Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows

TL;DR

This paper introduces a novel low-dissipation numerical scheme for hydrodynamic simulations, combining operator-splitting, Godunov, and piecewise-parabolic methods, validated on standard tests and a galactic disk model.

Contribution

It develops a new numerical approach that reduces dissipation in hydrodynamic simulations by integrating multiple established methods.

Findings

Effective in standard hydrodynamic tests

Successfully captures spiral structures in galactic disk

Demonstrates improved accuracy over traditional schemes

Abstract

An approach for constructing a low-dissipation numerical method is described. The method is based on a combination of the operator-splitting method, Godunov method, and piecewise-parabolic method on the local stencil. Numerical method was tested on a standard suite of hydrodynamic test problems. In addition, the performance of the method is demonstrated on a global test problem showing the development of a spiral structure in a gravitationally unstable gaseous galactic disk.