# Comoving coordinate system for relativistic hydrodynamics

## Abstract

The equations of relativistic hydrodynamics are transformed so that steps forward in time preserve local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to comoving observers. Aside from the time step varying as a function of the location on the mesh, the local velocity gradient and the local density then evolve according to nonrelativistic equations of motion. Analytic solutions are found for two one-dimensional cases with constant speed of sound. One solution has a Gaussian density profile when mapped onto the new coordinates. That solution is analyzed for the effects of longitudinal acceleration in relativistic heavy ion collisions at the Relativistic Heavy Ion Collider, especially in regards to two-particle correlation measurements of the longitudinal size.

- Authors:

- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-1321 (United States)

- Publication Date:

- OSTI Identifier:
- 20991033

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevC.75.024907; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; ANALYTICAL SOLUTION; BROOKHAVEN RHIC; COORDINATES; DENSITY; EQUATIONS OF MOTION; HEAVY ION REACTIONS; HYDRODYNAMICS; ONE-DIMENSIONAL CALCULATIONS; RELATIVISTIC RANGE

### Citation Formats

```
Pratt, Scott.
```*Comoving coordinate system for relativistic hydrodynamics*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVC.75.024907.

```
Pratt, Scott.
```*Comoving coordinate system for relativistic hydrodynamics*. United States. doi:10.1103/PHYSREVC.75.024907.

```
Pratt, Scott. Thu .
"Comoving coordinate system for relativistic hydrodynamics". United States.
doi:10.1103/PHYSREVC.75.024907.
```

```
@article{osti_20991033,
```

title = {Comoving coordinate system for relativistic hydrodynamics},

author = {Pratt, Scott},

abstractNote = {The equations of relativistic hydrodynamics are transformed so that steps forward in time preserve local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to comoving observers. Aside from the time step varying as a function of the location on the mesh, the local velocity gradient and the local density then evolve according to nonrelativistic equations of motion. Analytic solutions are found for two one-dimensional cases with constant speed of sound. One solution has a Gaussian density profile when mapped onto the new coordinates. That solution is analyzed for the effects of longitudinal acceleration in relativistic heavy ion collisions at the Relativistic Heavy Ion Collider, especially in regards to two-particle correlation measurements of the longitudinal size.},

doi = {10.1103/PHYSREVC.75.024907},

journal = {Physical Review. C, Nuclear Physics},

number = 2,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}