Higher Order Immersed Interface Methods for Hyperbolic Equations in Heterogeneous Media

複合介質中雙曲線型偏微分方程的高階沈浸介面法

陳開輝(Kai-Hui Chen) ； 簡志銘(Chih-Ming Chien)

《中原學報》 28卷3期 (2000/09) Pp. 1-13

https://doi.org/10.6358/JCYU.200009.0001

摘要

在本文中我們把複合介質中解線性變曲線型偏微分方程的沈浸介面法推廣至更高階精確度。我們假設在所考慮的微分方程中，係數函數爲片段常函數。延續[8]一文中所用的方法，我們把複合介質中連續面附近的有限差分方法，由二階提昇至四階精確度。經由在複合介質中光滑區段使用階有限差分方法如ENO-ROE法加以配合，所得的沈浸介面法證實針對複合介質中的波傳遞不需使用更細綱格便可産生高解析度。

關鍵字

ENO有限差分法 ； 沈浸介面法

並列摘要

We extend the immersed interface method for solving linear hyperbolic equations in heterogeneous media to higher order accuracy. The coefficient functions of the hyperbolic equations considered are assumed to be piecewise constant. We extend the treatment on each interface of discontinuity in [8] from second order accurate to fourth order accurate. By combining the resulting high order interface treatment with high order finite difference schemes, e.g. ENO-ROE schemes, for solving the hyperbolic equations in smooth regions, the resulting immersed interface method is capable of providing sharp resolution of the wave propagation on heterogeneous media without using very fine grids.

並列關鍵字

ENO schemes ； immersed interface method