Immersed Boundary Method

In FLOW-3D, a simple method is used to eliminate numerical boundary layers caused by fractional cell areas and volumes, in which any spatial velocity derivative that requires velocity values located within solid or void regions when computing the momentum advection term is set to zero, as illustrated in Figure 1. From the physical point of view, this method applies a free-slip (no-penetration) boundary condition to the advection at walls, thus suppresses the artificial boundary layer. Compared to the method without using zero derivatives, the flow solutions are more in accord with real flows, e.g. uniform flow in an inclined duct 1, 2, especially when coarse grids are used.

The loss of flux in the momentum equation is compensated by pressure. Therefore, in certain situations the portion of pressure to compensate the flux loss may grow in time, and at some point, causes a numerical instability called “secular instability”, which is expressed as a monotonic growth of velocities. In order to prevent the instability from developing, an empirical technique 3 in the solver has been used to “correct” the flux at the location where possible instability may emerge. However, this approach does not resolve the flux loss from the source, and could occasionally introduce a nonphysical behavior of the solution such as pressure oscillations.

A technique for approximating the advection term based on the immersed boundary method has been developed for FLOW-3DVersion 12.0, to fundamentally resolve the issue and provide more accurate force predictions at walls. The report describes the methodology of the technique and illustrates its capabilities and advantages, as well as its limitations.


Zongxian Liang, “Immersed Boundary Method for FLOW-3D,” Flow Science Report 12-18, October 2018, Copyright Flow Science