We present a general variable viscosity and variable density immersed boundary method that is first-order accurate in the variable density case and, for problems possessing sufficient regularity, second-order accurate in the constant density case. The viscosity and density are considered material properties and are defined by a dynamically updated tesselation. Empirical convergence rates are re...

The Interpolated Bounce-Back (IBB) method and Immersed-Boundary (IB) method are compared for fluid-solid boundary conditions in the Lattice Boltzmann Equation (LBE) in terms of their numerical accuracy and computational efficiency. We carry out simulations for the flow past a circular cylinder asymmetrically placed in the channel in two dimensions with the Reynolds number Re = 20 and 100, corre...

We present a rigorous procedure to derive coarse-grained red blood cell (RBC) models, which lead to accurate mechanical properties of realistic RBCs. Based on a semi-analytic theory linear and nonlinear elastic properties of the RBC membrane can be matched with those obtained in optical tweezers stretching experiments. In addition, we develop a nearly stress-free model which avoids a number of ...

We present an accurate Lagrangian method based on vortex particles, level-sets, and immersed boundary methods, for animating the interplay between two fluids and rigid solids. We show that a vortex method is a good choice for simulating bi-phase flow, such as liquid and gas, with a good level of realism. Vortex particles are localized at the interfaces between the two fluids and within the regi...

In this talk we consider the finite element discretization of the Immersed Boundary Method (IBM) introduced by Peskin [6] for fluid-structure interaction problems. With respect to the original finite differences discretization the finite element approach can take advantage from the variational formulation in handling the Dirac delta function which takes into account the presence of the structur...

We propose a fast and non-stiff approach for the solutions of the Immersed Boundary Method, for Newtonian, incompressible flows in two or three dimensions. The proposed methodology is built on a robust semi-implicit discretization introduced by Peskin in the late 70’s which is solved efficiently through the novel use of a fast, treecode strategy to compute flow-structure interactions. Optimal m...

The Immersed Boundary method is one of the most useful computational methods in studying fluid structure interaction. On the other hand, the Immersed Boundary method is also known to require small time steps to maintain stability when solved with an explicit method. Many implicit or approximately implicit methods have been proposed in the literature to remove this severe time step stability con...

Biological flows in swimming and flying bio-locomotion usually involve intricate flexible or rigid structures that undergo large deformations displacements, as well rich mechanisms of bio-fluid interactions. Immersed boundary methods (IBMs) have gained increasing prevalence numerical investigations such biological flow problems due to their simplicity capability for simulating these on a Cartes...

This paper treats the development and validation of a numerical method for the solution of the unsteady incompressible Navier-Stokes equations in two dimensions. The method of choice is a Godunov-type pressure-free correction method similar to the method developed by Lee and LeVeque. Validation is done by considering a two-dimensional boundary-layer flow along a flatplate. The resulting method ...

We present a 2D high-order and easily accessible immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method to solve fully nonlinear wave-structure interaction problems in marine hydrodynamics using potential-flow theory. To reduce the total number of cells without losing accuracy, quad-tree refinements are employed close free-surface structure boundaries. The is simpler implement tha...