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## Discrete regularization

## Abstract

We discuss discrete regularization, more specifically about how to add finite dissipation to the discretized Euler equations so as to ensure the stability and convergence of numerical solutions of high Reynolds number flows. We will briefly review regularization strategies widely used in Lagrangian shockwave simulations (artificial viscosity), in Eulerian nonoscillatory finite volume simulations, and in Eulerian simulations of turbulent flow (explicit and implicit large eddy simulations). We will describe an alternate strategy for regularization in which we introduce a finite length scale into the discrete model by volume averaging the equations over a computational cell. The new equations, which we term Finite Scale Navier-Stokes, contain explicit (inviscid) dissipation in a uniquely specified form and obey an entropy principle. We will describe features of the new equations including control of the small scales of motion by the larger resolved scales, a principle concerning the partition of total flux of conserved quantities into advective and diffusive components, and a physical basis for the inviscid dissipation.

- Authors:

- Los Alamos National Lab. (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)

- OSTI Identifier:
- 1511226

- Report Number(s):
- LA-UR-18-20241

Journal ID: ISSN 2163-2480

- Grant/Contract Number:
- 89233218CNA000001

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Evolution Equations & Control Theory

- Additional Journal Information:
- Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2163-2480

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; high Reynolds number; artificial viscosity; nonoscillatory differencing

### Citation Formats

```
Margolin, Len, and Plesko, Catherine. Discrete regularization. United States: N. p., 2019.
Web. doi:10.3934/eect.2019007.
```

```
Margolin, Len, & Plesko, Catherine. Discrete regularization. United States. doi:10.3934/eect.2019007.
```

```
Margolin, Len, and Plesko, Catherine. Fri .
"Discrete regularization". United States. doi:10.3934/eect.2019007.
```

```
@article{osti_1511226,
```

title = {Discrete regularization},

author = {Margolin, Len and Plesko, Catherine},

abstractNote = {We discuss discrete regularization, more specifically about how to add finite dissipation to the discretized Euler equations so as to ensure the stability and convergence of numerical solutions of high Reynolds number flows. We will briefly review regularization strategies widely used in Lagrangian shockwave simulations (artificial viscosity), in Eulerian nonoscillatory finite volume simulations, and in Eulerian simulations of turbulent flow (explicit and implicit large eddy simulations). We will describe an alternate strategy for regularization in which we introduce a finite length scale into the discrete model by volume averaging the equations over a computational cell. The new equations, which we term Finite Scale Navier-Stokes, contain explicit (inviscid) dissipation in a uniquely specified form and obey an entropy principle. We will describe features of the new equations including control of the small scales of motion by the larger resolved scales, a principle concerning the partition of total flux of conserved quantities into advective and diffusive components, and a physical basis for the inviscid dissipation.},

doi = {10.3934/eect.2019007},

journal = {Evolution Equations & Control Theory},

number = 1,

volume = 8,

place = {United States},

year = {2019},

month = {3}

}