【摘要】 松弛格式是Jin和Xin提出的无振荡有限差分方法,其主要思想是将守恒律转化为松弛方程组进行求解。本文用逐维五阶WENO重构和显隐式Runge-Kutta方法对松弛方程组的空间和时间进行离散,得到了一种求解二维双曲型守恒律五阶松弛格式。所得格式保持了松弛格式简单的优点,不用求解Riemann问题和计算通量函数的雅可比矩阵。通过二维Burgers方程和二维浅水方程的数值算例验证了格式的有效性。更多还原

【Abstract】 A fifth-order relaxation scheme is presented for the approximate solution of two-dimensional hyperbolic conservation laws, where the fifth-order weighted essentially nonoscillatory(WENO) reconstruction is adopted for spatial discretization and the implicit explicit Runge-Kutta method is chosen for the time discretization of relaxation system. The resulting scheme remains the primary advantage of relaxation schemes to avoid solution of Riemann problems and the computation of Jacobians. Several tests are performed on the two-dimensional Burgers equation and shallow water equations to demonstrate the effectiveness.更多还原