# The reality of artificial viscosity

## Abstract

Artificial viscosity is used in the computer simulation of high Reynolds number flows and is one of the oldest numerical artifices. In this work, I will describe the origin and the interpretation of artificial viscosity as a physical phenomenon. The basis of this interpretation is the finite scale theory, which describes the evolution of integral averages of the fluid solution over finite (length) scales. I will outline the derivation of finite scale Navier–Stokes equations and highlight the particular properties of the equations that depend on the finite scales. Those properties include enslavement, inviscid dissipation, and a law concerning the partition of total flux of conserved quantities into advective and diffusive components.

- Authors:

- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP) (NA-10)

- OSTI Identifier:
- 1440435

- Report Number(s):
- LA-UR-17-24540

Journal ID: ISSN 0938-1287

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Shock Waves

- Additional Journal Information:
- Journal Name: Shock Waves; Journal ID: ISSN 0938-1287

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Artificial viscosity; Computational fluid dynamics; Finite scale

### Citation Formats

```
Margolin, L. G.
```*The reality of artificial viscosity*. United States: N. p., 2018.
Web. doi:10.1007/s00193-018-0810-8.

```
Margolin, L. G.
```*The reality of artificial viscosity*. United States. doi:10.1007/s00193-018-0810-8.

```
Margolin, L. G. Sat .
"The reality of artificial viscosity". United States.
doi:10.1007/s00193-018-0810-8.
```

```
@article{osti_1440435,
```

title = {The reality of artificial viscosity},

author = {Margolin, L. G.},

abstractNote = {Artificial viscosity is used in the computer simulation of high Reynolds number flows and is one of the oldest numerical artifices. In this work, I will describe the origin and the interpretation of artificial viscosity as a physical phenomenon. The basis of this interpretation is the finite scale theory, which describes the evolution of integral averages of the fluid solution over finite (length) scales. I will outline the derivation of finite scale Navier–Stokes equations and highlight the particular properties of the equations that depend on the finite scales. Those properties include enslavement, inviscid dissipation, and a law concerning the partition of total flux of conserved quantities into advective and diffusive components.},

doi = {10.1007/s00193-018-0810-8},

journal = {Shock Waves},

number = ,

volume = ,

place = {United States},

year = {Sat Feb 24 00:00:00 EST 2018},

month = {Sat Feb 24 00:00:00 EST 2018}

}