摘要 :
In industrial applications, numerical computations are performed with the intention of estimating an integral quantity of interest. The error from a numerical scheme depends significantly on the mesh and node distributions. Optimi...
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In industrial applications, numerical computations are performed with the intention of estimating an integral quantity of interest. The error from a numerical scheme depends significantly on the mesh and node distributions. Optimization based reduced-space mesh adaptation is widely used to obtain an optimal node distribution, which minimizes the error in a final goal/functional. However, in reduced space methods, the flow solver's residual needs to be completely converged at each iteration of optimization and the number of non-linear Newton iterations scales with the size of design variables. On the other hand, the full space approach converges the mesh and flow solution simultaneously and the number of Newton iterations required by the optimizer are independent of problem size. The current work introduces a goal oriented full-space optimization based r-adaptation to get a mesh which accurately computes a functional of interest. The traditional goal oriented error estimate is modified for use with full space and an adjoint-based objective function is proposed along with the means to calculate its first and second derivatives to retain quadratic convergence of Newton's method. Convergence of the scheme is verified using 1D and 2D test cases with volume and boundary functionals and the approach is compared with the reduced-space method.
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