CAJ | 학술논문

采用基于一类半离散Godunov型中心迎风算法的网格自适应细化算法求解一维双曲守恒律方程。在时间方向上采用三阶TVD‐Runge‐Kutta格式，空间离散采用WENO方法。同时借助一个新的间断探测器来判断间断区域，并对这个区间进行网格加密，使其数值解的精度更高。在数值算例中，通过对非网格自适应和网格自适应结果的比较，可以得出，网格自适应细化算法可以很好的捕捉间断区域，且能有效地抑制非物理震荡的产生。
채용기우일류반리산Godunov형중심영풍산법적망격자괄응세화산법구해일유쌍곡수항률방정。재시간방향상채용삼계TVD‐Runge‐Kutta격식，공간리산채용WENO방법。동시차조일개신적간단탐측기래판단간단구역，병대저개구간진행망격가밀，사기수치해적정도경고。재수치산례중，통과대비망격자괄응화망격자괄응결과적비교，가이득출，망격자괄응세화산법가이흔호적포착간단구역，차능유효지억제비물리진탕적산생。
An adaptive mesh refinement algorithm is adopted to solve one‐dimensional hyperbolic conser‐vation laws ,which is based on a class of semi‐discrete central upwind Godunov type algorithm grid .A third‐order TVD‐Runge‐Kutta format is used in the time direction and WENO scheme is used in the dis‐crete space .At the same time ,a new discontinuity indicator is used to choose discontinuity region ,then refine this interval adaptively ,so the numerical solution has higher accuracy .In the numerical example , comparing the adaptive and non‐adaptive mesh grid results ,adaptive mesh refinement algorithm can cap‐ture the discontinuity region well and restrain non‐physical shocks effectively .