Variational Multiscale Modeling with Discontinuous Subscales: Analysis and Application to Scalar Transport
Provides a theoretically grounded and robust multiscale method for scalar transport problems, relevant to computational fluid dynamics.
The paper develops a variational multiscale method using discontinuous Galerkin for fine-scales, proving optimal convergence in the SUPG norm and robustness with respect to the Peclet number. Numerical tests on isogeometric NURBS discretizations show stability and accuracy in advection-dominated regimes.
We examine a variational multiscale method in which the unresolved fine-scales are approximated element-wise using a discontinuous Galerkin method. We establish stability and convergence results for the methodology as applied to the scalar transport problem, and we prove that the method exhibits optimal convergence rates in the SUPG norm and is robust with respect to the Peclet number if the discontinuous subscale approximation space is sufficiently rich. We apply the method to isogeometric NURBS discretizations of steady and unsteady transport problems, and the corresponding numerical results demonstrate that the method is stable and accurate in the advective limit even when low-order discontinuous subscale approximations are employed.