# A new relativistic viscous hydrodynamics code and its application to the Kelvin-Helmholtz instability in high-energy heavy-ion collisions

## TL;DR

This paper introduces a new relativistic viscous hydrodynamics code optimized for Milne coordinates, combining advanced numerical methods, and applies it to study the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.

## Contribution

The paper presents a novel relativistic viscous hydrodynamics code with a unique splitting method and validation, applied to Kelvin-Helmholtz instability analysis in heavy-ion collisions.

## Key findings

- Validated the code against analytical solutions and known theories.
- Demonstrated the code's capability to simulate Kelvin-Helmholtz instability.
- Provided insights into instability development in high-energy collisions.

## Abstract

We construct a new relativistic viscous hydrodynamics code optimized in the Milne coordinates. We split the conservation equations into an ideal part and a viscous part, using the Strang spitting method. In the code a Riemann solver based on the two-shock approximation is utilized for the ideal part and the Piecewise Exact Solution (PES) method is applied for the viscous part. We check the validity of our numerical calculations by comparing analytical solutions, the viscous Bjorken's flow and the Israel-Stewart theory in Gubser flow regime. Using the code, we discuss possible development of the Kelvin-Helmholtz instability in high-energy heavy-ion collisions.