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Award ID contains: 1825991

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  1. ; (, AIAA SciTech Forum)
    We present a smooth, differentiable formula that can be used to approximate an existing geometry as a level-set function. The formula uses data from a finite number of points on the surface and does not require solving a linear or nonlinear system, i.e., the formula is explicit. The baseline method is a smooth analog of a piecewise linear approximation to the surface, but a quadratic correction can be constructed using curvature information. Numerical experiments explore the accuracy of the level-set formula and the influence of its free parameters. For smooth geometries, the results show that the linear and quadratic versions of the method are second- and third-order accurate, respectively. For non-smooth geometries, the infinity norm of the error converges at a first-order rate. 
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  2. ; (, AIAA SciTech Forum)
    null (Ed.)
    We present a high-order discontinuous Galerkin difference (DGD) discretization for cut-cell meshes. We leverage the DGD reconstruction procedure to ameliorate the small-cell problem associated with cut-cells. Numerical experiments demonstrate that the conditioning of DGD discretizations is insensitive to cut-cell sizes for linear problems in one- and two-dimensions. In addition, results are presented that verify the accuracy of the DGD discretization applied to the Euler equations. 
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  3. ; (, International Journal for Numerical Methods in Fluids)
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  4. ; (, 2018 AIAA Fluid Dynamics Conference)
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