Residual Error Estimate for the Finite

Numerical simulation of uid ows has received a wide acceptance in the industrial environment in recent years. If the results of simulations are to be used with conndence, it is necessary to provide a measure of their accuracy. The numerical accuracy of a simulation depends on the control of the discretisation error, introduced through the discretisation and numerical solution procedure. Our goal is to provide a measure of the discretisation error, which allows the user to control the overall quality of the simulation. In this paper, a novel a-posteriori error estimate for the Finite Volume Method (FVM), measuring the absolute magnitude of the discretisation error, is presented. Unlike the more traditional truncation error estimates, the Residual Error Estimate is based on the cell residual, similar to the popular error estimates in the Finite Element community. An appropriate normalisation of the local residual creates the error estimate with the same dimensionality as the variable of interest, which allows the user to intuitively measure the numerical accuracy with reference to the underlying solution. The new error estimate is tested on a series of test cases, some of which have analytical solutions and is shown to perform considerably better than the traditional truncation error estimates.