标题： 分段保守、变步长、二阶方法用于埃尔萨瑟变量中的磁流体动力学 显示英文标题

标题： Partitioned Conservative, Variable Step, Second-Order Method for Magneto-hydrodynamics In Elsässer Variables

摘要： 磁流体动力学（MHD）描述了导电流体与电磁场之间的相互作用。 我们提出并分析了一种辛的、二阶算法，用于埃尔萨瑟变量中的演化MHD系统。 通过将耦合系统分成两个子问题，每个子问题的规模为原来的一半，并行求解，从而降低了每次时间步迭代非线性求解器的计算成本。 我们在类似全时空误差分析中所需的时间步长限制下，证明了迭代线性收敛。 变步长算法无条件地保持能量、交叉螺旋度和磁螺旋度的守恒，并且数值解在$L^{2}$和$H^{1}$-范数下具有二阶精度。 基于局部截断误差准则的时间自适应机制有助于变步长算法在精度和时间效率之间取得平衡。 多个数值测试支持理论结果，并验证了时间自适应的优势。 显示英文摘要

摘要： Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Els\"asser variables. We reduce the computational cost of the iterative non-linear solver, at each time step, by partitioning the coupled system into two subproblems of half size, solved in parallel. We prove that the iterations converge linearly, under a time step restriction similar to the one required in the full space-time error analysis. The variable step algorithm unconditionally conserves the energy, cross-helicity and magnetic helicity, and numerical solutions are second-order accurate in the $L^{2}$ and $H^{1}$-norms. The time adaptive mechanism, based on a local truncation error criterion, helps the variable step algorithm balance accuracy and time efficiency. Several numerical tests support the theoretical findings and verify the advantage of time adaptivity.