Immersed Boundary Lattice Green Function methods for External Aerodynamics

In this paper, we document the capabilities of a novel numerical approach - the immersed boundary lattice Green's function (IBLGF) method - to simulate external incompressible flows over complex geometries. This new approach is built upon the immersed boundary method and lattice Green's functions to solve the incompressible Navier-Stokes equations. We show that the combination of these two concepts allows the construction of an efficient and robust numerical framework for the direct numerical and large-eddy simulation of external aerodynamic problems at moderate to high-Reynolds numbers

An efficient implicit direct forcing immersed boundary method for incompressible flows

International audienceA novel efficient 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] fails to accurately impose the non-slip boundary condition on the immersed interface. In the present work, the calculation is based on the implicit treatment of the artificial force while in an effective way of system iteration. The accuracy is also improved by solving the Navier-Stokes equation with the rotational incremental pressure- correction projection method of Guermond and Shen [2]. Numerical simulations performed with the proposed method are in good agreement with those in the literature

A Second Order Penalized Direct Forcing for Hybrid Cartesian/Immersed Boundary Flow Simulations

International audienceFlows around complex stationary/moving solids take an important place in life-science context or in many engineering applications. Usually, these problems are solved by body-fitted approaches on unstructured meshes with boundary conditions directly imposed on the domain boundary. Another way is using immersed boundary (IB) techniques: the physical domain is immersed in a fixed fictitious one of simpler geometry on Cartesian grids. It allows to use efficient, fast and accurate numerical methods avoiding the tedious task of re-meshing in case of time varying geometry. In contrast, one needs specific methods to take into account the IB conditions (IBC). Here, we propose a second order penalized direct forcing method for unsteady incompressible flows with Dirichlet's IBC. It consists in adding a penalized forcing term to the initial problem, applied only on Cartesian nodes near the IB, in order to bring back the variable to the imposed one. Regarding Navier-Stokes solvers using a projection scheme, the forcing term is distributed both in the velocity prediction and in the correction equations. It leads to a natural way to prescribe the pressure boundary conditions around obstacles. Numerical experiments, performed for laminar flows around static/moving solids, assess the validity and illustrate the ability of our method, showing in particular a quadratic convergence rate

Towards the study of flying snake aerodynamics, and an analysis of the direct forcing method

Immersed boundary methods are a class of techniques in computational fluid dynamics where the Navier-Stokes equations are simulated on a computational grid that does not conform to the interfaces in the domain of interest. This facilitates the simulation of flows with complex moving and deforming geometries without considerable effort wasted in generating the mesh. The first part of this dissertation is concerned with the aerodynamics of the cross-section of a species of flying snake, Chrysopelea paradisi (paradise tree snake). Past experiments have shown that the unique cross-section of this snake, which can be described as a lifting bluff body, produces an unusual lift curve--with a pronounced peak in lift coefficient at an angle of attack of 35 degrees for Reynolds numbers 9000 and beyond. We studied the aerodynamics of the cross-section using a 2-D immersed boundary method code. We were able to qualitatively reproduce the spike in the lift coefficient at the same angle of attack for flows beyond a Reynolds number of 2000. This phenomenon was associated with flow separation at the leading edge of the body that did not result in a stall. This produced a stronger vortex and an associated reduction in pressure on the dorsal surface of the snake cross-section, which resulted in higher lift. The second part of this work deals with the analysis of the direct forcing method, which is a popular immersed boundary method for flows with rigid boundaries. We begin with the fully discretized Navier-Stokes equations along with the appropriate boundary conditions applied at the solid boundary, and derive the fractional step method as an approximate block LU decomposition of this system. This results in an alternate formulation of the direct forcing method that takes into consideration mass conservation at the immersed boundaries and also handles the pressure boundary conditions more consistently. We demonstrate that this method is between first and second-order accurate in space when linear interpolation is used to enforce the boundary conditions on velocity. We then develop a theory for the order of accuracy of the direct forcing method with linear interpolation. For a simple 1-D case, we show that the method can converge at a range of rates for different locations of the solid body with respect to the mesh. But this effect averages out in higher dimensions and results in a scheme that has the same order of accuracy as the expected order of accuracy of the interpolation at the boundary. The discrete direct forcing method for the Navier-Stokes equations exhibits an order of accuracy between 1 and 2 because the velocities at the boundary are linearly interpolated, but the resulting boundary conditions on the pressure gradient turn out to be only first-order accurate. We recommend linearly interpolating the pressure gradient as well to make the method fully second-order accurate. We have also developed two open source codes in the course of these studies. The first, cuIBM, is a two-dimensional immersed boundary method code that runs on a single GPU. It can simulate incompressible flow around rigid bodies with prescribed motion. It is based on the general idea of a fractional step method as an approximate block LU decomposition, and can incorporate any type of immersed boundary method that can be made to fit within this framework. The second code, PetIBM, can simulate both two and three-dimensional incompressible flow and runs in parallel on multiple CPUs. Both codes have been validated using well-known test cases

Topology-free immersed boundary method for incompressible turbulence flows: An aerodynamic simulation for 'dirty' CAD geometry

To design a method to solve the issues of handling 'dirty' and highly complex geometries, the topology-free method combined with the immersed boundary method is presented for viscous and incompressible flows at a high Reynolds number. The method simultaneously employs a ghost-cell technique and distributed forcing technique to impose the boundary conditions. An axis-projected interpolation scheme is used to avoid searching failures during fluid and solid identification. This method yields a topology-free immersed boundary, which particularly suits flow simulations of highly complex geometries. Difficulties generally arise when generating the calculation grid for these scenarios. This method allows dirty data to be handled without any preparatory treatment work to simplify or clean-up the geometry. This method is also applicable to the coherent structural turbulence model employed in this study. The verification cases, used in conjunction with the second-order central-difference scheme, resulted in first-order accuracy at finer resolution, although the coarser resolution retained second-order accuracy. This method is fully parallelized for distributed memory platforms. In this study, the accuracy and fidelity of this method were examined by simulating the flow around the bluff body, past a flat plate, and past dirty spheres. These simulations were compared with experimental data and other established results. Finally, results from the simulation of practical applications demonstrate the ability of the method to model highly complex, non-canonical three-dimensional flows. The countermeasure based on the accurate classification of geometric features has provided a robust and reasonable solution.Comment: 33 pages, 23 figure

Simulation of incompressible viscous flows around moving objects by a variant of immersed boundary-Lattice Boltzmann method

A variant of immersed boundary-lattice Boltzmann method (IB-LBM) is presented in this paper to simulate incompressible viscous flows around moving objects. As compared with the conventional IB-LBM where the force density is computed explicitly by Hook's law or the direct forcing method and the non-slip condition is only approximately satisfied, in the present work, the force density term is considered as the velocity correction which is determined by enforcing the non-slip condition at the boundary. The lift and drag forces on the moving object can be easily calculated via the velocity correction on the boundary points. The capability of the present method for moving objects is well demonstrated through its application to simulate flows around a moving circular cylinder, a rotationally oscillating cylinder, and an elliptic flapping wing. Furthermore, the simulation of flows around a flapping flexible airfoil is carried out to exhibit the ability of the present method for implementing the elastic boundary condition. It was found that under certain conditions, the flapping flexible airfoil can generate larger propulsive force than the flapping rigid airfoil