On Efficiently Obtaining Higher Order Accurate Discretization Error Estimates for Unstructured Finite-Volume Methods using the Error Transport Equation

[+] Author and Article Information
Gary Yan

Graduate Research Assistant, Department of Mechanical Engineering, The University of British Columbia, Vancouver, B.C., Canada V6T 1Z4

Carl Ollivier-Gooch

Professor, Fellow of ASME, Department of Mechanical Engineering, The University of British Columbia, Vancouver, B.C., Canada V6T 1Z4

1Corresponding author.

ASME doi:10.1115/1.4039188 History: Received May 03, 2016; Revised January 10, 2018


A numerical estimation of discretization error for steady compressible flow solutions is performed using the error transport equation (ETE). There is a deficiency in the literature for obtaining efficient, higher order accurate error estimates for finite-volume discretizations using non-smooth unstructured meshes. We demonstrate that sharp, higher order accurate error estimates can be obtained by discretizing the ETE to a higher order than the primal problem, a requirement not necessary for uniform meshes. Linearizing the ETE limits the added cost, rendering the overall computational time competitive, while retaining accuracy in the error estimate. For the Navier-Stokes equations, when the primal solution is corrected using this error estimate, for the same level of solution accuracy the overall computational time is more than two times faster than solving the higher order primal problem. In addition, our scheme has robustness advantages, because we solve the primal problem only to lower order.

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