Understanding of microfluidic mechanism of blood flows in an inertial system is crucial role in designing inertial microfluidic device [1]. Although numerical simulations are attractive tools to predict microfluid behaviors of the blood, it is a formidable task to deal with the system because the microfluidic motion in the inertial system includes extremely-large deformation and migration of individual blood cells.

Particle methods are known as one of the powerful tools for solving largely-moving boundary flow problems [2-4]. However, the particle methods require wide stencils for discretization of spatial derivatives attributed to heterogeneous particle positions which are updated over time, and thus its computational costs generally become higher than those of mesh-based methods. This also makes it difficult to keep a balance of computational loads between particles in massively-scale parallel computing.

To tackle this issue, we have developed the mesh-constrained discrete point (MCD) method for fixed boundary problems [5]. In the MCD method, the discrete points, termed DPs (similar to particles), are introduced in an analysis domain so that its number and position are constrained in the background meshes. This results in keeping homogeneous distribution of DPs and compact stencils for spatial discretization. Analogous to the least-squares moving particle semi-implicit/simulation (LSMPS) method [6, 7], the MCD method can treat arbitrary boundaries by applying a moving least-squares method for spatial discretization using the distributed DPs. Owing to these features, the MCD method could not be only comparable for computational efficiency to the finite difference method, but also has comparable numerical accuracy to boundary-fitted methods.

In this study, we extend the MCD method for moving boundary flow problems. The method updates both the position and role for respective DPs every time according with motions of arbitrary boundaries. Through a numerical validation for a two-dimensional cylinder inline oscillation problem, we obtained reasonable results that both the flow fields of the velocity and pressure and drag coefficient of the cylinder are in good agreement with available data in existing numerical methods.

References:

[1] R. Shi (2023), Eng. Appl. Comput. Fluid Mech. 17, 2177350.

[2] J.J. Monaghan (1992), Annu. Rev. Astron. Astrophys. 30, 543—574.

[3] S. Koshizuka and Y. Oka (1996), Nucl. Sci. Eng. 123, 421—434.

[4] M.B. Liu and G.R. Liu (2016), World Scientific.

[5] T. Matsuda, K. Tsukui, and S. Ii (2022), Mech. Eng. J. 9, 22-00204.

[6] T. Tamai and S. Koshizuka (2014), Comput. Part. Mech. 1, 277—305.

[7] T. Matsunaga, A. Södersten, K. Shibata, and S. Koshizuka (2020), Comput. Methods Appl. Mech Eng. 358, 112624.