarity problems as special cases, results proved in this paper continue to hold for these problems.

Numerical Simulation of Macrosegregation Formation in Binary Alloy Solidification Processing Based on Modified Projection Method

A simplified mathematical model for describing the solidification processing of fluid flow, heat and solute transfer in binary alloys is developed. The conservation equations are numerically solved on a staggered grid by using the control volume-based finite difference method. As the interdendritic flow in the mushy zone is governed by Darcy’s law, the Modified Projection Method is presented for solving the momentum and continuity equations. The solidification processing of Fe-C alloy in rectangular domains is simulated and discussed. The numerical result shows that, by using the Modified Projection Method technique, the presented model is able to predict the macrosegregation formation effectively.