Toshiyuki Hayase

A consistently formulated QUICK scheme for fast and stable convergence using finite-volume iterative calculation procedures

Abstract Previous applications of QUICK for the discretization of convective transport terms in finite-volume calculation procedures have failed to employ a rigorous and systematic approach for consistently deriving this finite difference scheme. Instead, earlier formulations have been established numerically, by trial and error. The new formulation for QUICK presented here is obtained by requiring that it satisfy four rules that guarantee physically realistic numerical solutions having overall balance. Careful testing performed for the wall-driven square enclosure flow configuration shows that the consistently derived version of QUICK is more stable and converges faster than any of the formulations previously employed. This testing includes the relative evaluation of boundary conditions approximated by second- and third-order finite-difference schemes as well as calculations performed at higher Reynolds numbers than previously reported.

Local Hemodynamics at the Rupture Point of Cerebral Aneurysms Determined by Computational Fluid Dynamics Analysis

Background: Cerebral aneurysms carry a high risk of rupture and so present a major threat to the patient’s life. Accurate criteria for predicting aneurysm rupture are important for therapeutic decision-making, and some clinical and morphological factors may help to predict the risk for rupture of unruptured aneurysms, such as sex, size and location. Hemodynamic forces are considered to be key in the natural history of cerebral aneurysms, but the effect on aneurysm rupture is uncertain, and whether low or high wall shear stress (WSS) is the most critical in promoting rupture remains extremely controversial. This study investigated the local hemodynamic features at the aneurysm rupture point. Methods: Computational models of 6 ruptured middle cerebral artery aneurysms with intraoperative confirmation of rupture point were constructed from 3-dimensional rotational angiography images. Computational fluid dynamics (CFD) simulations were performed under pulsatile flows using patient-specific inlet flow conditions. Time-averaged WSS (TAWSS) and oscillatory shear index (OSI) were calculated, and compared at the rupture point and at the aneurysm wall without the rupture point. We performed an additional CFD simulation of a bleb-removed model for a peculiar case in which bleb formation could be confirmed by magnetic resonance angiography. Results: All rupture points were located at the body or dome of the aneurysm. The TAWSS at the rupture point was significantly lower than that at the aneurysm wall without the rupture point (1.10 vs. 4.96 Pa, p = 0.031). The OSI at the rupture point tended to be higher than at the aneurysm wall without the rupture point, although the difference was not significant (0.0148 vs. 0.0059, p = 0.156). In a bleb-removed simulation, the TAWSS at the bleb-removed area was 6.31 Pa, which was relatively higher than at the aneurysm wall (1.94 Pa). Conclusion: The hemodynamics of 6 ruptured cerebral aneurysms of the middle cerebral artery were examined using retrospective CFD analysis. We could confirm the rupture points in all cases. With those findings, local hemodynamics of ruptured aneurysms were quanti-tatively investigated. The rupture point is located in a low WSS region of the aneurysm wall. Bleb-removed simulation showed increased WSS of the bleb-removed area, associated with the flow impaction area. Although the number of subjects in this study was relatively small, our findings suggest that the location of the rupture point is related to a low WSS at the aneurysm wall. Further investigations will elucidate the detailed hemodynamic effects on aneurysm rupture.

State Estimator of Flow as an Integrated Computational Method With the Feedback of Online Experimental Measurement

This paper deals with a state estimator or simply an observer of flow field. The observer, being a fundamental concept in the control system theory, also has a potential in the analysis of flow related problems as an integrated computational method with the aid of experiment. In the framework of the observer, the state of physical flow is estimated from the mathematical model with the feedback of on-line experimental measurement. A SIMPLER based flow simulation algorithm is used as the mathematical model of the real flow and partial experimental measurement of flow is fed back to the boundary condition through the feedback controller. The existence of the feedback-loop essentially distinguishes the observer from ordinary flow simulations. Time variation of the computational result of the observer is expected to converge exactly to that of the physical flow in the whole flow domain even for unstable turbulent flows. A numerical experiment has been performed to confirm the validity of the proposed observer for a turbulent flow through a duct of square cross section. The physical flow to be estimated is modeled by a numerical solution. Appropriate choice for the proportional feedback gain of the observer results in accelerated convergence of the simulation by a factor of 0.012 and reduced error in estimation of the perturbation velocity by a factor of 0.6 in the whole domain or a factor of 0.3 behind the output measurement plane in comparison with the ordinary flow simulation without feedback.

Experimental and Numerical study of forward flight aerodynamics of insect flapping wing

Experimental and numerical studies are conducted on the aerodynamic characteristics of a flapping wing of an insect in forward flight. Unsteady aerodynamic forces and flow patterns are measured using a dynamically scaled mechanical model in a water tunnel. The design of the model is based on the flapping wing of a bumblebee. The forces and flow patterns are also computed using a three-dimensional Navier-Stokes code. Comparisons between the experimental and numerical results show good agreement in the time histories of aerodynamic forces and flow patterns in both hovering and forward flight. Aerodynamic mechanisms of a flapping wing in forward flight, such as delayed stall, rotational effect, and wake capture are examined in detail. The results indicate that these aerodynamic mechanisms had an effect on the aerodynamic characteristics of the flapping wing in forward flight; however, these mechanisms function differently during the up- and downstroke, for different stroke plane angles, and for different advance ratios.

Fundamental study of ultrasonic-measurement-integrated simulation of real blood flow in the aorta.

Acquisition of detailed information on the velocity and pressure fields of the blood flow is essential to achieve accurate diagnosis or treatment for serious circulatory diseases such as aortic aneurysms. A possible way to obtain such information is integration of numerical simulation and color Doppler ultrasonography in the framework of a flow observer. This methodology, namely, Ultrasonic-Measurement-Integrated (UMI) Simulation, consists of the following processes. At each time step of numerical simulation, the difference between the measurable output signal and the signal indicated by numerical simulation is evaluated. Feedback signals are generated from the difference, and numerical simulation is updated applying the feedback signal to compensate for the difference. This paper deals with a numerical study on the fundamental characteristics of UMI simulation using a simple two-dimensional model problem for the blood flow in an aorta with an aneurysm. The effect of the number of feedback points and the feedback formula are investigated systematically. It is revealed that the result of UMI simulation in the feedback domain rapidly converges to the standard solution, even with usually inevitable incorrect upstream boundary conditions. Finally, an example of UMI simulation with feedback from real color Doppler measurement also shows a good agreement with measurement.

Effect of machine shape on swimming properties of the spiral-type magnetic micro-machine

The effect of machine shape on the swimming properties of a spiral-type magnetic micro-machine was examined by using a finite volume method. The optimum design of the blade shape was obtained by using the results of the simulation. According to the optimum design, the micro-machine was fabricated by stereolithography. The swimming properties of the machine agreed well with the analyzed results.

Numerical analysis for stability and self-excited oscillation in collapsible tube flow

This paper describes numerical analysis of collapsible tube flow based on the one-dimensional distributed parameter model of Hayashi. In the present model the effect of flow separation at the collapsed part is replaced with simple viscous friction along the tube, so no ad-hoc modeling for flow separation in former studies is required. A stable semi-implicit numerical procedure based on the SIMPLE method is developed for the problem of flow and tube interaction. The numerical result for a characteristic self-excited oscillation agrees qualitatively with the experimental result. Nonlinear stability of the steady state dependent on the amplitude of the disturbance is numerically investigated and the result is compared with the linear stability analysis based on the former lumped parameter model. Finally, initiation of the self-excited oscillation is examined by applying the initial disturbance at the upstream end of the tube. The disturbance propagates in the downstream direction and is amplified to the self-excited oscillation.

Three-dimensional analysis of swimming properties of a spiral-type magnetic micro-machine

The swimming properties of a spiral-type magnetic micro-machine were analyzed theoretically using 3D finite volume method. The basic equations of incompressible viscous fluid flow were integrated. The flow field around the micro-machine was calculated to estimate the swimming velocity, thrust, drag, and load torque of a spiral-type magnetic micro-machine. Good agreement was obtained between the experimental and theoretical results in a low Reynolds number. Therefore, the 3D analysis method without any fitting parameters was judged to be established.

Numerical experiment for ultrasonic-measurement-integrated simulation of three-dimensional unsteady blood flow.

Integration of ultrasonic measurement and numerical simulation is a possible way to break through limitations of existing methods for obtaining complete information on hemodynamics. We herein propose Ultrasonic-Measurement-Integrated (UMI) simulation, in which feedback signals based on the optimal estimation of errors in the velocity vector determined by measured and computed Doppler velocities at feedback points are added to the governing equations. With an eye towards practical implementation of UMI simulation with real measurement data, its efficiency for three-dimensional unsteady blood flow analysis and a method for treating low time resolution of ultrasonic measurement were investigated by a numerical experiment dealing with complicated blood flow in an aneurysm. Even when simplified boundary conditions were applied, the UMI simulation reduced the errors of velocity and pressure to 31% and 53% in the feedback domain which covered the aneurysm, respectively. Local maximum wall shear stress was estimated, showing both the proper position and the value with 1% deviance. A properly designed intermittent feedback applied only at the time when measurement data were obtained had the same computational accuracy as feedback applied at every computational time step. Hence, this feedback method is a possible solution to overcome the insufficient time resolution of ultrasonic measurement.

Numerical Validation of MR-Measurement-Integrated Simulation of Blood Flow in a Cerebral Aneurysm

This study proposes magnetic resonance (MR)-measurement-integrated (MR-MI) simulation, in which the difference between the computed velocity field and the phase-contrast MRI measurement data is fed back to the numerical simulation. The computational accuracy and the fundamental characteristics, such as steady characteristics and transient characteristics, of the MR-MI simulation were investigated by a numerical experiment. We dealt with reproduction of three-dimensional steady and unsteady blood flow fields in a realistic cerebral aneurysm developed at a bifurcation. The MR-MI simulation reduced the error derived from the incorrect boundary conditions in the blood flow in the cerebral aneurysm. For the reproduction of steady and unsteady standard solutions, the error of velocity decreased to 13% and to 22% in one cardiac cycle, respectively, compared with the ordinary simulation without feedback. Moreover, the application of feedback shortened the computational convergence, and thus the convergent solution and periodic solution were obtained within less computational time in the MR-MI simulation than that in the ordinary simulation. The dividing flow ratio toward the two outlets after bifurcation was well estimated owing to the improvement of computational accuracy. Furthermore, the MR-MI simulation yielded wall shear stress distribution on the cerebral aneurysm of the standard solution accurately and in detail.