A three-dimensional computational fluid dynamics (CFD) method has been developed to simulate the flow in a pumping left ventricle. The proposed method uses magnetic resonance imaging (MRI) technology to provide a patient specific, time dependent geometry of the ventricle to be simulated. Standard clinical imaging procedures were used in this study. A two-dimensional time-dependent orifice representation of the heart valves was used. The location and size of the valves is estimated based on additional long axis images through the valves. A semi-automatic grid generator was created to generate the calculation grid. Since the time resolution of the MR scans does not fit the requirements of the CFD calculations a third order bezier approximation scheme was developed to realize a smooth wall boundary and grid movement. The calculation was performed by a Navier-Stokes solver using the arbitrary Lagrange-Euler (ALE) formulation. Results show that during diastole, blood flow through the mitral valve forms an asymmetric jet, leading to an asymmetric development of the initial vortex ring. These flow features are in reasonable agreement with in vivo measurements but also show an extremely high sensitivity to the boundary conditions imposed at the inflow. Changes in the atrial representation severely alter the resulting flow field. These shortcomings will have to be addressed in further studies, possibly by inclusion of the real atrial geometry, and imply additional requirements for the clinical imaging processes.

Experiments were conducted in the free-piston shock tube and shock tunnel with dissociating nitrogen and carbon dioxide, ionizing argon and frozen argon to measure the transition condition in pseudosteady and steady flow. The transition condition in the steady flow, in which the wall was eliminated by symmetry, agrees with the calculated von Neumann condition. I n the real gases this calculation assumed thermodynamic equilibrium after the reflected shock. I n the pseudosteady flow of reflexion from a wedge the measured transition angle lies on the Mach-reflexion side of the calculated detachment condition by an amount which may be explained in terms of the displacement effect of the boundary layer on the wedge surface. A single criterion based on the availability of a length scale a t the reflexion point explains the difference between the pseudosteady and steady flow transition condition and predicts a hysteresis effect in the transition angle when the shock angle is varied during steady flow. No significant effects on the transition condition due to finite relaxation length could be detected. However, new experiments in which interesting relaxation effects should be evident are suggested.

The fluid-structure coupled simulation of the heart, though at its developing stage, has shown great prospect in heart function investigations and clinical applications. The purpose of this paper is to verify a commercial software based fluid-structure interaction scheme for the left ventricular filling. The scheme applies the finite volume method to discretize the arbitrary Lagrangian-Eulerian formulation of the Navier-Stokes equations for the fluid while using the nonlinear finite element method to model the structure. The coupling of the fluid and structure is implemented by combining the fluid and structure equations as a unified system and solving it simultaneously at every time step. The left ventricular filling flow in a three-dimensional ellipsoidal thin-wall model geometry of the human heart is simulated, based on a prescribed time-varying Young's modulus. The coupling converges smoothly though the deformation is very large. The pressure-volume relation of the model ventricle, the spatial and temporal distributions of pressure, transient velocity vectors as well as vortex patterns are analyzed, and they agree qualitatively and quantitatively well with the existing data. This preliminary study has verified the feasibility of the scheme and shown the possibility to simulate the left ventricular flow in a more realistic way by adding a myocardial constitutive law into the model and using a more realistic heart geometry.

The development of the wake behind a flat plate at a supercritical Reynolds number (Re= 200, based on the plate thickness and free-stream velocity) is simulated numerically by solving the two-dimensional unsteady Navier-Stokes equations with a finite-difference Galerkin method. The intermediate quasi-steady state of the wake development is investigated with an Orr-Sommerfeld analysis for complex frequencies and wavenumbers. Based on this linear, local stability analysis it can be shown that the quasi-steady state can be divided into regions of local absolute and local convective instability. One goal of this work is to determine the validity of the linear, local stability theory by comparing the predictions of the Orr-Sommerfeld analysis to the results of a numerical wake simulation. Based on this comparison, for the investigated flow field, the frequency selection mechanisms recently proposed by several authors are discussed. Base bleed is applied in the numerical simulation of the wake as a control parameter, following the well-known experimental result that sufficient base bleed reduces the strength of the vortex street (see e.g. Wood 1964). It can be shown that from a critical base-bleed ratio, disturbances grow no longer in time but only in space, indicating a change of the global stability characteristics. In addition the linear, local stability analysis is used to investigate to what extent this global transition can be described.

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The extension of the classic Rayleigh–Bénard problem of a horizontal layer heated from below to the three-dimensional convection in rectangular boxes is dealt with in this paper both numerically and experimentally. Also discussed is the influence of shear flows in tilted boxes and the transition to time-dependent oscillatory convection. Three-dimensional numerical simulations allow the calculation of stationary solutions and the direct simulation of oscillatory instabilities. We limited ourselves to laminar and transcritical flows. For studying the particular characteristics of three-dimensional convection in horizontal containers, we carefully selected two container geometries with aspect ratios of 10:4:1 and 4:2:1. The onset of steady cellular convection in tilted boxes is calculated by an iterative application of a combined finite-difference method and a Galerkin method. The appearance of longitudinal and transverse convection rolls is determined by means of inter-ferometrical measuring techniques and is compared with the results of the linear stability theory. The spatial flow structure and the transition to oscillatory convection is calculated for selected examples in the range of supercritical Rayleigh numbers. Experimental investigations concerning the stability behaviour of the steady solutions with regard to time-dependent disturbances show a distinct influence of the Prandtl number and confirm the importance of nonlinear effects.

We present a 3D code-coupling approach which has been specialized towards cardiovascular blood flow. For the first time, the prescribed geometry movement of the cardiovascular flow model KaHMo (Karlsruhe Heart Model) has been replaced by a myocardial composite model. Deformation is driven by fluid forces and myocardial response, i.e., both its contractile and constitutive behavior. Whereas the arbitrary Lagrangian-Eulerian formulation (ALE) of the Navier-Stokes equations is discretized by finite volumes (FVM), the solid mechanical finite elasticity equations are discretized by a finite element (FEM) approach. Taking advantage of specialized numerical solution strategies for non-matching fluid and solid domain meshes, an iterative data-exchange guarantees the interface equilibrium of the underlying governing equations. The focus of this work is on left-ventricular fluid-structure interaction based on patient-specific magnetic resonance imaging datasets. Multi-physical phenomena are described by temporal visualization and characteristic FSI numbers. The results gained show flow patterns that are in good agreement with previous observations. A deeper understanding of cavity deformation, blood flow, and their vital interaction can help to improve surgical treatment and clinical therapy planning.