The method of regularised stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly-varying regularised stokeslet kernel. Here we show how Richardson extrapolation with coarse values of the regularisation parameter is ideally-suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency.
翻译:由于实施方便,对复杂移动的几何进行自然处理,并去除要整合的单项功能,因此在微型生物流体动态中广泛使用正规化的石墨板方法,由于将线性系统大小与解决快速变化的正规化石墨板内核所需的数字分辨率相混合,该方法的标准实施需要较高的计算成本。这里我们展示了理查森对常规化参数粗值的外推方法如何最适宜于减少二次误差,从而大幅度降低储存和溶解成本而不丧失准确性。斯托克斯的抗力和移动问题数字实验支持了分析,证实了精度和(或)效率的几级提高。