Numerical experiments on the efficiency of local grid refinement based on truncation error estimates

Abstract

Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to associate the discretisation error with an easily computable quantity in each control volume. Often the grid refinement criterion is based on an estimate of the truncation error in each control volume, because the truncation error is a natural measure of the discrepancy between the algebraic finite-volume equations and the original differential equations. However, it is not a straightforward task to associate the truncation error with the optimum grid density because of the complexity of the relationship between truncation and discretisation errors. In the present work several criteria based on a truncation error estimate are tested and compared on a regularised lid-driven cavity case at various Reynolds numbers. It is shown that criteria where the truncation error is weighted by the volume of the grid cells perform better than using just the truncation error as the criterion. Also it is observed that the efficiency of local refinement increases with the Reynolds number. The truncation error is estimated by restricting the solution to a coarser grid and applying the coarse grid discrete operator. The complication that high truncation error develops at grid level interfaces is also investigated and several treatments are tested.

References in corpus (2)

• Estimate of the truncation error of a finite volume discretisation of the Navier-Stokes equations on colocated grids
• Finite volume adaptive solutions using SIMPLE as smoother

Cited by in corpus (7)

• A critical analysis of some popular methods for the discretisation of the gradient operator in finite volume methods
• Performance of the finite volume method in solving regularised Bingham flows: inertia effects in the lid-driven cavity flow
• A p-Multigrid Strategy with Anisotropic p-Adaptation Based on Truncation Errors for High-Order Discontinuous Galerkin Methods
• Truncation Error Estimation in the p-Anisotropic Discontinuous Galerkin Spectral Element Method
• Divergence error based $p$-adaptive discontinuous Galerkin solution of time-domain Maxwell's equations
• A Truncation Error Estimation Scheme for the Finite Volume Method on Unstructured Meshes
• $p$-adaptive algorithms in Discontinuous Galerkin solutions to the time-domain Maxwell's equations