CAJ | 학술논문

工程实际中的许多间断问题,例如空气动力学中的激波问题,其数学模型大都是非线性双曲守恒律方程.本文在 Runge-Kutta 间断 Galerkin (RKDG)框架下,结合 h 型自适应方法处理了一维非线性守恒律方程初值问题和初边值问题.此方法不仅能准确描述间断的出现和位置,而且还能在间断附近适当加密网格,提高计算效率.最后,数值算例验证了算法的有效性.
공정실제중적허다간단문제,례여공기동역학중적격파문제,기수학모형대도시비선성쌍곡수항률방정.본문재 Runge-Kutta 간단 Galerkin (RKDG)광가하,결합 h 형자괄응방법처리료일유비선성수항률방정초치문제화초변치문제.차방법불부능준학묘술간단적출현화위치,이차환능재간단부근괄당가밀망격,제고계산효솔.최후,수치산례험증료산법적유효성.
@@@@Some discontinuous problems like the shock wave problem of aerodynamics can be described by a nonlinear hyperbolic conservation law. In this paper, we present a adap-tive discontinuous Galerkin method for the initial value and initial-boundary value problem of one-dimensional nonlinear hyperbolic conservation law. The method introduces a h-adaptive strategy in the framework of Runge-Kutta discontinuous Galerkin finite element (RKDG). Then the appearance and position of discontinuity is captured by the method, and the mesh is prop-erly refined near the discontinuity to improve calculation e?ciency. Finally, the correctness of the propose results is verified by numerical examples.