Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling

Abstract

Computational fluid dynamics simulations using the WENO-LF method are applied to high Mach number nonrelativistic astrophysical jets, including the effects of radiative cooling. Our numerical methods have allowed us to simulate astrophysical jets at much higher Mach numbers than have been attained (Mach 20) in the literature. Our simulations of the HH 1-2 astrophysical jets are at Mach 80. Simulations at high Mach numbers and with radiative cooling are essential for achieving detailed agreement with the astrophysical images.

Positive Scheme Numerical Simulation of High Mach Number Astrophysical Jets

“…This positive scheme makes use of Roe's scheme [14], with an "entropy fix" [15] which guarantees a nonzero diffusive term through the choice of μ and β. 2 An advantage-and a disadvantage-of positive schemes is that they have many parameters which can be adjusted to obtain high resolution of different flows.…”

“…For high Mach number jets, the WENO-LF3 method performs better than WENO-LF5 (see [2]). The jet inflow (u j = 300 km/s) is Mach 80 with respect to the soundspeed in the heavy jet gas and Mach 25 with respect to the soundspeed In all 2D jet figures, the physical quantities are plotted on a logarithmic scale: log 10 {ρ(x, y, t f )/ρ}, log 10 {P (x, y, t f )/P }, and log 10 {T (x, y, t f )/T } in the light ambient gas.…”

“…In this investigation, we simulate the evolution of high Mach number astrophysical jets with radiative cooling using a positive scheme introduced by Liu and Lax [4,5], and compare with results [2] obtained with the third-and fifth-order WENO-LF methods [6,7]. Robust numerical methods are needed to handle the intense radiative shocks in front of (bow shock) and within the propagating jet (including the terminal Mach disk 1 ), as well as the Kelvin-Helmholtz vortex rollup of the jet tip.…”

Explicit solutions to a convection-reaction equation and defects of numerical schemes

“…The scientific computation for the solutions to systems of hyperbolic conservation laws has been successful thanks to the development of accurate numerical schemes (e.g., see [2,11,19,20]). The unfortunate situation we still have here is that there is no meaningful progress in the analysis of such schemes due to their complexity and it is hard to find any useful error estimate.…”

“…Properties of three well-known schemes, Lax-Friedrichs, MacCormack and Lax-Wendroff, are tested in Section 4, which show interesting blowups (see Figs. [1][2][3][4][5]. In Section 5, three fully discrete schemes are tested, the first and the second-order Godunov schemes and the NT scheme, while Section 6 is devoted for two semi discrete schemes, the KNP and the WENO schemes.…”