Lagrange柱坐标高阶中心型守恒格式

Lagrange High Order Cell-Centered Conservative Scheme in Cylindrical Geometry

提出Lagrange柱坐标高阶中心型守恒格式.基于用对守恒律的单调迎风算法(MUSCL)构造的高阶子网格压力,引入了柱坐标高阶体权子网格力和柱坐标高阶面权子网格力,构造了柱坐标高阶体权中心型守恒格式和柱坐标高阶面权中心型格式.柱坐标高阶体权中心型守恒格式满足动量守恒、能量守恒,但不能确定保持一维球对称性.柱坐标高阶面权中心型格式满足能量守恒,保持一维球对称性.两种格式里,格点速度以与网格面的数值通量相容的方式计算.对Saltzman活塞问题等进行了数值模拟,数值结果显示Lagrange柱坐标高阶中心型守恒格式的有效性和精确性.

A Lagrange high order cell-centered conservative scheme in cylindrical geometry was presented for gas dynamics.The high order volume weighting subcell force in cylindrical geometry and the high order area weighting subcell force in cylindrical geometry were introduced by means of the MU SCL type method to construct 2 Lagrange high order cell-centered conservative schemes in cylindrical geometry.The vertex velocities and the numerical fluxes through the cell interfaces were evaluated in a consistent manner due to an original solver located at the nodes.The volume weighting scheme satisfies the momentum conservation and energy conservation,but does not surely keep the 1D spherical symmetry.The area weighting scheme satisfies the energy conservation and preserves the 1D spherical symmetry.2 numerical tests were conducted.The results demonstrate that the newscheme is a high order one with satisfactory validity and accuracy.