# Parallel Adaptive Mesh Refinement

## Abstract

As large-scale, parallel computers have become more widely available and numerical models and algorithms have advanced, the range of physical phenomena that can be simulated has expanded dramatically. Many important science and engineering problems exhibit solutions with localized behavior where highly-detailed salient features or large gradients appear in certain regions which are separated by much larger regions where the solution is smooth. Examples include chemically-reacting flows with radiative heat transfer, high Reynolds number flows interacting with solid objects, and combustion problems where the flame front is essentially a two-dimensional sheet occupying a small part of a three-dimensional domain. Modeling such problems numerically requires approximating the governing partial differential equations on a discrete domain, or grid. Grid spacing is an important factor in determining the accuracy and cost of a computation. A fine grid may be needed to resolve key local features while a much coarser grid may suffice elsewhere. Employing a fine grid everywhere may be inefficient at best and, at worst, may make an adequately resolved simulation impractical. Moreover, the location and resolution of fine grid required for an accurate solution is a dynamic property of a problem's transient features and may not be known a priori. Adaptive meshmore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 952096

- Report Number(s):
- UCRL-JRNL-210250

TRN: US200913%%370

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Journal Article

- Journal Name:
- Parallel Processing For Scientific Computing, Chapter 8, N/A, N/A, December 31, 2006, pp. 143-162

- Additional Journal Information:
- Journal Name: Parallel Processing For Scientific Computing, Chapter 8, N/A, N/A, December 31, 2006, pp. 143-162

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS; ACCURACY; ALGORITHMS; COMBUSTION; COMPUTERS; FLAMES; HEAT TRANSFER; HELICOPTERS; PARTIAL DIFFERENTIAL EQUATIONS; RESOLUTION; REYNOLDS NUMBER; SIMULATION; TRANSIENTS

### Citation Formats

```
Diachin, L, Hornung, R, Plassmann, P, and WIssink, A.
```*Parallel Adaptive Mesh Refinement*. United States: N. p., 2005.
Web.

```
Diachin, L, Hornung, R, Plassmann, P, & WIssink, A.
```*Parallel Adaptive Mesh Refinement*. United States.

```
Diachin, L, Hornung, R, Plassmann, P, and WIssink, A. Fri .
"Parallel Adaptive Mesh Refinement". United States. https://www.osti.gov/servlets/purl/952096.
```

```
@article{osti_952096,
```

title = {Parallel Adaptive Mesh Refinement},

author = {Diachin, L and Hornung, R and Plassmann, P and WIssink, A},

abstractNote = {As large-scale, parallel computers have become more widely available and numerical models and algorithms have advanced, the range of physical phenomena that can be simulated has expanded dramatically. Many important science and engineering problems exhibit solutions with localized behavior where highly-detailed salient features or large gradients appear in certain regions which are separated by much larger regions where the solution is smooth. Examples include chemically-reacting flows with radiative heat transfer, high Reynolds number flows interacting with solid objects, and combustion problems where the flame front is essentially a two-dimensional sheet occupying a small part of a three-dimensional domain. Modeling such problems numerically requires approximating the governing partial differential equations on a discrete domain, or grid. Grid spacing is an important factor in determining the accuracy and cost of a computation. A fine grid may be needed to resolve key local features while a much coarser grid may suffice elsewhere. Employing a fine grid everywhere may be inefficient at best and, at worst, may make an adequately resolved simulation impractical. Moreover, the location and resolution of fine grid required for an accurate solution is a dynamic property of a problem's transient features and may not be known a priori. Adaptive mesh refinement (AMR) is a technique that can be used with both structured and unstructured meshes to adjust local grid spacing dynamically to capture solution features with an appropriate degree of resolution. Thus, computational resources can be focused where and when they are needed most to efficiently achieve an accurate solution without incurring the cost of a globally-fine grid. Figure 1.1 shows two example computations using AMR; on the left is a structured mesh calculation of a impulsively-sheared contact surface and on the right is the fuselage and volume discretization of an RAH-66 Comanche helicopter [35]. Note the ability of both meshing methods to resolve simulation details by varying the local grid spacing.},

doi = {},

journal = {Parallel Processing For Scientific Computing, Chapter 8, N/A, N/A, December 31, 2006, pp. 143-162},

number = ,

volume = ,

place = {United States},

year = {2005},

month = {3}

}