This paper presents a development history of unsteady subsonic lifting surface computation. Our emphasis is restricted to the “pure or conventional lifting surface theory”, namely that for out-of-plane motions. The numerical method belongs to “Boundary Element Methods” among various numerical schemes, and so requires only rather little computation cost.
Therefore it seems to be useful continuously in future, even if within somewhat restricted practical purpose. The whole content is divided into several branches-analytical method, kernel function, and numerical method, the last of which is subdivided into mode method, interpolation method, discrete method, and generally applicable techniques. It is emphasized that there are two ways depending on whether chordwise or spanwise integral is carried out first. Now the methods carrying out spanwise integral first are not-so-many, but seem to be remarkably more promising.

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Mechanical energy is isoentropically transmitted to fluid-flow only by means of unsteady pressure forces, but the flow may be steady with respect to the rotating coordinate system in cases of turbomachines. If it flows along a cylindrical surface, the relative flow field is independent of the angular velocity of the system, but the field is significantly modified by the Coriolis acceleration if it flows changing the radial distance from the axis.
The flow field in a turbomachine is a slightly skewed three-dimensional one even if it is invisid flow. The real flow is much more complicated including secondary flows induced by different kinds of causes. They are, skewed boundary layer due to relative motion of walls, secondary flow induced in the endwall boundary layer of a curved channel, horse shoe vortex generated around the blunt leading edge of a blade at the root, secondary flow in the boundary layers of a stationary blade and of a rotating blade, as well as leakage flow through the clearance between the blade tip and the casing. Furthermore, in cases of transonic compressors, the Mach number relative to the blade varies considerably from the root to the tip of blade and complicated three-dimensional shock waves are generated.

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Gas dynamics plays an important role in astrophysical phenomena. Since it is generally impossible to perform experiments in astrophysics, computer simulation on cosmic gas dynamics is getting more and more important. In this review, general characteristics of cosmic gas dynamics are discussed and a simulation of accration flow is described as an example.
In the accretion flow, gas is attracted by the gravity of an astronomical object and huge energy may be liberated in the process. We show our numerical computations on an accretion flow on to an compact object, such as a white dwarf, a neutron star and a black hole, in a close binary system. We obtained unexpected new results by using a supercomputer and a modern algorithm of computational fluid dynamics. This work may open a new dimension in the accretion flow dynamics.

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A Reynolds stress model for near-wall and low-Reynolds-number regions is extended to adverse pressure gradient conditions. In the development of the model, the generation and diffusion terms in the transport equation for the turbulence energy dissipation rate and a model function for viscosity-dependent regions are recasted by examining a typical failure of prediction. The development of turbulent boundary layer in a strong adverse pressure gradient in an experiment by Samuel and Joubert is numerically predicted with the model. The predictions are compared extensively with the experimental data including th turbulence intensities in three directions. It is shown that the predictions are generally in good agreement with the experiment.

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The present paper is concerned with the flow in a two-dimensional channel, whose wall is partially compliant. The flow is calculated by the finite-difference method. The results are as follows :
(1) When the upstream condition is given by steady flow (Reynolds number Re-=50), the compliant part of the wall oscillates with the frequency, which is nearly equal to the characteristic frequency of the wall. The absolute value of pressure drop across the compliant part becomes small compared with that of plane Poiseuille flow with rigid walls. This ensures under the physiological condition that the blood can be more easily transported toward the distal vessels because of the compliance of walls.
(2) When the upstream condition is given by pulsatile flow (Womersley number α=8), there appears interaction between the characteristic frequency of the wall and the basic frequency of the main stream near the compliant wall. As the basic frequency of the pulsatile flow decreases, the absolute value of pressure drop across the compliant wall also becomes small compared with that of pulsatile flow between a rigid channel.

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