A hybrid data-driven/linear shock-capturing scheme with low numerical dissipation for contact discontinuities

Shock-capturing schemes based on the classic nonlinear weighting technique tends to continuously smear out a traveling contact discontinuity. Recently, a data-driven procedure [B. Stevens and T. Colonius, Theor. Comput. Fluid Dyn. 34, 483–496 (2020)], which modifies the nonlinear weights of a fifth-order weighted essentially non-oscillatory scheme, has shown promising results in preserving the profiles of contact discontinuities. However, the convergence order degrades to only first order, and unexpected anomalous results are observed, which will certainly reduce the reliability of the method. To address these issues, we propose a hybrid interpolation method, where the data-driven interpolation and classic high-order linear interpolation are used in the discontinuous region and smooth region, respectively. The switch between the two interpolations is realized by an enhanced discontinuity sensor. The numerical results of several benchmark tests suggest that the new hybrid scheme not only preserves moving contact discontinuities in long-time simulations but also shows optimal convergence order in smooth regions and higher resolution for small-scale structures compared with the classic scheme.