# ICM: an Integrated Compartment Method for numerically solving partial differential equations

## Abstract

An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.

- Authors:

- Publication Date:

- Research Org.:
- Oak Ridge National Lab., TN (USA)

- OSTI Identifier:
- 6530640

- Report Number(s):
- ORNL-5684

TRN: 81-010133

- DOE Contract Number:
- W-7405-ENG-26

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; 42 ENGINEERING; COMPUTER CODES; I CODES; DIFFERENTIAL EQUATIONS; NUMERICAL SOLUTION; NAVIER-STOKES EQUATIONS; ALGORITHMS; COMPARTMENTS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; SIMULATION; EQUATIONS; ITERATIVE METHODS; MATHEMATICAL LOGIC; PARTIAL DIFFERENTIAL EQUATIONS; 658000* - Mathematical Physics- (-1987); 053000 - Nuclear Fuels- Environmental Aspects; 420400 - Engineering- Heat Transfer & Fluid Flow

### Citation Formats

```
Yeh, G T.
```*ICM: an Integrated Compartment Method for numerically solving partial differential equations*. United States: N. p., 1981.
Web. doi:10.2172/6530640.

```
Yeh, G T.
```*ICM: an Integrated Compartment Method for numerically solving partial differential equations*. United States. https://doi.org/10.2172/6530640

```
Yeh, G T. Fri .
"ICM: an Integrated Compartment Method for numerically solving partial differential equations". United States. https://doi.org/10.2172/6530640. https://www.osti.gov/servlets/purl/6530640.
```

```
@article{osti_6530640,
```

title = {ICM: an Integrated Compartment Method for numerically solving partial differential equations},

author = {Yeh, G T},

abstractNote = {An integrated compartment method (ICM) is proposed to construct a set of algebraic equations from a system of partial differential equations. The ICM combines the utility of integral formulation of finite element approach, the simplicity of interpolation of finite difference approximation, and the flexibility of compartment analyses. The integral formulation eases the treatment of boundary conditions, in particular, the Neumann-type boundary conditions. The simplicity of interpolation provides great economy in computation. The flexibility of discretization with irregular compartments of various shapes and sizes offers advantages in resolving complex boundaries enclosing compound regions of interest. The basic procedures of ICM are first to discretize the region of interest into compartments, then to apply three integral theorems of vectors to transform the volume integral to the surface integral, and finally to use interpolation to relate the interfacial values in terms of compartment values to close the system. The Navier-Stokes equations are used as an example of how to derive the corresponding ICM alogrithm for a given set of partial differential equations. Because of the structure of the algorithm, the basic computer program remains the same for cases in one-, two-, or three-dimensional problems.},

doi = {10.2172/6530640},

url = {https://www.osti.gov/biblio/6530640},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1981},

month = {5}

}