A Pressure-Correction Ensemble Scheme for Computing Evolutionary Boussinesq Equations
A Pressure-Correction Ensemble Scheme for Computing Evolutionary Boussinesq Equations
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DOI：
10.1007/s10915-019-00939-w
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发表时间：
2019-03
影响因子：
2.5
通讯作者：
N. Jiang
中科院分区：
文献类型：
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作者：
N. Jiang
研究了一种快速计算热流系综的压力修正系综方案。该方案（1）将Boussinesq系统分解为两个更小的子物理问题;（2）将非线性从Navier-Stokes方程的不可压缩性条件中分离出来，并将动量方程线性化，使其简化为一个标量方程组;（3）在所有实现下，得到具有相同系数矩阵的线性系统。这减少了在每个时间步要求解的线性系统的大小，并允许高效的直接/迭代线性求解器进行快速计算。我们证明了该格式在时间步长条件下是长时间稳定的，且时间上是一阶收敛的。数值试验证实了理论结果并证明了格式的有效性。
We study a pressure-correction ensemble scheme for fast calculation of thermal flow ensembles. The proposed scheme (1) decouples the Boussinesq system into two smaller subphysics problems; (2) decouples the nonlinearity from the incompressibility condition in the Navier–Stokes equations and linearizes the momentum equation so that it reduces to a system of scalar equations; (3) results in linear systems with the same coefficient matrix for all realizations. This reduces the size of linear systems to be solved at each time step and allows efficient direct/iterative linear solvers for fast computation. We prove the scheme is long time stable and first order in time convergent under a time step condition. Numerical tests are provided to confirm the theoretical results and demonstrate the efficiency of the scheme.