# A point implicit time integration technique for slow transient flow problems

## Abstract

We introduce a point implicit time integration technique for slow transient flow problems. The method treats the solution variables of interest (that can be located at cell centers, cell edges, or cell nodes) implicitly and the rest of the information related to same or other variables are handled explicitly. The method does not require implicit iteration; instead it time advances the solutions in a similar spirit to explicit methods, except it involves a few additional function(s) evaluation steps. Moreover, the method is unconditionally stable, as a fully implicit method would be. This new approach exhibits the simplicity of implementation of explicit methods and the stability of implicit methods. It is specifically designed for slow transient flow problems of long duration wherein one would like to perform time integrations with very large time steps. Because the method can be time inaccurate for fast transient problems, particularly with larger time steps, an appropriate solution strategy for a problem that evolves from a fast to a slow transient would be to integrate the fast transient with an explicit or semi-implicit technique and then switch to this point implicit method as soon as the time variation slows sufficiently. We have solved several test problemsmore »

- Authors:

- Yildiz Technical Univ., Davutpasa-Esenler, Istanbul (Turkey). Dept. of Mathematical Engineering
- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Publication Date:

- Research Org.:
- Idaho National Lab. (INL), Idaho Falls, ID (United States)

- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)

- OSTI Identifier:
- 1184723

- Report Number(s):
- INL/JOU-12-26133

Journal ID: ISSN 0029-5493; TRN: US1500206

- DOE Contract Number:
- AC07-05ID14517

- Resource Type:
- Journal Article

- Journal Name:
- Nuclear Engineering and Design

- Additional Journal Information:
- Journal Volume: 286; Journal Issue: C; Journal ID: ISSN 0029-5493

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; TRANSIENTS; MATHEMATICAL SOLUTIONS; IMPLEMENTATION; INTEGRALS; COMPRESSIBLE FLOW; SCALARS; STABILITY; POINT IMPLICIT METHOD; SLOW TRANSIENT COMPRESSIBLE FLOW PROBLEMS

### Citation Formats

```
Kadioglu, Samet Y., Berry, Ray A., and Martineau, Richard C.
```*A point implicit time integration technique for slow transient flow problems*. United States: N. p., 2015.
Web. doi:10.1016/j.nucengdes.2015.02.002.

```
Kadioglu, Samet Y., Berry, Ray A., & Martineau, Richard C.
```*A point implicit time integration technique for slow transient flow problems*. United States. doi:10.1016/j.nucengdes.2015.02.002.

```
Kadioglu, Samet Y., Berry, Ray A., and Martineau, Richard C. Fri .
"A point implicit time integration technique for slow transient flow problems". United States. doi:10.1016/j.nucengdes.2015.02.002.
```

```
@article{osti_1184723,
```

title = {A point implicit time integration technique for slow transient flow problems},

author = {Kadioglu, Samet Y. and Berry, Ray A. and Martineau, Richard C.},

abstractNote = {We introduce a point implicit time integration technique for slow transient flow problems. The method treats the solution variables of interest (that can be located at cell centers, cell edges, or cell nodes) implicitly and the rest of the information related to same or other variables are handled explicitly. The method does not require implicit iteration; instead it time advances the solutions in a similar spirit to explicit methods, except it involves a few additional function(s) evaluation steps. Moreover, the method is unconditionally stable, as a fully implicit method would be. This new approach exhibits the simplicity of implementation of explicit methods and the stability of implicit methods. It is specifically designed for slow transient flow problems of long duration wherein one would like to perform time integrations with very large time steps. Because the method can be time inaccurate for fast transient problems, particularly with larger time steps, an appropriate solution strategy for a problem that evolves from a fast to a slow transient would be to integrate the fast transient with an explicit or semi-implicit technique and then switch to this point implicit method as soon as the time variation slows sufficiently. We have solved several test problems that result from scalar or systems of flow equations. Our findings indicate the new method can integrate slow transient problems very efficiently; and its implementation is very robust.},

doi = {10.1016/j.nucengdes.2015.02.002},

journal = {Nuclear Engineering and Design},

issn = {0029-5493},

number = C,

volume = 286,

place = {United States},

year = {2015},

month = {5}

}