# Inaccuracy of Spatial Derivatives in Riemann Solver Simulations of Supersonic Turbulence

@article{Pan2019InaccuracyOS, title={Inaccuracy of Spatial Derivatives in Riemann Solver Simulations of Supersonic Turbulence}, author={Liubin Pan and Paolo Padoan and {\AA}ke Nordlund}, journal={The Astrophysical Journal}, year={2019}, volume={876} }

We examine the accuracy of spatial derivatives computed from numerical simulations of supersonic turbulence. Two sets of simulations, carried out using a finite-volume code that evolves the hydrodynamic equations with an approximate Riemann solver and a finite-difference code that solves the Navier–Stokes (N–S) equations, are tested against a number of criteria based on the continuity equation, including exact results at statistically steady state. We find that the spatial derivatives in the N…

## 3 Citations

### The Probability Distribution of Density Fluctuations in Supersonic Turbulence

- PhysicsThe Astrophysical Journal
- 2019

A theoretical formulation is developed for the probability distribution function (pdf) of gas density in supersonic turbulence at steady state, connecting it to the conditional statistics of the…

### Evolution of the Density PDF in Star-forming Clouds: The Role of Gravity

- PhysicsThe Astrophysical Journal
- 2020

We derive an analytical theory of the PDF of density fluctuations in supersonic turbulence in the presence of gravity in star-forming clouds. The theory is based on a rigorous derivation of a…

### Generalized Transport Equation for the Autocovariance Function of the Density Field and Mass Invariant in Star-forming Clouds

- PhysicsThe Astrophysical Journal Letters
- 2021

In this Letter, we study the evolution of the autocovariance function of density-field fluctuations in star-forming clouds and thus of the correlation length l c (ρ) of these fluctuations, which can…

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