应用协调单元计算三维对流问题

在数值求解三维对流问题时，关键是要寻找一种高精度的空间单元插值模式，使之既要保证解的稳定性，又要防止产生过大的数值伪扩散，因而成为数值求解的主要困难之一。文中探讨的任意空间六面体协调单元，能保证单元节点上的函数，一阶导数及其二、三阶混合导数是连续的。其例表明，本文提出的空间协调单元数值计算方法，具有同时满足稳定性好和数值伪扩散低的优点，不但较常用的非协调单元线性插值方法，而且比拟协调单元插值方法，均有效地提高了三维对流数值求解的精度。

Numerical solution for three-dimensional advective problems using consistent hexahedral element method

A consistent hexahedra1 element method for three-dimensional advective problems is presented in this paper. The flow domain is discretized into arbitrary hexahedral elements. A third-order polynomial based on three-dimensional Cartesian coordinates (x, y, z) is adoped as the element interpolating function to make sure that first derivatives and second and third mixed derivatives of the variable functions over the entire domain are continuous. Results from calculations of two examples show that the consistent hexahedral element method has not only of good numerical stability but also of low damping. It is a significant improvement on the precision of numerical solution for three-dimensional advective problems over the non-consistence linear methods and quasi-consistence tetrahedral element method.