Anvar Gilmanov

A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids

In the present note a general reconstruction algorithm for simulating incompressible flows with complex immersed boundaries on Cartesian grids is presented. In the proposed method an arbitrary three-dimensional solid surface immersed in the fluid is discretized using an unstructured, triangular mesh, and all the Cartesian grid nodes near the interface are identified. Then, the solution at these nodes is reconstructed via linear interpolation along the local normal to the body, in a way that the desired boundary conditions for both pressure and velocity fields are enforced. The overall accuracy of the resulting solver is second-order, as it is demonstrated in two test cases involving laminar flow past a sphere.

A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains

We present a new numerical methodology for simulating fluid-structure interaction (FSI) problems involving thin flexible bodies in an incompressible fluid. The FSI algorithm uses the Dirichlet-Neumann partitioning technique. The curvilinear immersed boundary method (CURVIB) is coupled with a rotation-free finite element (FE) model for thin shells enabling the efficient simulation of FSI problems with arbitrarily large deformation. Turbulent flow problems are handled using large-eddy simulation with the dynamic Smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries. The CURVIB and FE solvers are coupled together on the flexible solid-fluid interfaces where the structural nodal positions, displacements, velocities and loads are calculated and exchanged between the two solvers. Loose and strong coupling FSI schemes are employed enhanced by the Aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems. The coupled CURVIB-FE-FSI method is validated by applying it to simulate two FSI problems involving thin flexible structures: 1) vortex-induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low Reynolds number; and 2) the more challenging high Reynolds number problem involving the oscillation of an inverted elastic flag. For both cases the computed results are in excellent agreement with previous numerical simulations and/or experiential measurements. Grid convergence tests/studies are carried out for both the cantilever and inverted flag problems, which show that the CURVIB-FE-FSI method provides their convergence. Finally, the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the FSI of a tri-leaflet, prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions.

Flow- Structure Interaction Simulations for Ballutes in Supersonic Flow

An improved methodology for flow structure interaction problems involving large structural deformations and all speeds in a cost-eective and accurate manner is developed. A particle-based meshless method for the structural deformations (called material point method or MPM) is integrated with a Cartesian-based flow solver. The development of the MPM and the integration with the all speed flow solver that embodies the hybrid immersed boundary (HIBM) method for handling complex deforming and moving geometries on any grid (Cartesian or curvilinear) is discussed in this paper. Two features of this integrated approach make it very suitable for inflatable Entry, Descent, and Landing (EDL) systems: 1) the MPM enables simulation of large of deformations of the EDL system from its packed to fully open state since it is a meshless method, and 2) it is possible, at low computational cost, to simulate interaction of the inflating EDL with the surrounding gas flow due to the use of the HIBM that allows the solution of an arbitrary moving and deformable body. Simulations have been performed for a tension cone geometries in its fully-inflated stage. Validation tests for HIBM in supersonic flows and for the MPM have been completed. The Entry, Descent, and Landing system (EDL) plays a conclusive role in the completion of the NASA Mars Exploration Program (NASA MEP). For the purposes of NASA MEP, a new EDL systems based on the concept of an inflatable ballute has advantages in comparison with traditional rigid or parachute decelerators. In order to develop the new system with greater and more controlled deceleration capabilities and behavior, it is important to have computational tools that provide realistic and high fidelity simulations of all stages of EDL. The computational method should be capable of simulating extremely nonsteady interaction of flexible ballutes with an aggressive environment of the atmosphere of Mars. For such simulations it is necessary to develop a new computational approach which is described in the present work. Major challenges in developing a model/code for the above mentioned problem are: (a) simulation of the deployment of the EDL system from its packaged to fully open condition, that should change its volume (shape) more than 10 times, (b) simulation of the interaction of the highly nonsteady flexible inflating ballute with surrounding gases when the velocity of the gas flow has to change from hypersonic to subsonic regimes, and (c) to resolve behavior of the flexible inflating system in the gas flow with needed accuracy. We estimated, on the literature publications that there are no existing methods that satisfy such requirements. In this paper we present the new FSI approach that, in general, has all the properties described above.

High Resolution Simulation of Tri-Leaflet Aortic Heart Valve in an Idealized Aorta

Aortic valve replacement is a common procedure for many patients when their native aortic valve malfunction either because of aortic stenosis or aortic insufficiency. Due to the superior hemodynamic performance, Bio-prosthetic heart valve (bPHV) has been implanted in a large number of patients. bPHVs, however, have a number of drawbacks, including mechanically induced fatigue and leaflet tearing and calcification. Many of these complications are thought to be linked to hemodynamic factors and the mechanical forces imparted by the blood flow on blood cells. Previous works have shown that valve hemodynamics is greatly influenced by the fluid-structure interaction (FSI) of blood flow with tissues and/or valve leaflets, and the location where the valve is surgically implanted.

Non-linear rotation-free shell finite-element models for aortic heart valves

Hyperelastic material models have been incorporated in the rotation-free, large deformation, shell finite element (FE) formulation of (Stolarski et al., 2013) and applied to dynamic simulations of aortic heart valve. Two models used in the past in analysis of such problem i.e. the Saint-Venant and May-Newmann-Yin (MNY) material models have been considered and compared. Uniaxial tests for those constitutive equations were performed to verify the formulation and implementation of the models. The issue of leaflets interactions during the closing of the heart valve at the end of systole is considered. The critical role of using non-linear anisotropic model for proper dynamic response of the heart valve especially during the closing phase is demonstrated quantitatively. This work contributes an efficient FE framework for simulating biological tissues and paves the way for high-fidelity flow structure interaction simulations of native and bioprosthetic aortic heart valves.

An Immersed Boundary and Material Point Methodology for Moving/Compliant Surfaces With Heat Transfer

Simulations of flow and heat transfer in complex geometries with flow-structure-interaction (FSI) require special treatment. In this paper, an approach that combines the immersed boundary method (IBM) for handling complex moving boundaries and the material point method (MPM) for resolving structural stresses and movement is presented as an approach for solving FSI problems. In the IBM, a Cartesian grid is generally defined, and the variable values at grid points adjacent to a non-Cartesian boundary are forced or interpolated to satisfy the boundary conditions. MPM is used to solve equations of solid structure (stresses and deflection) and communicates with the fluid through appropriate interface-boundary conditions. Several examples of using this combination of IBM&MPM are presented and the advantages and disadvantages of this approach are outlined.Copyright

Numerical simulation of aquatic locomotion on Cartesian grids

Publisher Summary This chapter develops a numerical method for solving the 3D, unsteady, incompressible Navier-Stokes equations in domains with flexible immersed boundaries. Geometrically complex bodies are treated as sharp interfaces using a hybrid Cartesian/immersed-boundary formulation. Results have been presented for flow past a flexible fishlike body and a dorsoventrally flattened, flexible body whose shape is inspired by the morphology of ray fishes. The chapter demonstrates the promise of a Cartesian/immersed boundary formulation in simulations of flows in domains containing complex, 3D, flexible immersed boundaries. The computations have provided new insight into the 3D structure of coherent vortices in the wake of swimming fishes. It focuses on: refining the geometrical features of the biologically inspired bodies to closely mimic the anatomy of real fishes; prescribing biologically inspired kinematics; and investigating the ensuing fluid/structure interaction for various body shapes and kinematical scenarios to identify mechanisms that lead to drag reduction and enhance propulsive efficiency.