The paper discusses a reuse of matrix factorization as a building block in the Augmented Lagrangian (AL) and modified AL preconditioners for non-symmetric saddle point linear algebraic systems. The strategy is applied to solve two-dimensional incompressible fluid problems with efficiency rates independent of the Reynolds number. The solver is then tested to simulate motion of a surface fluid, an example of a 2D flow motivated by an interest in lateral fluidity of inextensible viscous membranes. Numerical examples include the Kelvin--Helmholtz instability problem posed on the sphere and on the torus. Some new eigenvalue estimates for the AL preconditioner are derived.
翻译:论文讨论了重新利用矩阵因子化作为拉格朗吉亚增压(AL)和修改的非对称马鞍点线性代数系统中的AL先决条件的构件的问题。战略用于解决二维不压缩液体问题,其效率率独立于Reynolds 号。然后,对溶剂进行测试,模拟表面液体的移动,这是一个2D流动的范例,其动机是对不可延伸的粘膜横向流力的兴趣。数字实例包括球体和托鲁斯造成的Kelvin-Helmholtz不稳定问题。对AL的前提性做了一些新的估计。