Numerical solutions of Navier-Stokes equations

Conference · Thu Jan 01 04:00:00 EST 1981

OSTI ID:6378804

Yeh, G T

A unified computational algorithm is developed for numerically solving the Navier-Stokes equations. The algorithm is based on an integrated Compartment Method (ICM). The procedures of 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 (FEM). 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. Furthermore, because link matrices are always the 2 x 2 matrices, 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. It is shown that the scheme yields conditionally stable solutions. Conditions for both linear and nonlinear stabilities are derived. The program is applied to the square cavity problem for demonstrative purposes. Results are compared with those reported by others using finite difference methods and analytical techniques. The agreement is excellent and it shows that the unified algorithm can definitely simulate the behavior of the Navier-Stokes equations.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: W-7405-ENG-26
• OSTI ID: 6378804
• Report Number(s): CONF-810621-3; ON: DE81024118
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGEBRA
ALGORITHMS
COMPUTER CALCULATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE ELEMENT METHOD
MATHEMATICAL LOGIC
MATHEMATICS
MATRICES
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
THREE-DIMENSIONAL CALCULATIONS