Single Grid Error Estimation Using Error Transport Equation

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Abstract
This paper presents an approach to quantify the discretization error as well as other errors related to mesh size using the error transport equation (ETE) technique on a single grid computation. The goal is to develop a generalized algorithm that can be used in conjunction with computational fluid dynamics (CFD) codes to quantify the discretization error in a selected process variable. The focus is on applications where the conservation equations are solved for primitive variables, such as velocity, temperature and concentration, using finite difference and/or finite volume methods. An error transport equation (ETE) is formulated. A generalized source term for the ETE is proposed based on the Taylor series expansion and accessible influence coefficients in the discretized equation. Representative examples, i.e., one-dimensional convection diffusion equation, two-dimensional Poisson equation, two-dimensional convection diffusion equation, and non-linear one-dimensional Burger’s equation are presented to verify this method and elucidate its properties. Discussions are provided to address the significance and possible potential applications of this method to Navier-Stokes solvers.

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