In this paper, two-dimensional and axisymmetric, time dependent transonic and supersonic flows over a projectile overtaking a moving shock wave are considered. The flow is simulated numerically by solving full time averaged Navier-Stokes equations. The equations are linearized by Newton approach. The roe’s flux splitting method, second order central difference scheme for the diffusion terms, an...

The stationary hydrodynamic equations for the transonic accretion disks and flows around rotating black holes are presented by using the Kerr-Schild coordinate where there is no coordinate singularity at the event horizon. We use two types of the causal viscosity prescription, and the boundary conditions for the transonic accretion flows are given at the sonic point. For one type of the causal ...

S U M M A R Y The transonic flow near the throat of a converging-diverging nozzle of a gas with infinite electrical conductivity is considered. The magnetic field B is everywhere aligned with the velocity q so that the equations describing the flow are reducible to those of ordinary gasdynamics. Thus, it is possible to utilize the transonic similarity solution of Tomotika and Tamada [3] to stud...

We present fully general relativistic equations governing viscous transonic flows in vertical equilibrium in Kerr geometry. We find the complete set of global solutions (both for Optically thick and optically thin flows) in the weak viscosity limit. We show that for a large region of parameter space, centrifugal pressure supported standing shocks can form in accretion and winds very close to th...

It is well-known that stationary transonic solutions of the compressible Euler equations are hard to compute using the stationary form of the equations. Therefore, time marching methods with explicit or implicit time integration are normally employed. In this paper a method is described that computes one-dimensional transonic flows directly from the stationary equations. The method is based on ...

Edge poloidal flows exceeding the poloidal sound speed lead to the formation of a pedestal structure [GUAZZOTTO, L. and BETTI, R., Phys. Rev. Lett. 107 (2011) 125002]. This result is based on the existence of “transonic” equilibria, in which the edge region of the plasma flows supersonically with respect to the poloidal sound speed (i.e., the sound speed reduced by a factor Bθ/B), while the pla...

The time accuracy of the exponentially accurate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward difference formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for ...

In this paper we prove existence, uniqueness and regularity of certain perturbed (subsonic–supersonic) transonic potential flows in a two-dimensional Riemannian manifold with “convergent–divergent” metric, which is an approximate model of the de Laval nozzle in aerodynamics. The result indicates that transonic flows obtained by quasi-one-dimensional flow model in fluid dynamics are stable with ...

In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total variation of the incoming supersonic flow over a solid right-wedge. It is a free boundary problem in Eulerian coordinates and, across the free boundary (character...