Biological membranes contain many types of embedded proteins whose collective organization and functions depend importantly on the mechanical interplay with the lipid bilayer. We introduce new methods at the level of individual proteins embedded within the bilayer in a manner closely related to the Immersed Boundary Method [1, 27]. Our approach accounts for the bidirectional coupling between th...

In this study, the immersed boundary-thermal lattice Boltzmann method has been used to simulate non-Newtonian fluid flow over a heated circular cylinder. The direct-forcing algorithm has been employed to couple the off-lattice obstacles and on-lattice fluid nodes. To investigate the effect of boundary sharpness, two different diffuse interface schemes are considered to interpolate the velocity ...

A level-set method for the simulation of fluid interfaces with insoluble surfactant is presented in two-dimensions. The method can be straightforwardly extended to three-dimensions and to soluble surfactants. The method couples a semi-implicit discretization for solving the surfactant transport equation recently developed by Xu and Zhao [J. Xu, H. Zhao. An Eulerian formulation for solving parti...

In recent years, the immersed-boundary method that is based on the structured mesh has gained considerable popularity in computational fluid dynamics for solving complex and moving-boundary problems. Despite its wide applications, so far there is not a unified definition of the method, possibly because there are many variations in the existing implementations. Here we follow the classification ...

A three-dimensional numerical model of vesicle electrohydrodynamics in the presence of DC electric fields is presented. The vesicle membrane is modeled as a thin capacitive interface through the use of a semi-implicit, gradient-augmented level set jet scheme. The enclosed volume and surface area are conserved both locally and globally by a new Navier–Stokes projection method. The electric field...

A sharp interface immersed boundary method for simulating incompressible viscous flow past three-dimensional immersed bodies is described. The method employs a multi-dimensional ghost-cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three-dimensional, stationary, moving and/or deforming bodies. The complex immersed ...

The immersed finite element method based on a uniform Cartesian mesh has been developed for elasticity equations with discontinuous physical parameters across an interface in this paper. The interface does not have to be aligned with the mesh. The main idea is to modify the basis function over those triangles in which the interface cuts through so that the natural interface conditions are satis...

In the curvilinear/immersed boundary (CURVIB) method developed by our group the background computational domain could be discretized with a curvilinear grid within which immersed bodies are treated as sharp-interface boundaries discretized with an unstructured triangular mesh (Fig. 1). The effect of moving immersed bodies is accounted for by reconstructing boundary conditions at the nodes in th...

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. The forces are related to the jumps in pressure and the jumps in t...

Abstract. The immersed finite element method based on a uniform Cartesian mesh has been developed for the linear elasticity equations with discontinuous coefficients across an interface in this paper. The interface does not have to be aligned with the mesh. The main idea is to modify the basis function over those triangles in which the interface cuts through so that the natural interface condit...