Curvilinear grid

The preceding technique, notwithstanding its requirements for additional memory, does not influence the total computational burden. On the contrary, its ability to manipulate curvilinear grids and relatively smooth material interfaces is proven to be fairly convenient and instructive. 

Figure 6. Preprocessing for determination of which uniform Cartesian grid nodes reside in each curvilinear grid cell.

Figure 8. (a) A coarse curvilinear grid and (b) rigid body motion of the drop. The drop is enlarged three times at the locations shown by the thick arrows. 

Shyy W, Francois M, Udaykumar HS (2001) Cartesian and curvilinear grid methods for multi-domain, moving boundary problems. In Debit M et al (eds) Thirteenth international conference on domain decomposition method. CIMNE, Barcelona... 

The immersed boundary method was first introduced by Peskin [5] to simulate the blood flow in the heart. Since then a few variants have emerged and the method has been used to compute many flows with complex and/or moving geometries (Mittal and laccarino [4]). The distinguishing feature of this method is that the computations are done on either a Cartesian grid or a curvilinear grid which do not necessarily conform to the flow boundary. 

In this article, we consider incompressible Newtonian flows and briefly describe the underlying numerical methodology of the immersed boundary method. We will use the Cartesian grids for the purpose of illustration. The same methodology can be applied to the compressible flows (e. g., Ghias et al. [2]) and on the curvilinear grids (e. g., Luo et al. [3]). 

Sharpe, H.N., and Anderson, D.A., Orthogonal Curvilinear Grid Generation with Preset Internal Boundaries for Reservoir Simulation, Paper No. 21235, Eleventh SPE Symposium on Reservoir Simulation, Anaheim, CA, Feb. 17-20, 1991. 

A.A. Amsden and C.W. Hirt (1973) A simple scheme for generating general curvilinear grids. J. Comput. Phys. 11, 348-359. 

C.L. Earmer and D.E. Heath (1990) Curvilinear grid generation techniques. Proceedings of the 2nd European Conference on the Mathematics of Oil Recovery (ECMOR ii). Arles, Erance, 11-14 September, 1990. 

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