Comparison of residual and interpolation error estimators for mesh adaptation

This paper aims to compare three distinct error estimators on a series of partial differential equations discretized using a cell-centered finite volume method, and to measure their capacity to control mesh resolution to improve solution accuracy. Two residual-based error estimators, one proposed by Jasak[1] and the other by Vohralik[2], are compared to interpolation error estimation using a reconstruction of second order derivatives of the solution. The estimated errors are used to improve the mesh in the regions of high error. The adaptive mesh technique is presented for two-dimensional meshes of triangles and meshes of quadrilaterals, refined using tools implemented in the OpenFOAM [3] and OORT [4] software systems. The methodology is based on extensions to currently available a-posteriori error estimator techniques implemented in OpenFOAM, as well as mesh adaptation techniques available in OORT. Validation tests for some classical laminar flow problems are presented and solved using a gradation of flow models from Poisson type equation to advection-diffusion equation. [1] JASAK, H. (1996). Error Analysis and Estimation for the Finite Volume Method with Applications to Fluid Flows. PhD Thesis, Imperial College. [2] VOHRALIK, M. (2008). Residual flux-based A-posteriori error estimates for finite volume and related locally conservative methods. Numer. Math., 111, 121-158. [3] OpenFOAM (2011). OpenFOAM. The Open Source CFD Toolbox. User Guide. [4] DOMPIERRE, J. et LABBE, P. (2001). OORT (Object-Oriented Remeshing Toolkit). Manuel de l'usager. version 2001. Centre de Recherche en Calcul Applique (CERCA).