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首页> 外文期刊>Journal of Computational Physics >The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement
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The immersed boundary method for advection-electrodiffusion with implicit timestepping and local mesh refinement

机译：具有隐式时间步长和局部网格细化的对流-电扩散沉浸边界方法

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摘要

We describe an immersed boundary method for problems of fluid-solute-structure interaction. The numerical scheme employs linearly implicit timestepping, allowing for the stable use of timesteps that are substantially larger than those permitted by an explicit method, and local mesh refinement, making it feasible to resolve the steep gradients associated with the space charge layers as well as the chemical potential, which is used in our formulation to control the permeability of the membrane to the (possibly charged) solute. Low Reynolds number fluid dynamics are described by the time-dependent incompressible Stokes equations, which are solved by a cell-centered approximate projection method. The dynamics of the chemical species are governed by the advection-electrodiffusion equations, and our semi-implicit treatment of these equations results in a linear system which we solve by GMRES preconditioned via a fast adaptive composite-grid (FAC) solver. Numerical examples demonstrate the capabilities of this methodology, as well as its convergence properties.
机译：我们描述了一种解决流体-溶质-结构相互作用问题的沉浸边界方法。数值方案采用线性隐式时间步长，可以稳定使用比显式方法所允许的时间步长大得多的时间步长，并且可以进行局部网格细化，从而有可能解决与空间电荷层以及空间电荷层相关的陡峭梯度化学势，在我们的配方中用于控制膜对（可能带电的）溶质的渗透性。低雷诺数流体动力学由与时间有关的不可压缩Stokes方程描述，该方程通过以单元为中心的近似投影方法求解。化学物质的动力学受对流-电扩散方程式的控制，我们对这些方程式的半隐式处理导致了一个线性系统，该系统由GMRES通过快速自适应复合网格（FAC）求解器进行预处理。数值示例说明了该方法的功能及其收敛性。

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