On uncertainty quantification via the ensemble of independent numerical solutions

Abstract

The instance of the epistemic uncertainty quantification concerning the estimation of the approximation error norm is analyzed using the ensemble of numerical solutions obtained via independent numerical algorithms. The analysis is based on the geometry considerations: the triangle inequality and the diameter of the ensemble related with the measure concentration phenomenon in spaces of great dimension. In result, nonintrusive postprocessing may be performed that provides the approximation error norm estimation on the ensemble of the solutions. The ensemble of numerical results obtained by five OpenFOAM solvers (based on independent algorithms) is analyzed from this viewpoint. The numerical tests are made for the inviscid compressible flow around a cone at zero angle of attack. The norm of the approximation error and the error of the valuable functional (drag coefficient) are successfully estimated via ensemble based approach that is confirmed by the comparison with the etalon precise solution. The considered approach provides the error estimation with the acceptable value of the efficiency index.