Conservative symmetric second-order one-step integrators are derived using the Discrete Multiplier Method for a family of vortex-blob models approximating the incompressible Euler's equations on the plane. Conservative properties and second order convergence are proved. A rational function approximation was used to approximate the exponential integral that appears in the Hamiltonian. Numerical experiments are shown to verify the conservative property of these integrators, their second-order accuracy, and as well as the resulting spatial and temporal accuracy of the vortex blob method. Moreover, the derived implicit conservative integrators are shown to be better at preserving conserved quantities than standard higher-order explicit integrators on comparable computation times.

翻译：保守对称二阶单步融合器是使用离散乘数法来计算出,该方法用于对平面上接近不压缩尤勒方程式的涡流-浮点模型组群进行分解乘法。保守性质和第二阶次趋同得到证明。一个合理的函数近似值用于接近汉密尔顿市出现的指数集成。数字实验用来核查这些集成器的保守性能、其第二阶次精确度,以及由此产生的涡流体浮点数方法的空间和时间准确性。此外,衍生的隐含保守融合器在保存保留数量方面比可比计算时间的标准更高顺序的直线化集成器要好。