论文标题
部分可观测时空混沌系统的无模型预测
An assessment of implicit-explicit time integrators for the pseudo-spectral approximation of Boussinesq thermal convection in an annulus
论文作者
论文摘要
我们分析了由圆柱形环中描述BousSinesQ对流的方程式的光谱离散化导致的半混凝土问题的时间积分器的行为。这些方程式以涡旋 - 流函数公式施放，该公式产生差异代数方程（DAE）。该集合包括28个成员：4个隐式宣传多步度方案，22个隐式解释runge-kutta（imex-rk）方案，以及2种用于参考的完全显式方案。评估了11种涵盖层流和动荡政权的不同物理设置的方案。在所有情况下，MultIstep和2 imex-RK方法都表现出其预期的收敛顺序。高阶的IMEX-RK方法显示偶尔降低降低，从而影响代数和差异场变量。我们将降低顺序归因于问题的刚度，并在更大程度上归因于DAE的存在。将流行的曲柄 - 尼科尔森·亚当斯·布什福斯（Adams-Bashforth）作为参考，以最大可接受的时间步长与执行一项迭代的成本的比率来定义性能；最大可允许的时间步骤是通过检查系统内的粘性耗散时间序列来确定的，这保证了物理上可接受的解决方案。在所有研究的配置中，相对性能在0.5至1.5之间。考虑到与性能共同的准确性，我们发现6个方案始终胜过CNAB2，这意味着除了允许更有效的计算外，它们在稳定性的操作限制下达到的准确性还会产生较低的误差。在我们最动荡的设置中，这些方法的行为几乎完全取决于其显式组件，而13 IMEX-RK集成器就准确性和效率而言优于CNAB2。
We analyze the behaviour of an ensemble of time integrators applied to the semi-discrete problem resulting from the spectral discretization of the equations describing Boussinesq convection in a cylindrical annulus. The equations are cast in a vorticity-streamfunction formulation that yields a differential algebraic equation (DAE). The ensemble comprises 28 members: 4 implicit-explicit multistep schemes, 22 implicit-explicit Runge-Kutta (IMEX-RK) schemes, and 2 fully explicit schemes used for reference. The schemes are assessed for 11 different physical setups that cover laminar and turbulent regimes. Multistep and order 2 IMEX-RK methods exhibit their expected order of convergence under all circumstances. IMEX-RK methods of higher-order show occasional order reduction that impacts both algebraic and differential field variables. We ascribe the order reduction to the stiffness of the problem and, to a larger extent, the presence of the DAE. Using the popular Crank-Nicolson Adams-Bashforth of order 2 (CNAB2) integrator as reference, performance is defined by the ratio of maximum admissible time step to the cost of performing one iteration; the maximum admissible time step is determined by inspection of the time series of viscous dissipation within the system, which guarantees a physically acceptable solution. Relative performance is bounded between 0.5 and 1.5 across all studied configurations. Considering accuracy jointly with performance, we find that 6 schemes consistently outperform CNAB2, meaning that in addition to allowing for a more efficient calculation, the accuracy that they achieve at their operational limit of stability yields a lower error. In our most turbulent setup, where the behaviour of the methods is almost entirely dictated by their explicit component, 13 IMEX-RK integrators outperform CNAB2 in terms of accuracy and efficiency.
