Adding confidence to solution verification: USING MMS-informed MEA to better understand discretization error
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© 2018 International Topical Meeting on Advances in Thermal Hydraulics, ATH 2018 - Embedded Topical Meeting. All rights reserved. Applying solution verification methods to computational fluid dynamic (CFD) simulations has substantially increased within the past three decades, especially with the introduction of the grid convergence index (GCI) metric. Since then, numerical and meshing schemes and the governing equations have increased in complexity, which makes understanding the discretization error for a simulation even more complex. Greater understanding of how discretization error develops from local truncation error (LTE) within a simulation can provide additional evidence to determine the adequacy of the error model used in current solution verification methods. It also provides meshing strategies to improve the adequacy of the error model. When the error model is determined to be adequate, additional confidence is added to the solution verification studies. One way of understanding how discretization error develops from LTE is to quantify the LTE and track how it propagates through time and space using the partial differential equation. Propagating LTE through time and space was completed using two methods: difference of difference quotients (DDQ) method and method of manufactured solutions-informed modified equation analysis (MMS-informed MEA) method. These methods justify the adequacy of the error model implemented in most Richardson extrapolation (RE) methods for the implemented numerical and meshing scheme. In addition, an example problem is provided that showed the implementation of both discretization error estimation methods using a first-order method and a uniform, structured mesh. The discretization error estimation results were then compared to the exact discretization error.
author list (cited authors)
Krueger, A. M., Mousseau, V. A., & Hassan, Y. A.