Session EL: CFD III: Immersed Boundary Methods

Adaptive finite volume incompressible Navier--Stokes solver for 3D flows with complex immersed boundaries

We propose a generalisation of the CURVIB methodology (Ge \& Sotiropoulos, JCP 2007) for the solution of the unsteady incompressible Navier--Stokes equations on arbitrary polygonal meshes in domains containing arbitrarily complex, moving immersed bodies. The new finite volume flow solver employs the hybrid staggered/non--staggered approach of Ge \& Sotiropoulos (2007) in conjunction with generalised and robust discretisation procedures, so that it can be readily extended to handle adaptive meshes. The flow solver is combined with an isotropic adaptation strategy that effectively tracks flow features of interest and selectively enhances grid resolution. The resulting generic adaptive finite volume flow solver allows for computationally efficient, high resolution numerical simulations of a wide range of engineering and biological flows at Reynolds numbers much higher than what was possible with the original CURVIB methodology.   

Coherent-Structure Resolving Simulations of Turbulence in Natural Streams with the Curvilinear Immersed-Boundary Method

Critical prerequisite for developing a science-based approach to restoring natural streams is being able to model turbulence in real-life aquatic environments. We develop a powerful computational model for carrying out coherent structure resolving simulations of turbulent flows in natural streams at field scale conditions. The model employs the curvilinear immersed boundary method (CURVIB) of Ge and Sotiropoulos (J. Comp. Phys., 2007) to handle the arbitrarily complex channel geometries. To enable efficient simulations in the large-aspect ratio domains and highly stretched grids, arising due to the very small depth-to-length ratio of natural streams, we employ a fully implicit matrix-free GMRES method for the momentum equations coupled with a parallel algebraic multigrid method for the pressure Poisson equation. The capabilities of the method are demonstrated by carrying out high resolution LES as well as coarser resolution RANS simulations for the field scale meandering stream flow in the St. Anthony Falls Laboratory Outdoor StreamLab.   

An overset curvilinear/immersed boundary framework for high resolution simulations of wind and hydrokinetic turbine flows

We generalize the curvilinear/immersed boundary method to incorporate overset grids to enable the simulation of more complicated geometries and increase grid resolution locally near complex immersed boundary. The new method has been applied to carry out high resolution simulations of wind and hydrokinetic turbine rotors. An interior fine mesh contains the rotor blades and is embedded within a coarser background mesh. The rotor blades can be treated either as immersed boundaries or using curvilinear, boundary-conforming overset grids. The numerical methodology has been generalized to include both inertial and non-inertial frame formulations. The method is validated by applying it to simulate the flow for the NREL wind turbine rotor for various turbine operating points. Inviscid, unsteady RANS and LES simulations are carried out and compared with experimental data. Preliminary results will also be presented for the hydrokinetic turbine rotor installed at the Roosevelt Island Tidal Energy project in New York City.   

A second-order immersed boundary method with near-wall physics

The NIST Fire Dynamics Simulator is a variable-density large-eddy simulation code tuned for low-speed fire dynamics and heat transfer. The gas-phase numerics utilize a Cartesian staggered-grid arrangement and are generally second- order accurate. Until now, complex geometry has been treated with an immersed boundary method in which objects in the flow are forced to conform to the Cartesian grid. This method exactly corresponds to first interpolation method described in Fadlun et al. (J. Comp. Phys. 2000) and has been shown to exhibit zeroth order errors for non-conformal geometries. In the work presented here, we implement a variant on the second-order interpolation scheme of Fadlun et al. and extend the method to include the near-wall stress model of Werner and Wengle (8th Symp. Turb. Shear Flows 1991). To accomplish this we transform the first off-wall velocity into a streamwise coordinate system and update the components based on a momentum equation with a Werner and Wengle wall stress. The streamwise system components are then transformed back to the grid system to form the force terms required in the immersed boundary method. The new approach is tested in laminar and turbulent channel flow with the channel rotated through a range of angles relative to the Cartesian grid.   

An immersed boundary method using the discrete streamfunction approach with an implicit forcing

Recently, Colonius and Taira (Comput. Methods Appl. Mech. Engrg. 2008) present an immersed boundary method in which the discrete streamfunction approach is used to solve the incompressible Navier-Stokes equations. In this talk, we proposed a novel immersed boundary method in the framework of the discrete streamfunction approach. Similar to the method of Colonius and Taira, the forcing term to impose the non-slip boundary condition is determined implicitly (by solving a linear system). However, in the present method, the linear system is in a simpler form and much easier to solve. The time to compute the forcing term is found to be negligible comparing with that to solve the Navier-Stokes equations. Some verifications and validations of this new method are presented. An accuracy test is first performed by using the decaying-vortex problem, both with and without the presence of immersed boundaries. Some canonical cases are then simulated, such as the flow over stationary and oscillating cylinders and flow over a vertical plate of zero thickness. All numerical results are in good agreement with those in literature. This is an indication that the method can handle boundaries of different shapes with acceptable accuracy.   

A hybrid formulation to suppress the numerical oscillations caused by immersed moving boundaries

A family of immersed-boundary methods, based on the sharp-interface representation of the boundary and local interpolation/extrapolation, has been recently developed to handle complex and moving boundary problems encountered in biological flows. Implemented typically on structured meshes, these methods save the computational cost of grid generation and take advantage of efficient computations on structured grids. However, since some of the nodes near the immersed boundary do not have the regular finite-difference stencil available for discretizing the Navier-Stokes equation, a local interpolation or extrapolation scheme is often used to reconstruct the flow field around the nodes. The drawback of this approach is that when a non-stationary boundary moves across the mesh points, the change of the stencil for the solution reconstruction causes artificial oscillations in the pressure. To suppress the oscillations, we have introduced a set of hybrid nodes on which both the Navier-Stokes solution and flow reconstruction are sought, and they are weighted according to the distance to the immersed boundary. The method has been implemented in both two- and three-dimensional solvers to handle a class of biological locomotion problems including flow-structure interaction. The accuracy and capability of the solvers will be demonstrated.   

Immersed boundary method modeling of elastic capsules in superpositions of plane and axisymmetric extensional flows

Physics of elastic capsules in fluid is important to understanding biology, especially microcirculation, and is also useful in design of microfluidic devices. Linear flows, such as shear, plane extensional, and axisymmetric extensional flows, appear in many microfluidic applications, so understanding their effect on the deformation of capsules is necessary. The rotational component of the flow has no effect on deformation, and is neglected. The velocity gradient, not magnitude, leads to deformation, so the velocity magnitude is likewise neglected. Under eigendecomposition, any linear flow can then be represented as a superposition of a plane extensional and a plane axisymmetric flows, for analysis of capsule deformation. Computational modeling results using the immersed boundary method are reported.   

An Efficient Algorithm for Computing Physiological Fluid Flows

A new, efficient algorithm is presented for solving the one-dimensional model equations for internal physiological fluid flows. The models equations are a set of coupled, 1D nonlinear partial differential equations that govern the evolution of the pressure, velocity, and cross sectional area in internal biological fluid flows. The solution algorithm for these equations, the pulsed flow algorithm (PFA), begins with a partial asymptotic solution of the discretized model equations, then combines the equations and linearizes them, reducing them to tridiagonal form. The algorithm is applied to blood flow computations in the human arterial system and is compared to the most commonly used method for solving the model equations, the Lax-Wendroff (LW) scheme. The PFA algorithm is found to be approximately 40 times faster than LW for a single arterial segment, and approximately 6 times faster than LW for a model of the human arterial tree that includes the 55 largest arteries.