# An implicit Smooth Particle Hydrodynamic code

## Abstract

An implicit version of the Smooth Particle Hydrodynamic (SPH) code SPHINX has been written and is working. In conjunction with the SPHINX code the new implicit code models fluids and solids under a wide range of conditions. SPH codes are Lagrangian, meshless and use particles to model the fluids and solids. The implicit code makes use of the Krylov iterative techniques for solving large linear-systems and a Newton-Raphson method for non-linear corrections. It uses numerical derivatives to construct the Jacobian matrix. It uses sparse techniques to save on memory storage and to reduce the amount of computation. It is believed that this is the first implicit SPH code to use Newton-Krylov techniques, and is also the first implicit SPH code to model solids. A description of SPH and the techniques used in the implicit code are presented. Then, the results of a number of tests cases are discussed, which include a shock tube problem, a Rayleigh-Taylor problem, a breaking dam problem, and a single jet of gas problem. The results are shown to be in very good agreement with analytic solutions, experimental results, and the explicit SPHINX code. In the case of the single jet of gas case it hasmore »

- Authors:

- Univ. of New Mexico, Albuquerque, NM (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 754046

- Report Number(s):
- LA-13685-T

TRN: AH200016%%204

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); Submitted to Univ. of New Mexico, Albuquerque, NM (US); PBD: 1 Apr 2000

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; S CODES; HYDRODYNAMICS; FLUIDS; SOLIDS; ITERATIVE METHODS; JACOBIAN FUNCTION; MEMORY MANAGEMENT

### Citation Formats

```
Knapp, Charles E.
```*An implicit Smooth Particle Hydrodynamic code*. United States: N. p., 2000.
Web. doi:10.2172/754046.

```
Knapp, Charles E.
```*An implicit Smooth Particle Hydrodynamic code*. United States. doi:10.2172/754046.

```
Knapp, Charles E. Mon .
"An implicit Smooth Particle Hydrodynamic code". United States. doi:10.2172/754046. https://www.osti.gov/servlets/purl/754046.
```

```
@article{osti_754046,
```

title = {An implicit Smooth Particle Hydrodynamic code},

author = {Knapp, Charles E.},

abstractNote = {An implicit version of the Smooth Particle Hydrodynamic (SPH) code SPHINX has been written and is working. In conjunction with the SPHINX code the new implicit code models fluids and solids under a wide range of conditions. SPH codes are Lagrangian, meshless and use particles to model the fluids and solids. The implicit code makes use of the Krylov iterative techniques for solving large linear-systems and a Newton-Raphson method for non-linear corrections. It uses numerical derivatives to construct the Jacobian matrix. It uses sparse techniques to save on memory storage and to reduce the amount of computation. It is believed that this is the first implicit SPH code to use Newton-Krylov techniques, and is also the first implicit SPH code to model solids. A description of SPH and the techniques used in the implicit code are presented. Then, the results of a number of tests cases are discussed, which include a shock tube problem, a Rayleigh-Taylor problem, a breaking dam problem, and a single jet of gas problem. The results are shown to be in very good agreement with analytic solutions, experimental results, and the explicit SPHINX code. In the case of the single jet of gas case it has been demonstrated that the implicit code can do a problem in much shorter time than the explicit code. The problem was, however, very unphysical, but it does demonstrate the potential of the implicit code. It is a first step toward a useful implicit SPH code.},

doi = {10.2172/754046},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2000},

month = {5}

}