二维Lagrangian坐标系下可压气动方程组的间断Petrov-Galerkin方法

构造矩形网格下求解Lagrangian坐标系下气动方程组的单元中心型格式. 空间离散采用控制体积间断Petrov-Galerkin方法，时间离散采用二阶TVD Runge-Kutta方法. 利用限制器来抑制非物理震荡并保证RKCV算法的稳定性. 构造的算法可以保证物理量的局部守恒. 与Runge-Kutta间断Galerkin（RKDG）方法相比较，RKCV方法的计算公式少一项积分项使得计算较简单. 给出一些数值算例验证了算法的可靠性及效率.

A Discontinuous Petrov-Galerkin Method for Two-dimensional Compressible Gas Dynamic Equations in Lagrangian Coordinates

A cell-centered scheme is constructed for two-dimensional gas dynamics equations in Lagrangian coordinates on rectangular grids. Spacial discretizations are accomplished by control volume discontinuous Petrov-Galerkin method and temporal discretization is accomplished by second order total variation diminishing Runge-Kutta method. A limiter is used to maintain stability and non-oscillatory property of Runge-Kutta control volume (RKCV) method. The method preserves local conservation of physical variables. Compared with Runge-Kutta discontinuous Galerkin (RKDG) method, computational formula of RKCV method is simpler since it contains no volume quadrature in RKDG method. Numerical examples are given to demonstrate reliability and efficiency of the algorithm.