Positive Scheme Numerical Simulation of High Mach Number Astrophysical Jets

Abstract

High Mach number astrophysical jets are simulated using a positive scheme, and are compared with WENO-LF simulations. A version of the positive scheme has allowed us to simulate astrophysical jets with radiative cooling up to Mach number 270 with respect to the heavy jet gas, a factor of two times higher than the maximum Mach number attained with the WENO schemes and ten times higher than with CLAWPACK. Such high Mach numbers occur in many settings in astrophysical flows, so it is important to develop a scheme that can simulate at these Mach numbers.

Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics

“…This problem is very much like the problem presented in Ha et al [21] and Ha and Gardner [22]. It consists of a dense fluid slab jet in two dimensions propagating through a lighter ambient medium.…”

On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes

“…To simulate the gas flows and shock wave patterns which are revealed by the Hubble Space Telescope images, one can implement theoretical models in a gas dynamics simulator, see [7][8][9]. For example, the two-dimensional model without radiative cooling is governed by (3.1).…”

Parametrized Positivity Preserving Flux Limiters for the High Order Finite Difference WENO Scheme Solving Compressible Euler Equations

“…The computational domain is taken to be [−5, 15] × [−5, 15] and (x 0 , y 0 ) = (5,5). The boundary condition is periodic.…”

“…We consider the vortex evolution problem[7] to test the accuracy. For this problem, the mean flow is ρ = p = u = v = 1 and is added by an isentropic vortex perturbation centered at (x 0 , y 0 ) in (u, v) withT = p/ρ, no perturbation in entropy S = p/ρ γ , (δu, δv) = ε vortex 2π e 0.5(1−r 2 ) (−ȳ,x), δT = − (γ − 1)ǫ 2 8γπ 2 e (1−r 2 ) , δS = 0,(4.2)where (x,ȳ) = (x − x 0 , y − y 0 ), r 2 =x 2 +ȳ 2 .The computational domain is taken to be [−5, 15] × [−5,15] and (x 0 , y 0 ) =(5,5). The boundary condition is periodic.…”