Efficient h-adaptive isogeometric discontinuous Galerkin solver for turbulent flows

Abstract

The numerical simulation of turbulent flows is still a significant challenge for the complex interplay of scales and nonlinear dynamics that characterize these phenomena. This work presents a method for the accurate simulation of turbulent compressible flows, while preserving the accuracy of the geometric representation provided by the CAD. The proposed method combines high-order CAD-consistent meshes with adaptive refinement, enabling the use of the exact CAD geometry without approximation, as in the isogeometric analysis framework. Key elements include the use of the discontinuous Galerkin method for solving the compressible Reynolds-Averaged Navier-Stokes equations, and the integration of the NURBS representation for enhanced geometric accuracy. Local mesh refinement based on NURBS properties allows for dynamic adaptation that can capture specific flow phenomena. The accuracy of this methodology is assessed through different test cases, demonstrating the robustness and the computational efficiency for different flow regimes, from inviscid to turbulent subsonic and transonic flows.