We present an immersed interface method for the incompressible Navier Stokes equations capable of handling rigid immersed boundaries. The immersed boundary is represented by a set of Lagrangian control points. In order to guarantee that the no-slip condition on the boundary is satisfied, singular forces are applied on the fluid at the immersed boundary. The forces are related to the jumps in pr...

The objective of this paper is to present an overview of the newly proposed immersed continuum method in conjunction with the traditional treatment of fluidstructure interaction problems, the immersed boundary method, the extended immersed boundary method, the immersed finite element method, and the fictitious domain method. In particular, the key aspects of the immersed continuum method in com...

The objective of this work is to present a novel, robust, high-order accurate Immersed Interface/Boundary Method (IIM ). In contrast to other immersed methods, which lack a posteriori check of the numerical stability, the method presented herein combines a local Taylor-series expansion at irregular grid points with a local stability condition as part of the design process. Furthermore, this wor...

In this paper, the sharp interface, direct forcing immersed boundary method developed by Yang and Stern (A simple and efficient direct forcing immersed boundary framework for fluidstructure interactions, J. Comput. Phys. 231 (2012) 5029-5061) is applied to the fully resolved simulation of particulate flow. This method uses a discrete forcing approach and maintains a sharp profile of the fluid/s...

A novel e cient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries is presented. In the previous work [1], the calculation is performed on the Cartesian grid regardless of the immersed object, with a fictitious force evaluated on the Lagrangian points to mimic the presence of the physical boundaries. However the explicit direct forcing method [1] f...

A method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp-interface immersed boundary methods (IBMs) is proposed. By first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary, we adopt a cut-cell based approach to strictly enforce geometric conservati...

Abstract. In a flow of two immiscible incompressible viscous fluids, jump discontinuities of flow quantities appear at the two-fluid interface. The immersed interface method can accurately and efficiently simulate the flow without smearing the sharp interface by incorporating necessary jump conditions into a numerical scheme. In this paper, we systematically derive the principal jump conditions...

Article history: Received 29 January 2017 Received in revised form 14 June 2017 Accepted 25 June 2017 Available online 28 June 2017

Article history: Received 31 January 2011 Received in revised form 17 August 2011 Accepted 6 November 2011 Available online 16 November 2011

A linear stability analysis is performed on a two-dimensional version of the \immersed ber problem", formulated by C. Peskin to model the ow of uid in the presence of a mesh of moving, elastic bers. The purpose of the analysis is to isolate the modes in the solution which are associated with the ber, and thereby determine the eeect of the presence of a ber on the uid. The results are used not o...