Abstract

the meshes to obtain more accurate solutions at each sample point in stochastic space, such a procedure can be both cumbersomeandcomputationally expensive. Toimprove theefficiencyof this process,anew robust gridadaptation technique is proposed that is aimed at minimizing the numerical error over a range of variations of the uncertain parameters of interest about a nominal state. Using this approach, it is possible to generate computational grids that are insensitive to small variations of the uncertain parameters that can both locally and globally change the solution and, as a result, the error distribution. This is in contrast with classical adjoint techniques, which seek to adapt the gridwiththeaimofminimizingnumericalerrorsforaspecific flowcondition(andgeometry).Itisdemonstratedthat flow computations on these robust grids result in low numerical errors under the expected range of variations of the uncertain input parameters. The effectiveness of this strategy is demonstrated in problems involving the Poisson equation and the Euler equations at transonic and supersonic/hypersonic speeds.

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