保持对称性的新积分梯度格式

A Integrated Gradient Scheme for Preservation of Symmetry

针对柱坐标系下拉氏流体力学的动量方程,提出一种积分梯度格式IGTSP(Integral Gradient Total Symmetry-Preserving),它具备现有积分梯度格式IGA(Integral Gradient Average)和IGT(Integral Gradient Total)的优点,不仅克服了IGT格式不能保持柱坐标系下的一维球对称性的缺点,而且系统的总动量守恒误差为O(h),比IGA格式更好地保持系统的总动量守恒.数值试验进一步显示了该格式理论分析的优点.

An integrated gradient total symmetry-preserving （IGTSP） scheme for momentum equations of Lagrangian hydrodynamics in cylindrical coordinates is presented. The scheme inherits advantages of both IGT and IGA schemes, that is, the scheme not only overcomes nonsymmctry of the IGT scheme but also has a momentum conservation error of order O（h） , one order higher than that of IGA scheme. A number of numerical examples are tested to demonstrate advantages of IGTSP scheme.