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UBC Theses and Dissertations

Truncation error analysis for diffusion schemes in boundary regions of unstructured meshes Puneria, Varun Prakash


Accuracy of numerical solution is of paramount importance for any CFD simulation. The error in satisfying the continuous partial differential equations by their discrete form results in truncation error and it has a direct influence on discretization errors. Discretization error, which is the difference in the numerical solution and the exact solution to a CFD problem, is generally the largest source of numerical errors. Understanding the relationship between the discretization and truncation error is crucial for reducing numerical errors. Studies have been carried out to understand the truncation-discretization error relationship in the interior regions of a computational domain but fewer for the boundary regions. The effect of different solution reconstruction methods, face gradient averaging schemes and boundary condition implementation methods on boundary truncation error in specific and overall truncation and solution error are the subject of research for this thesis. To achieve the goals laid out, the error has to be quantified first and then tests performed to compare the schemes. The Poisson's equation is chosen as the model diffusion equation. The truncation error coefficients, analogous to the analytical coefficients of the spatial derivatives in Taylor series expansion of truncation error, are quantified using error metrics. The solution error calculation is made possible by a careful selection of exact solutions and their appropriate source terms for Poisson's equation. Analytic tests are performed on a family of topologically regular meshes to test and verify the theoretical implementation of different schemes and to eliminate schemes performing poorly from consideration for numerical tests. The numerical tests are performed on unstructured triangular, mixed and pure quad meshes to extend the accuracy assessment for general meshes. The results obtained from both the tests are utilized to arrive at schemes where the overall truncation error and discretization error can be minimized simultaneously.

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