Abstract
A higher-order accurate discretization error estimation procedure for finite-volume schemes is presented. Discretization error estimates are computed using the linearized error transport equations (ETE). ETE error estimates are applied as a correction to the primal solution. The ETE are then relinearized about the corrected primal solution, and discretization error estimates are recomputed. This process, referred to as ETE relinearization, is performed in an iterative manner to successively increase the accuracy of discretization error estimates. Under certain conditions, ETE relinearization is shown to correct error estimates, or equivalently the entire primal solution, to higher-order accuracy. In terms of computational cost, ETE relinearization has a competitive advantage over conventional higher-order discretizations when used as a form of defect correction for the primal solution. Furthermore, ETE relinearization is shown to be particularly useful for problems where the error incurred by the linearization of the ETE cannot be neglected. Results are presented for several steady-state inviscid and viscous flow problems using both structured and unstructured meshes.
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