Numerical solutions of Navier‐Stokes equations with an integrated compartment method (ICM)

The most common numerical methods that are used by physical scientists to approximate partial differential equations employ finite differences and/or finite elements. In addition, compartment analyses have been adopted by ecological system analysts 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 Navier‐Stokes equations to yield the computational algorithm from which computer programs can be coded. The computer code is designed to solve one‐, two‐, or three‐dimensional 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. These preliminary applications have shown promising results.