Automatic resolution control for the finite-volume method, Part 1: A-posteriori error estimates

Automatic Resolution Control, consisting of an a-posteriori error estimate and a local adjustment of the discretisation scheme, aims at producing a numerical solution of prescribed accuracy with minimum computational effort. In this paper, two a-posteriori error estimates concentrating on the absolute error levels are presented. The Taylor Series Error Estimate is based on a single-grid Taylor series truncation error analysis. The Moment Error Estimate is derived from the balance condition for the higher moments of the transported variable. Two error estimates ave validated on two test cases with analytical solutions, where they typically bound the exact error.