Unconditionally stable, second order, decoupled ensemble schemes for computing evolutionary Boussinesq equations
Unconditionally stable, second order, decoupled ensemble schemes for computing evolutionary Boussinesq equations
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DOI：
10.1016/j.apnum.2023.06.011
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发表时间：
2023-10
影响因子：
2.8
通讯作者：
N. Jiang;Huanhuan Yang
中科院分区：
文献类型：
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作者：
N. Jiang;Huanhuan Yang
在本报告中，我们提出了两种用于计算演化 Boussinesq 方程的无条件稳定、二阶、解耦系综方案：稳定标量辅助变量 Crank-Nicolson 蛙跳系综方案 (Stab-SAV-CNLF-En) 和稳定标量辅助变量 BDF2 系综方案 (Stab-SAV-BDF2-En)。这两种集成方案采用了最近发展的稳定标量辅助变量（SAV）思想和集成时间步长，以实现高效率和无条件稳定性。具体来说，稳定 SAV 方法使得设计无条件长时间稳定方案成为可能，其中 Boussinesq 方程中的非线性项和耦合项完全显式，从而在空间离散化后求解具有常系数矩阵的线性系统。集成时间步长通过使所有实现的系数矩阵相同，进一步提高了效率，从而可以应用高效的块求解器来求解相应的具有多个右侧的线性系统，从而大大降低了计算成本。我们证明所提出的方案是无条件稳定的并且存在实施细节。进行了大量的数值测试以显示组合方法的效率和有效性。
In this report we present two unconditionally stable, second order, decoupled ensemble schemes for computing evolutionary Boussinesq equations: the stabilized scalar auxiliary variable Crank-Nicolson leap-frog ensemble scheme (Stab-SAV-CNLF-En) and the stabilized scalar auxiliary variable BDF2 ensemble scheme (Stab-SAV-BDF2-En). The two ensemble schemes adopt the recently developed stabilized scalar auxiliary variable (SAV) idea and ensemble timestepping to achieve both high efficiency and unconditional stability. Specifically, the stabilized SAV approach makes it possible to devise unconditionally long time stable schemes for which the nonlinear terms and coupling terms in the Boussinesq equations are made fully explicit, leading to linear systems with constant coefficient matrices to be solved after spatial discretization. The ensemble timestepping further improves the efficiency by making the coefficient matrices of all realizations the same, so that efficient block solvers can be applied to solve the corresponding one linear system with multiple right hand sides and thus greatly reduce the computational cost. We prove the proposed schemes are unconditionally stable and present implementation details. Ample numerical tests are performed to show the efficiency and effectiveness of the combined approach.