用时空守恒方法求带源项及刚性源项的守恒律方程

Applications of space time conservation schemes to conservation laws with stiff source terms

时空守恒元和解元方法（ＣＥ／ＳＥ）是近年来在国际上兴起的一种崭新的数值方法，它与传统的数值方法相比具有许多独特的优点，但是该方法推广到多维情形（尤其是三维）及高阶格式时会变得非常复杂。该文对其构造方法进行了改进，由此得到的新时空守恒格式不仅可保留原方法的优点，而且格式更简单、实用，尤其易于推广到多维情形。将这种新的格式构造方法应用于带有源项及刚性源项的守恒律方程，得到了相应的时空守恒格式。运用本文格式对几个典型流动问题进行了检验计算。其结果与精确解或实验结果符合很好。

The method of space time conservation element and solution element (CE/SE) is a new numerical method. It has many nontraditional features, such as its conceptual simplicity, generality, high accuracy and high shock resolution, etc. But, it will become very complicated when it is extended to multi dimensional cases. So, the ‘CE/SE’ method is modified and a new constructing approach is developed by the authors. The resulting schemes not only maintain all the features which the CE/SE method has, but also are much simpler and easier to be extended to multi dimensional problems in a straight forward manner. This new constructing approach is applied to conservation laws with source terms or stiff source terms, and the corresponding space time schemes are obtained. Numerical results of three flow problems show many advantages of the present schemes.