【摘要】 给出了一种求解一维双曲型守恒律的五阶松弛格式。该格式以五阶WENO重构和显隐式Runge-Kutta方法为基础。本文格式保持了松弛格式简单的优点,即不用Riemann解算器和计算非线性通量函数的雅可比矩阵。用该格式对一维Euler方程进行了数值试验,并与三阶和四阶松弛格式的计算结果进行了比较,结果表明本文的格式具有更低的数值耗散和更高的分辨率。更多还原

【Abstract】 For hyperbolic conservation laws,a fifth-order relaxation scheme was presented.The scheme is based on the fifth-order weighted essentially nonoscillatory(WENO) reconstruction and the implicit-explicit Runge-Kutta scheme.The resulting scheme does not require Riemann solvers and the computation of Jacobians,so it enjoys the advantages of relaxation schemes.The one-dimensional Euler equations subject to different initial data are used to test the present scheme.To illustrate the improvement of our method,the results are compared with numerical solutions computed by the third-order relaxation scheme.The numerical experiments demonstrate that the present method has the higher shock resolution and smaller numerical dissipation than the third-order relaxation scheme.更多还原