Error Estimation Using Hybrid Methods

Abstract

New formalisms are developed for robust calculation of the discretization errors in CFD applications. The new methods are based on the premise that the true error (i.e. the difference between the exact solution and the numerical solution) on a given mesh is similar to the approximate error (i.e. the difference between the fine grid solution and the coarse grid solution). The proportionality constant can be calculated theoretically for a given scheme and it is, to a first order approximation, only a function of the grid refinement ratio. This method is called Approximate Error Scaling (AES) method. Although AES is a viable method for error estimation it does not directly take into account the transport of error nor the error sources at the boundaries. To remedy this, a new method which is referred to, here and after, as the residual source in transport (REST-IC) method is formulated. This paper presents the theoretical details and the results from several test cases that are used for validation of the newly proposed methods. Application to the 1D and 2D steady scalar transport equation and 2D Navier-Stokes (N-S) equations has revealed excellent performance with a pressure based segregated N-S finite volume solver. Implementation of these methods into CFD commercial codes such as ANSYS-FLUENT can be done with the help of expert developers of the code who can handle residuals for the selected equation and the variable through user defined subroutines.

Quantifying the uncertainty introduced by discretization and time‐averaging in two‐fluid model predictions

“…We employ the Approximate Error Scaling (AES) method proposed by Celik and others to estimate the local discretization error in time‐averaged gas‐velocity, . This method utilizes three substantially different grids preferably with a constant grid refinement ratio, and assumes that the “true error” in the coarse solution is proportional to an “approximate error,” the difference between the fine and coarse grid solutions.…”