Numerical solutions of NavierStokes equations with an integrated compartment method /ICM/
Abstract
The most common numerical methods that are used to approximate partial differential equations employ finite differences and/or finite elements. In addition, compartment analyses have been adopted to simulate the evolution of processes governed by differential equations without spatial derivatives. An integrated compartment method (ICM) is proposed to combine the merits of these three numerical techniques. The basic procedures of the 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. These procedures are applied to the NavierStokes equations to yield the computational algorithm from which computer programs can be coded. The computer code is designed to solve one, two, or threedimensional problems as desired. The program is applied to two simple cases: wake formation behind an obstacle in a channel and circulatory motion of a body of fluid in the square cavity.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 September 1981
 DOI:
 10.1002/fld.1650010303
 Bibcode:
 1981IJNMF...1..207Y
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Incompressible Flow;
 NavierStokes Equation;
 Algorithms;
 Boundary Value Problems;
 Computer Techniques;
 Finite Element Method;
 Interpolation;
 Velocity Distribution;
 Viscous Flow;
 Fluid Mechanics and Heat Transfer