Treatment of solid objects in the Pencil Code using an immersed boundary method and overset grids

Abstract

Two methods for solid body representation in flow simulations available in the Pencil Code are the immersed boundary method and overset grids. These methods are quite different in terms of computational cost, flexibility and numerical accuracy. We present here an investigation of the use of the different methods with the purpose of assessing their strengths and weaknesses. At present, the overset grid method in the Pencil Code can only be used for representing cylinders in the flow. For this task it surpasses the immersed boundary method in yielding highly accurate solutions at moderate computational costs. This is partly due to local grid stretching and a body-conformal grid, and partly due to the possibility of working with local time step restrictions on different grids. The immersed boundary method makes up the lack of computational efficiency with flexibility in regards to application to complex geometries, due to a recent extension of the method that allows our implementation of it to represent arbitrarily shaped objects in the flow.

Performance of Overset Mesh in Modeling the Wake of Sharp-Edge Bodies

“…This indicated that OGA implementation yields a similar accuracy in terms of modeling wake characteristics compared to other techniques. Aarnes et al [22] further showed that for the study of two dimensional flow over a circular cylinder using IBM implementation, the domain requires an approximately 18.1 times more grid points than that used in the Overset method to achieve a similar accuracy [22]. The cost and time required for computation would therefore increase, as was observed in another study by Tay et al [36] for flapping airfoil simulations.…”

“…Here, we provide benchmark results for the wake of finite aspect ratio stationary and pitching panels, using the overset solution technique implemented in OpenFOAM. The requirement of smaller grids in overset method, as seen in a study by Aarnes et al [22] for simulating flows over two dimensional bodies, highlighted its potentially better computational efficiency compared to other techniques, such as IBM [11,23]. We therefore utilize OGA method for simulating flows over three dimensional square panels.…”

The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained

“…• Flows around immersed solid objects (Aarnes et al, 2019(Aarnes et al, , 2020; N. E. L. Haugen & Kragset, 2010), • Test-field method for turbulent MHD transport (A. Warnecke et al, 2018), • Mean-field MHD (Jabbari et al, 2013;Kemel et al, 2013),…”

Introduction

“…a cylinder in a cross flow, and the use of more complex boundary conditions. In this connection, Aarnes et al (2020) have compared two different approaches for handling solid bodies within a fluid flow. One is the immersed boundary method and the other is the overset grid method.…”