High-order Doubly Asymptotic Transmitting Boundary And Application In Dam-reservoir Interaction

More accuracy and efficiency of the numerical simulation methods on unbounded domain are required as the advancement of various engineering practice. High-order local transmitting boundary and scaled boundary finite element method are two type of promising numerical simulation method on unbounded domain developed in recent years. In this paper, the high-order transmitting boundaries are established directly on the discrete boundary nodes under the theory framework of scaled boundary finite element method. This method of constructing transmitting boundary is applicable to the general unbounded domain with arbitrary geometrical boundary. The study of this paper includes1. Two types of high-order transmitting boundaries are developed based on local Higdon differential operators and the continued-fraction approximation of dynamic stiffness. They are local in time and non-local in space. The accuracy of them is improved as the order increases and computational work increases linearly. They both own high computational efficiency. By using the scaling technique during the introducing of auxiliary variables, it is proved that the high-order higdon-like transmitting boundary with the same artificial wave speeds is just the high-frequency single asymptotic part of high-order doubly asymptotic transmitting boundary. In addition, because these transmitting boundaries are established on boundary nodes, the coupling with finite element method is direct and convenient.2. High-order doubly asymptotic transmitting boundary developed in this paper converges to exact solution quickly as the order increases during the whole frequency domain. This characteristic of convergency in frequency domain makes it simulate the long-time dynamic response accurately in time domain and is better than the common single asymptotic transmitting boundaries in accuracy and stability.3. Employing the high-order doubly asymptotic boundary and finite element method, the direct coupled model and patitioned coupled model are established for the dynamic interaction analysis of concrete dam and reservoir. Based on the restarted function in ABAQUS, the partitioned coupled model is then implemented by using the weak coupled method of sequential solution. The numerical results show that the partitioned coupled model using high-order doubly asymptotic transmitting boundary behaves high computational accuracy.4. By decoupling the time modes of a single space modal transmitting boundary, the recursive convolution algorithm is established in a binary modal space constructed by completely decoupled space and time modes. The numerical results show that the recursive convolution algorithm is more efficient than the time step integration algorithm and the computational efficiency of recursive convolution algorithm is improved more as the order increases or the response history becomes longer.