Automatic Resolution Control for the FiniteVolume Method

Automatic Resolution Control for the Finite Volume Method (FVM) shows signs of rapid development in recent years. The objective of the procedure is to obtain a numerical solution of prescribed accuracy with minimum eeort in terms of time and computational resources. It consists of two parts: an a-posteriori error estimate and an appropriate modii-cation of the spatial and temporal discretisation. In this paper, two new a-posteriori error estimates concentrating on the absolute error levels are presented. The rst, the Taylor Series Error Estimate, is based on Taylor series truncation error analysis and, unlike Richardson extrapolation, is capable of estimating the discretisation error from a single solution. In an attempt to overcome some deeciencies of the rst method, the Moment Error Estimate is derived using the balance condition in the transport equation for the higher moments of the variable. It slightly overestimates the error, making it particularly useful in conjunction with the rst error estimate, as the two regularly bound the exact error. The error estimates are validated against the exact error on two test cases with analytical solutions.