Estimation of the accuracy of numerical simulations using Richardson extrapolation and a Hessian technique. (1st March 2010) - De Saint Victor, Xavier
The part of experimental studies tends to decrease for the benefit of numerical simulations. The interest for the numerical simulations comes along with new requirements: the statement of certification criteria for the simulation codes and the proofs these criteria are really respected. Once the solution was obtained, the question arises to know what is its reliability degree and how possibly to adapt the problem resolution for obtaining a solution with better quality without increasing the calculation costs. We are interested here in two kinds of error estimation methods. The method based on the Richardson extrapolation allows the quantitative improvement of the precision and the increase of the numerical scheme order. The method dealing with the Hessian matrix of the studied variable is of a much more recent formalism. Both techniques are tested here in two-dimensional cases: the flow over a flat plate and the in viscid flow around the NACA0012 profile.