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

Technical Report · Fri May 01 04:00:00 EDT 1981

DOI:https://doi.org/10.2172/6530640· OSTI ID:6530640

Yeh, G T

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.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 6530640
• Report Number(s): ORNL-5684
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
COMPARTMENTS
COMPUTER CODES
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
FINITE ELEMENT METHOD
I CODES
ITERATIVE METHODS
MATHEMATICAL LOGIC
NAVIER-STOKES EQUATIONS
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PARTIAL DIFFERENTIAL EQUATIONS
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