YIC2025

Asymptotic preserving verification tests for particle transport codes

  • Bennett, William (LANL)
  • Ferguson, Jim (LANL)

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Verification considerations typically focus solely on mesh convergence of numerical results. If a code produces numerical results with a proper convergence rate with respect to the spatial mesh, then it is assumed the required verification due diligence has been performed. This approach is sufficient for single-physics models with a single length scale, or possibly no length scale. However, the multi-physics models that are of more interest typically have multiple length scales and may evolve on multiple time scales. Establishing mesh convergence results on the smallest length- and time-scales may not be computationally feasible. Efficient asymptotic preserving (AP) methods have been devised to handle these disparate space and time scales in numerical models [2, 3]. Verifying that the algorithms implementing these methods are asymptotic preserving is not straightforward. For particle transport applications, we present a code-verification semi-analytic solver that creates useful benchmark problems for the radiation transport and radiative transfer equations [9, 10]. We show that solutions from these benchmark problems asymptotically scale at the correct rate. One major impediment to verifying codes with the aforementioned AP benchmark solutions is the intrusiveness of the asymptotic scaling parameter and the multiplicity of simulation runs required. We present new analysis that reveals a pathway into the asymptotic regime via mean free times, a non-intrusive parameter. Finally, a time-as-resolution verification test is given where latent symmetries in the governing equations inform transformation into a self similar variable ξ= x/(√t) and it is shown how increasing time can be considered as increasing resolution in self-similar space. Though particle transport is not explicitly self-similar, this relation is used to perform a mesh convergence test with only one mesh resolution. This type of asymptotic verification test tests whether a code preserves fundamental symmetries of the governing equations.