Higher-order finite volume method for modelling shock waves in the interstellar medium

Author: Mervin Yap

The interstellar medium (ISM) plays an integral role in the evolution of stars. It provides the materials and conditions necessary for stars to form, and continues interacting with the stars throughout the stars' lifetime. Some of these interactions involve shock waves, which affect the dynamics of the ISM and the stellar evolution cycle; shock waves can compress regions of the ISM and induce star formation (Li et al., 2014), or create turbulence in the post-shock regions and inhibit star formation (Joung & Mac Low, 2006; Foley et al., 2025). Due to their common occurrence and their effects on the ISM, shock waves play an important factor in astrophysical processes in the ISM.

Numerical simulations allow us to study these astrophysical processes, such as the aforementioned shock waves, as well as the dynamics of the ISM. Typically, the ISM contains a combination of complex physics and turbulent features, making it difficult for everything to be captured in the numerical simulation accurately. Shock waves appear as sharp discontinuities too in these simulations, further complicating the task for the numerical scheme. We would therefore require higher-order numerical schemes, which refer to methods having a spatial and temporal order of accuracy of greater than 2, to model the ISM in our numerical simulations.

To this end, we incorporated several higher-order numerical schemes, such as the fourth-order piecewise-parabolic method (PPM) by Felker & Stone (2018) and the fifth-order weighted essentially non-oscillatory (WENO) method by Shu (2009), into the multi-dimensional code astrea ab initio, and verified their accuracy as shown in Figure 1.

Numerical tests were then run with these higher-order schemes to evaluate the schemes' performance in capturing turbulent features and shock waves in the simulation. These tests try to model the ISM, and one of these tests include the `Lax-Liu 19' configuration, which is a two-dimensional hydrodynamics test that is designed to include shock waves, rarefaction waves, and contact discontinuities (Lax & Liu, 1998). Figure 2 shows the result of the `Lax-Liu 19' test. Other tests include the Sod shock tube (Sod, 1978) and the Sedov blast test (Sedov, 1946).

The higher-order numerical schemes should thus be incorporated in production astrophysical codes, such as FLASH and dispatch, and the astrea code may serve as a possible benchmark tool for simulating shock waves in the interstellar medium.