We prove the existence of global solutions to the Euler equations of compressible isentropic gas dynamics with geometrical structure, including transonic nozzle flow and spherically symmetric flow. Due to the presence of the geometrical source terms, the existence results themselves are new, especially as they pertain to radial flow in an unbounded region, |~x| ≥ 1, and to transonic nozzle flow...

The effects of poloidal and toroidal flows on tokamak plasma equilibria are examined in the magnetohydrodynamic limit. “Transonic” poloidal flows of the order of the sound speed multiplied by the ratio of poloidal magnetic field to total field B /B can cause the normally elliptic Grad– Shafranov GS equation to become hyperbolic in part of the solution domain. It is pointed out that the range of...

Among the adaptive-grid methods, redistribution and embedding techniques have been the focus of more attention by researchers. Simultaneous or combined adaptive techniques have also been used. This paper describes a combination of adaptive-grid embedding and redistribution methods on semi-structured grids for two-dimensional invisid flows. Since the grid is semi-structured, it is possible to us...

13. The introduction of a second new hypothetical gas. In the foregoing sections, we have investigated some transonic fields of flow by employing a hypothetical gas which closely approximates the real gas during an isentropic flow in the transonic range. Although such a hypothetical gas has a merit that the fundamental equation governing its flow assumes a rather simple form and can be solved e...

Among the adaptive-grid methods, redistribution and embedding techniques have been the focus of more attention by researchers. Simultaneous or combined adaptive techniques have also been used. This paper describes a combination of adaptive-grid embedding and redistribution methods on semi-structured grids for two-dimensional invisid flows. Since the grid is semi-structured, it is possible to us...

In this paper, an unified high-order algorithm for all speeds is developed. The preconditioning matrix of Weiss and Smith combined with a 5th-order WENO scheme for inviscid flux and a fully conservative 4th order central differencing for viscous terms are employed. The unfactored implicit Gauss-Seidel relaxation scheme is used for time marching. The numerical simulation of a natural convective ...