Abstract
Optimization methods are used for mesh adaption with the goal of reducing discretization error. Given that truncation error is the local source of discretization error, an objective function is created to minimize the truncation error therefore effectively minimizing the discretization error on a given mesh. As a proof of concept, the objective function and objective function gradients are calculated assuming that the exact solution and the exact truncation error are known. The mesh adaption procedure is explored using 1D and 2D Burgers’ equation for various Reynolds numbers. Other issues including adaption efficiency and global minimums are also addressed. For both 1D and 2D Burgers’ equation, results show several orders of magnitude reduction in discretization error as compared to that found on a uniform mesh.
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