Spirals in 2-D Gas Dynamics Systems

Abstract

In this paper, the phenomena of spirals are numerically presented by MmB scheme [1] for initial value problems of 2-D gas dynamics $(γ=1.4)$, which include 2-D Riemann problems and continuous initial value problems. The numerical results are well coincide with on the exact solution in [2] and the conjectures on solution structure in [3] for 2-D isentropic  and adiabatic flows. In isentropic flow, for high speed rotation $(v_0/c_0 >\sqrt{2})$, there is a region of vacuum at the origin and for low speed rotation $(v_0/c_0 <\sqrt{2})$, there is no vacuum, and for adiabatic flow, the structure of spirals is also discussed.