# zbMATH — the first resource for mathematics

A high-order discontinuous Galerkin solver for unsteady incompressible turbulent flows. (English) Zbl 1390.76344
Summary: In this work, we investigate the use of adaptive linearly implicit Rosenbrock-type Runge-Kutta and explicit singly diagonally implicit Runge-Kutta schemes to integrate in time high-order discontinuous Galerkin space discretizations of the incompressible Navier-Stokes (INS) and Reynolds averaged Navier-Stokes (URANS) equations. The objective of this activity is to assess the efficiency and accuracy of the considered schemes coupled with a time-step adaptation technique for incompressible URANS simulations. The schemes have been first investigated for the computation of the laminar travelling waves and of the turbulent flow around a circular cylinder at a Reynolds number $$\mathrm{Re} = 5 \times 10^4$$, verifying the convergence order, a simple relation to set the system tolerance starting from the tolerance of the adaptation strategy, and their computational efficiency. Finally, the best scheme resulting from our analysis has been applied to the URANS simulation of the flow through a vertical axis wind turbine, comparing the results with CFD and experimental data available in literature.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 76F65 Direct numerical and large eddy simulation of turbulence
##### Software:
MEBDF; PETSc; ROS3P
Full Text: