Criteria for the reliability of numerical approximations to the solution of fluid flow problems
Abstract
The numerical approximation of the solutions of fluid flows models is a difficult problem in many cases of energy research. In all numerical methods implementable on digital computers, a basic question is if the number (N) of elements (Galerkin modes, finitedifference cells, finiteelements, etc.) is sufficient to describe the long time behavior of the exact solutions. It was shown using several approaches that some of the estimates based on physical intuition of N are rigorously valid under very general conditions and follow directly from the mathematical theory of the NavierStokes equations. Among the mathematical approaches to these estimates, the most promising (which can be and was already applied to many other dissipative partial differential systems) consists in giving upper estimates to the fractal dimension of the attractor associated to one (or all) solution(s) of the respective partial differential equations.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 January 1986
 Bibcode:
 1986STIN...8629162F
 Keywords:

 Approximation;
 Fluid Flow;
 Fluid Mechanics;
 NavierStokes Equation;
 Partial Differential Equations;
 Data Processing;
 Digital Computers;
 Estimates;
 Fourier Transformation;
 Reliability;
 Fluid Mechanics and Heat Transfer