An Overview of Combined Uncertainty and A Posteriori Error Bound Estimates for CFD Calculations

摘要

This paper discusses ongoing work in the development of combined uncertainty and error bound estimates for computational fluid dynamics (CFD) calculations subject to imposed random parameters and random fields. These error bound estimates may be used by CFD practitioners to systematically determine how accurately CFD realizations should be approximated and how accurately uncertainty statistics should be approximated to obtain efficient and accurate estimates of uncertainty statistics for output quantities of interest. Formal error bounds formulas for moment statistics have been previously presented in Barth that properly account for the presence of numerical errors in CFD calculations and numerical quadrature errors in the calculation of moment statistics. Computable estimates for all terms appearing in the the error bound formulas are also developed in this previous work and further refined in Barth . In this past and present work, hierarchical node-nested dense and sparse tensor product quadratures are used to calculate moment statistics integrals. The hierarchical structure of these quadratures also simplifies the calculation of an estimate of the quadrature error needed in error bound formulas. For output uncertainties that are not well-characterized by moment statistics, numerical realization error is used to improve estimates of output probability density distributions calculated using standard kernel density estimation techniques . Numerical results are presented for CFD problems with uncertainty to showcase capabilities of this framework.