Instantaneous contours of vorticity magnitude on a plane through the aorta during the systolic-diastolic phase show the opening and closing process of the right-left bicuspid aortic valve (RL-BAV). From the right, the black dot in the inset identifies the corresponding instant during the cardiac cycle.

The Fluid-Structure Interaction simulation of bicuspid aortic valve (BAV) in a 3D anatomic aorta is shown in this movie. The curvilinear immersed boundary (CURVIB) method (Gilmanov, et al., 2015) coupled with an efficient, rotation-free thin-shell FE formulation (Stolarski, et al., 2013) to carry out FSI simulations of a BAV placed in the anatomic aorta is employed. The specific BAV morphology we consider in this movie is the R-L type (RL-BAV) because this case occurs in approximately 70% of the patients with BAV.

A cantilever mounted at the downstream face of a square cylinder is considered. Depending on the flow regime, which is determined by the Reynolds number based on the inflow velocity and cylinder size, and the geometric, material and structural properties of the cantilever, the cantilever may develop complex vibration modes. More specifically, vibrations with frequency and kinematics close to either the first or the second natural modes of the cantilever may be excited in such a configuration (Gilmanov, et al., 2015).

The FSI simulations of the trileaflets aortic valve (TAV) in a 3D anatomic aorta are shown in this movie. The curvilinear immersed boundary (CURVIB) method coupled with an efficient, rotation-free thin-shell FE formulation to carry out FSI simulations of a TAV placed in the anatomic aorta is employed. As a property of aortic valve tissue, the nonlinear anisotropic May-Newman&Yin (MNY) model is used.

Simulation of a cardiovascular cycle (systole-diastole) with fragmentation from MRI the phases of the left ventricle. Mitral and aortic valves were modeled as in inflow and outflow blood.

The contours of vorticity magnitude during moving walls of LV shown on the left. On the right, the blood flux through mitral/aortic valves shown. Clearly seen formations of E and A waves.

Iso-surfaces of the Q-criterion for a trileaflet aortic valve during systolic phase showing the opening heart valve. Linear isotropic the Saint-Venant material model has been used to simulate material of heart valve leaflets.

Iso-surfaces of the Q-criterion for a bi-cuspid aortic valve during systolic phase showing the opening heart valve. Linear isotropic the Saint-Venant material model has been used to simulate material of heart valve leaflets.

Flapping of inverted flag. Iso-surfaces of helicity (the cross product of velocity and vorticity) show the three-dimensional structures of this highly unsteady and massively separated wake. These structures separate from the flag and break up into small scale turbulence in the wake.

Instantaneous streamlines colored with velocity magnitude contours for the trileaflet aortic valve.

For the trileaflet aortic valve case, the valve jet preserves its direction and does not impinge on the aortic wall.

This problem represents a model of a biological deformable red blood cell (RBC) which is deformed under the action of shear stresses and pressure acting on its boundary surface. We consider this RBC as a capsule freely suspended in a viscous shear flow. The capsule consists of an elastic membrane containing another viscous fluid. We used the same fluid properties both inside and outside of the capsule. The shear flow is generated by initial conditions and by imposed shear velocity boundary conditions on the left and right sides of the channel.

We carry out viscous flow calculations for a set of kinematics, which corresponds to what biologist refer to as an escape maneuver typically performed when a copepod is attempting to escape a predator. During this maneuver, the animal attempts to maximize hydrodynamic thrust and deploys sequentially all of its major appendages, first the two antennules, followed by the tail, and then the legs, with the rear pair being deployed first.

Instantaneous streamlines and pressure contours on the horizontal plane of the 3D computational region. This is an example of vortex induced vibration (VIV).

A deformable tube is immersed in a flow of viscous fluid with the flow directed from left to right. The tube is started to oscillate under the action of fluid's pressure and shear stresses. The ends of the tube are fixed.

Contours of instantaneous out of plane vorticity at the vertical plane of symmetry. The 2D problem is solved as 3D with symmetry boundary conditions in the transverse direction.

An inverted cantilever mounted at the wake of a square cylinder is considered. Initially, the cantilever vibrates with the frequency of vortexes are shed from the cube. After a transient period, the cantilever changes its frequency to a lower

Instantaneous streamlines and xy-vorticity contours on the horizontal plane of the 3D computational region.

Viscous flow past an undulating mackerel for Re = 3000 and Slip = 0.6. Fine mesh (210x120x120) solution showing reverse Karman street in the wake.

Deflation-Inflation of Ballute (Balloon-Parachute).

The shape of ballute is deflated or inflated under the decreasing or increasing of internal pressure inside the torus.

Soft sphere falling in water under gravity. Pressure contours and streamlines.
As an example of FSI problem, we have solved the problem of a falling soft sphere in an unbounded channel. Here, non-reflecting boundary conditions were used on all sides of the computational region. The figure shows the pressure contours and streamlines. It can be seen in Figure that considerable deformation of the sphere occurs under the action of the stresses that act on the surface of the sphere. The originally spherical solid body assumes a kidney-bean shape with a pronounced concave arch along the bottom. The pressure contours can be seen to be considerably altered relative to the rigid sphere leading to a higher difference of the pressure between the front and back side of the sphere.

Simulation of moving fish-like body was implemented with Immersed Boundary Method (Gilmanov and Sotiropoulos, 2005, J Comp Phys.)

Fish-like swimming motion is prescribed by specifying the lateral displacement of the fish backbone as a function of time. We consider biologically inspired kinematics mimicking body and caudal fin (BFC) locomotion, which is the most frequently encountered swimming mode in fishes. In the BFC mode fish swim by bending their body into a backward-traveling undulatory wave that extends all the way to their caudal fin.

For the bicuspid aortic valve (BAV) case, the aortic valve vortex ring is seen to grow in complexity rapidly and ultimately break into turbulence much sooner during the accelerating phase of systole than for the trileaflet aortic valve (TAV) case. Another striking difference between the two valves is the fact that, while for the TAV case the valve jet preserves its direction and does not impinge on the aortic wall, the BAV jet undergoes a significant change in orientation causing it to impinge on the ascending aorta wall. This impingement is associated with the eccentricity of the BAV and provides the mechanism via which the BAV increases the shear stress on the wall of the ascending aorta.

A vortex ring simulations in a piston elliptical cylinder.
At the time when the piston is stopped the vortex starts to detach from the cylinder and it is moving in the axial direction with constant velocity. After a small time interval, one can see that minor axis X is turned into major axis X and vice versa major axis Y is turned into a minor axis of the elliptical vortex.

The Navier–Stokes calculations using the kinematical scenario of Drosophila wing cycle considered in (J.M. Birch, M. H. Dickinson, J. Exp. Biol.,2003), which involves both translational and rotational motion of the wing. Instantaneous streamlines at the z=constant mid-plane for one complete stroke.