Verification of Solutions of Equations Governing Fluid Flows

9th Thai Society of Mechanical Engineers, International Conference on Mechanical Engineering

Watanabe, T.^1

Graduate School of Informatics, Nagoya University, Nagoya

464-8601, Japan^1

关键词: Elimination method;    Fixed point theorems;    Gaussian elimination method;    Interval analysis;    Krawczyk operators;    Linear interval equations;    Solutions of equation;    Two-dimensional Navier-Stokes equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/501/1/012039/pdf
DOI  :  10.1088/1757-899X/501/1/012039

来源: IOP

【 摘 要 】

We have carried out the verifications of the solutions for the equations governing fluid flows. The equations solved are the similar equation of the boundary layer flow and the two-dimensional Navier-Stokes equations in the formulation of the stream function and the vorticity. The methods of the verification are the interval analysis and the Krawczyk operator based on the fixed point theorem. A modified Gaussian elimination method is introduced to solve the system of linear interval equations. The Krawczyk operator presents the results with a high accuracy. The modified elimination method gives the results with an accuracy of one or two order(s) of magnitude higher than those obtained by the original interval analysis.