Analysis of Residual Estimate of Local Truncation Error

Abstract

This thesis focuses on understanding the behaviour of the residual error estimator, referred to as R- parameter, in the context of Finite Volume Method. R-parameter measures the local truncation error (LTE) which is generated locally in each cell due to spatial and temporal discretization. Even though there are numerous applications of R-parameter, it is also sensitive to various parameters. The sensitivities associated to R-parameter are studied through numerical experiments and theoretical analysis. For this, steady circular convection and scalar convection-diffusion problems are considered.

The different gradient-finding methods employed for evaluating LTE can influence the R-parameter. The accuracy of these methodologies is studied empirically using 2D test function. Consistent to finite volume method, the cell-averaged values are used for accuracy studies.

The comparison of error fall rates and error levels obtained from different variants of error estimators are discussed in detail. We have also proposed a simple method based on generalized finite difference for determining the residual, which shows a lot of promise owing to the simplicity of its implementation.

Patch analysis is performed to establish the relevance of the procedures analysed to AMR. In order to understand the correctness of the estimated errors, the qualitative and quantitative analysis of the local error distribution over the whole domain are carried out for scalar convection problem. This work also establishes the suitability of QLS based error estimator to determine errors associated with a viscous flux discretization.