Numerical solutions of Navier-Stokes equations

A unified computational algorithm is developed for numerically solving the Navier-Stokes equations. The algorithm is based ICM are applied to Navier-Stokes equations to set up two systems of algebraic equations describing the spatially discrete velocity and pressure fields. The coefficient matrices are obtained by assembling the link matrices in the same way as in the finite element method. However, the link matrices are obtained by interpolations for the function and/or its derivatives as in the finite difference approximations. As a result, the ICM algorithm combines the merits of the flexibility of spatial discretization in compartment analyses, of the automatic generation of global matrices in finite element methods, and of the simple interpolation of the function and its derivatives in finite difference approximations. A unified computer program can be used to study one, two, and three dimensional problems without any modification. The time split scheme is used to solve the resulting systems of equations. Conditions for both linear and nonlinear stabilities are derived. The program is applied to the square cavity problem for demonstrative purposes.