间断有限元方法在重力场下欧拉方程中的应用

Discontinuous Galerkin Methods for Euler Equations under Gravitational Fields

重力场作用下的欧拉方程在满足熵恒定的前提下,方程保持等熵定常状态。通过等价改写欧拉方程源项并对改写的方程源项进行合理离散,以及修正方程的数值流通量设计出well-balanced间断有限元方法。在离散状态下,well-balanced间断有限元方法可以保持方程的等熵定常状态,并且大、小振幅波的传播测试表明在网格较粗前提下该方法能有效捕捉方程等熵定常状态的小扰动。

Euler equations under gravitat ional fields admit isentropic equilibrium state. To obtain the dis-continuous Galerkin methods with the help of the isentropic equilibrium state solutions, we first reformu-late the governing equations in an equivalent form, and then propose a novel source term approximation as well as well-balanced numerical fiuxes. The present methods maintain the well-balanced property and have the ability to capture small perturbation of such isentropic equilibrium state.