# On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes

## Abstract

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle thismore »

- Authors:

- Departamento de Astronomía y Astrofísica, Universidad de Valencia, C/Dr. Moliner 50, E-46100 Burjassot (Spain)
- Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, D-85748 Garching (Germany)

- Publication Date:

- OSTI Identifier:
- 22661118

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal, Supplement Series; Journal Volume: 230; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ALFVEN WAVES; ANALYTICAL SOLUTION; COMPARATIVE EVALUATIONS; EQUATIONS; MAGNETIC FIELDS; MAGNETIC RECONNECTION; MAGNETOHYDRODYNAMICS; RESOLUTION; RIEMANN SPACE; STARS; TEARING INSTABILITY; THREE-DIMENSIONAL CALCULATIONS; VELOCITY; VISCOSITY; WAVELENGTHS

### Citation Formats

```
Rembiasz, Tomasz, Obergaulinger, Martin, Cerdá-Durán, Pablo, Aloy, Miguel-Ángel, and Müller, Ewald, E-mail: tomasz.rembiasz@uv.es.
```*On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes*. United States: N. p., 2017.
Web. doi:10.3847/1538-4365/AA6254.

```
Rembiasz, Tomasz, Obergaulinger, Martin, Cerdá-Durán, Pablo, Aloy, Miguel-Ángel, & Müller, Ewald, E-mail: tomasz.rembiasz@uv.es.
```*On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes*. United States. doi:10.3847/1538-4365/AA6254.

```
Rembiasz, Tomasz, Obergaulinger, Martin, Cerdá-Durán, Pablo, Aloy, Miguel-Ángel, and Müller, Ewald, E-mail: tomasz.rembiasz@uv.es. Thu .
"On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes". United States.
doi:10.3847/1538-4365/AA6254.
```

```
@article{osti_22661118,
```

title = {On the Measurements of Numerical Viscosity and Resistivity in Eulerian MHD Codes},

author = {Rembiasz, Tomasz and Obergaulinger, Martin and Cerdá-Durán, Pablo and Aloy, Miguel-Ángel and Müller, Ewald, E-mail: tomasz.rembiasz@uv.es},

abstractNote = {We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfvén waves, and the tearing mode (TM) instability using the MHD code Aenus. By comparing the simulation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of TMs, we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependence of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results, we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is most advantageous to resort to ultra-high-order methods (e.g., the ninth-order monotonicity-preserving method) to tackle this problem properly, in particular, in three-dimensional simulations.},

doi = {10.3847/1538-4365/AA6254},

journal = {Astrophysical Journal, Supplement Series},

number = 2,

volume = 230,

place = {United States},

year = {Thu Jun 01 00:00:00 EDT 2017},

month = {Thu Jun 01 00:00:00 EDT 2017}

}