一种用于流体问题的人工压缩性集合时间步进算法
An Artificial Compressibility Ensemble Timestepping Algorithm for Flow Problems
AI总结：
本文提出一种一阶人工压缩性集合算法，通过人工压缩解耦速度与压力，降低计算复杂度和执行时间，并通过分离对流项进一步减少存储和计算时间，证明了方法的非线性能量稳定性和一阶收敛性。
摘要：
集合计算对于具有不确定数据的系统至关重要，但需要显著增加计算资源，这严重限制了集合大小。为突破当前限制，我们提出了一种一阶人工压缩性集合算法。该算法通过人工压缩有效解耦速度和压力求解，从而降低计算复杂度和执行时间。进一步通过分离对流项实现存储和计算时间的进一步减少。在涉及速度波动的CFL型条件下，证明了该方法的非线性能量稳定性和一阶收敛性。提供的数值测试验证了理论分析并展示了集合计算的价值。
英文摘要：
Ensemble calculations are essential for systems with uncertain data but require substantial increase in computational resources. This increase severely limits ensemble size. To reach beyond current limits, we present a first-order artificial compressibility ensemble algorithm. This algorithm effectively decouples the velocity and pressure solve via artificial compression, thereby reducing computational complexity and execution time. Further reductions in storage and computation time are achieved via a splitting of the convective term. Nonlinear energy stability and first-order convergence of the method are proven under a CFL-type condition involving fluctuations of the velocity. Numerical tests are provided which confirm the theoretical analyses and illustrate the value of ensemble calculations.
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