In transient simulations of particulate Stokes flow, to accurately capture the interaction between the constituent particles and the confining wall, the discretization of the wall often needs to be locally refined in the region approached by the particles. Consequently, standard fast direct solvers lose their efficiency since the linear system changes at each time step. This manuscript presents a new computational approach that avoids this issue by pre-constructing a fast direct solver for the wall ahead of time, computing a low-rank factorization to capture the changes due to the refinement, and solving the problem on the refined discretization via a Woodbury formula. Numerical results illustrate the efficiency of the solver in accelerating particulate Stokes simulations.
翻译:在粒子斯托克斯流的瞬时模拟中,为了准确捕捉组成粒子与封闭墙之间的相互作用,墙的离散往往需要在粒子所接近的区域进行当地改进,因此,标准的快速直接解决器由于线性系统每一步都发生变化而丧失了效率。本手稿提出了一种新的计算方法,通过预先为墙壁建造快速直接解决器来避免这一问题,计算低等级的因子化来捕捉由于改进而产生的变化,并通过Woodbury公式解决关于精细离散的问题。数字结果表明解器在加速微粒斯托克斯模拟方面的效率。