Immersed boundary and overset grid methods assessed for Stokes flow due to an oscillating sphere

JOURNAL OF COMPUTATIONAL PHYSICS

卷:423

Article

Vreman, A. W.^1,2 

[1] Nouryon, Res Dev & Innovat, Proc Technol, POB 10, NL-7400 AA Deventer, Netherlands

[2] Eindhoven Univ Technol, Dept Mech Engn, POB 513, NL-5600 MB Eindhoven, Netherlands

关键词: Immersed boundary methods;    Overset grid methods;    Moving body problems;   

DOI  :  10.1016/j.jcp.2020.109783

来源: Elsevier

【 摘 要 】

A systematic comparison of three types of immersed boundary methods and an overset grid method is performed for incompressible Stokes flow due to an oscillating sphere. For each simulation the error between the numerical solution and the analytical solution is reported in terms of the maximum and L-2 norms of the errors in the velocity, the pressure and the velocity gradient fields. The three types of immersed boundary methods are: (A) a diffuse-interface immersed boundary method (IBM), (B) a sharp-interface IBM with standard treatment of the pressure, and (C) a sharp-interface IBM with pressure decoupling at interfaces. Upon grid refinement, the velocity gradient and pressure fields generated by methods A and B do not converge to the analytical solution in the maximum norm, while the total force on the sphere does converge. An inspection of the norms as function of the distance to the surface shows that the lack of convergence mainly occurs in the first layer of grid cells outside the sphere. If the pressure Poisson equation is not solved inside the sphere (method C), the velocity gradient and pressure seem to converge in the maximum norm. However, high resolution is required to achieve a smaller maximum error in the pressure in method C than in methods A and B. Overall, method C is somewhat more accurate than method B and the latter is somewhat more accurate than method A. In this assessment, the overset grid method clearly outperforms the IBMs and is able to produce errors down to one percent in the maximum norm at 32 grid points per sphere diameter. Within each of the four classes of methods, several variants are tested. For the overset grid method and in several sharp-interface IBMs, nonincremental projection is found to produce a more accurate pressure than incremental projection does. Finally, variants of method C and the overset grid method are proposed in which the projection method is replaced by an artificial compressibility method, while the staggered grid is maintained. This simplifies the methods, and it strongly reduces the maximum error in the pressure in case C, at the expense of an increased maximum error in the velocity divergence. (C) 2020 The Author. Published by Elsevier Inc.

【 授权许可】

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