We propose a simple and efficient class of direct solvers for Poisson equation in finite or infinite domains related to spherical geometry. The solver was developed based on truncated spherical harmonics expansion, where the differential mode equations were solved by second-order finite difference method without handling coordinate singularities. The solver was further extended to study the dynamics of a diffusiophoretic particle suspended in Stokes flow. Numerical experiments suggested that the particle can achieve a self-sustained unidirectional motion at moderate Péclet numbers, whereas the particle motion becomes chaotic in high Péclet number regimes. The statistical analysis illustrates the run-and-tumble-like nature at short times and diffusive nature at long times without any source of noise.

我们为与球面几何相关的有限或无限域中的Poisson方程提出了一种简单有效的直接求解器。该解算器是基于截断的球谐展开而开发的，其中的微分模式方程式是通过二阶有限差分法求解的，而无需处理坐标奇异点。该求解器被进一步扩展以研究悬浮在斯托克斯流中的扩散电泳粒子的动力学。数值实验表明，粒子可以在中等的佩克利数下实现自持的单向运动，而粒子运动在高的佩克利数下变得混乱。统计分析表明，在短时间内类似奔跑的性质，在长时间内没有扩散源，而具有扩散性质。