When employing the immersed interface method (IIM) to simulate a fluid flow around a moving rigid object, the immersed object can be replaced by a virtual fluid enclosed by singular forces on the interface between the real and virtual fluids. These forces represent the impact of the rigid motion on the fluid flow and cause jump discontinuities across the interface in the whole flow field. Then, the IIM resolves the fluid flow on a fixed computational domain by directly incorporating the jump conditions across the interface into numerical schemes. Previous development of the method is limited to simple smooth boundaries. For complex geometries, the necessary jump conditions have been derived on a polygonal representation of a 2D object, and the Cartesian jump conditions have been computed from the given principal jump conditions on a triangular mesh representation of a 3D object. In this study, we derive the principal jump conditions on a triangular mesh representation of smooth and non-smooth 3D boundaries using the boundary condition capturing approach. Then, we compute the Cartesian jump conditions from the principal jump condition on the triangular mesh. We then implement the jump conditions in the immersed interface method. Numerical tests demonstrate that the method is accurate, efficient, and robust.

Degree Date

Spring 2023

Document Type


Degree Name





Sheng Xu

Subject Area

Mathematics, Applied, Mathematics, General/Other



Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License