Historical perspective on the integration of testing and evaluation methodologies at the Arnold Engineering Development Center

Benek, John A.; Langham, T F; Baker, W. Douglas

doi:10.2514/6.1994-2470

Cited by 2 publications

(2 citation statements)

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“…At each stage of the Runge-Kutta integration, Dirichlet and Neumann boundary conditions are applied either directly using the procedure developed by Carpenter et al [43] (i.e., for Dirichlet data) or by using the penalty formulation [44] that will modify Eq. (11) on the boundary (i.e., for Dirichlet and/or Neumann data). The magnitudes of the wavelet coefficients at the new time will determine if the grid prediction must be corrected.…”

Section: Numerical Implementationmentioning

confidence: 99%

“…Several novel numerical methods have been developed to address this computational challenge. For example, adaptive mesh refinement (AMR) [6,7], multigrid methods [8,9,10], Chimera overset grids [11], and remeshing/refining finite element methods (FEM) [12,13,14,15] have been used to accomplish a great deal of contemporary computational modeling. However all of these methods become computationally expensive when the user does not know a priori the spatial and temporal locations of interesting solution features.…”

Section: Introductionmentioning

confidence: 99%

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A multiresolution adaptive wavelet method for nonlinear partial differential equations

Harnish¹,

Dalessandro²,

Matouš³

et al. 2021

Preprint

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The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

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Section: Numerical Implementationmentioning

confidence: 99%