摘要
寻找一种高精度的空间单元插值模式是数值求解三维对流问题的关键．在前人研究的基础上，探讨了一种任意空间六面体的拟协调单元，保证节点上的物理量函数及其一阶导数连续．算例表明，该方法具有良好的计算稳定性和低数值阻尼的优点，且计算工作量大大小于协调单元法，有利于推广应用于对流扩散方程的数值求解．
There are a fundamental difficulty in solving equations due mainly to advective transport. Numerical problems associated with advective domainted transport include spurious oscillation, numerical dispersion, peak clipping, and grid oriention. It is well known and has been well demonstrated that the classical first order scheme would generate excessive numerical dispersion while higher order scheme have been presented to prevent numerical dispersion without the problems of spurious oscillation around the shock. However, the key of numerical solution of three-dimensional advective problem is searching for a high-precision interpolating function, which keep the numerical stability and low damping. For the pure 3D advection problem, solutions are found by the method of characteristics. The solution algorithm involves tracing the characteristic lines backwards in time from a vortex of an element of an interior point. Based on the reference [9], a advanced quasi-consistence hexahedral element method for three-dimensional advective problem is developed in this paper. The flow domain is discretized into arbitrary hexahedral elements. A third-order polynomial based on three-dimensional cartesiajn coordinates (x, y) z) is adopted as the element interpolating function to ensure that the variable functions and their first derivatives over the entire domain are continuous. The function is different from that of the reference [9], avoid solving the linear equations which is 64 × 64 order at every time step, and can only spend 1/50 computer time for the algorithm on reference [9]. The verification of the algorithm are performed using a Guass-distributed concentration ball and a stock wave at steady flow in an open channel, respectively. The comparison with an analytical problem solution show that the precision and the stability of this algorithm is as good as that of the reference [9], better than that of the linear interpolating function method.
出处
《力学学报》
EI
CSCD
北大核心
2000年第6期676-685,共10页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金!(59579009)
关键词
三维对流问题
拟协调单元
数值稳定性
数值阻尼
数值计算
水力学
六面体
Three-dimensional advective problem, quasi-consistence element, numerical stability, numerical damping, numerical method
