A NURBS-Based Discontinuous Galerkin Method for Turbulent Flows Simulations

Computational fluid dynamics (CFD) is becoming increasingly important relevant in many industrial and scientific fields, promoting the development of more accurate and efficient CFD solvers. In particular, a modern CFD solver should be characterized by (i) a direct interface with geometric modelling software to reduce the generation time of the computational grid, (ii) the ability to use different approaches for the accurate description of turbulent flows, and (iii) a dynamic adaptation algorithm of the computational mesh to reduce computing time. Isogeometric high-order discontinuous Galerkin (dG) methods, where B-splines or non-uniform rational B-splines (NURBS) are used to describe both geometry and unknowns, can serve as a viable option for achieving these objectives, because they guarantee an exact representation of the geometry and high accuracy, even when using unstructured, strongly distorted, and curved meshes. In the present work, an isogeometric high-order dG solver is extended to solve the Reynolds Averaged Navier-Stokes (RANS) equations and Spalart-Allmaras turbulence model equations for compressible flows, am it is validated in the computation of some benchmark test-cases.