# Test cases

## VL1 Laminar Joukowski airfoil at Re=1000

This test case concerns the laminar flow around a symmetric Joukowski airfoil at zero incidence. It is designed as a verification case of the viscous terms of the Navier-Stokes equations. A low Reynolds number of 1,000 is employed to emphasise the viscous terms. For an adjoint consistent discretization, the optimal convergence rate for an output functional is 2P. Otherwise, the convergence rate can be expected to be P+1. The Joukowski airfoil is used for this test as the cusped trailing edge removes the inviscid singularity at the trailing edge. However, there is still a singularity in skin friction. The provided grids are design to cluster nodes at both the trailing edge singularity and the stagnation point in order to capture the expected order of accuracy. Hence, all participants must use the provided grids.

- Read more about VL1 Laminar Joukowski airfoil at Re=1000
- Log in to post comments

## VR1 RANS Joukowski airfoil

This test case is designed as a verification case of the turbulence model of the RANS equations. Participants are required to use the provided grids, as they have been demonstrated to be able to provide the optimal convergence rate in drag. A Reynolds number of 1,000,000 is employed. For an adjoint consistent discretization, the optimal convergence rate of an output functional is 2P. Otherwise, the convergence rate can be expected to be P+1. The Joukowski airfoil is used for this test as the cusped trailing edge removes the inviscid singularity at the trailing edge. However, there is still a singularity in skin friction. The provided grids are design to cluster nodes at both the trailing edge singularity and the stagnation point in order to capture the expected order of accuracy. Hence, all participants must use the provided grids.

- Read more about VR1 RANS Joukowski airfoil
- Log in to post comments

## WS1 DNS of the Taylor-Green vortex at Re=1600

This problem is aimed at testing the accuracy and the performance of high-order methods on the direct numerical simulation of a three-dimensional periodic and transitional flow defined by a simple initial condition: the Taylor-Green vortex. The computational domain is a triply periodic cubic domain, in which initially 8 vortices reside, described by an analytical formula. This flow transitions to turbulence, with the creation of small scales, followed by a decay phase similar to decaying homogeneous turbulence.

Participants are expected to perform a grid independence study on Cartesian meshes, as well as a few computations on unstructured/perturbed meshes at similar resolution as the Cartesian ones. The assessment criteria consist of the evolution of the energy dissipation rate as well as the enstrophy. Further verification is done on the basis of the kinetic energy spectrum as well as the trace of the vorticity on the periodic plane at selected time steps.

Computations need to be run on Cartesian meshes with specified equivalent resolutions 64, 128 and 256. If applicable, it is expected that participants use the unstructured and perturbed meshes provided by the test case leader to guarantee a level playing field. These will be generated in function of the interpolation (order) used by the discretization.

- Read more about WS1 DNS of the Taylor-Green vortex at Re=1600
- Log in to post comments

## WS2 LES of the plane channel at Ret=550

This test case concerns the LES of the channel flow at Reτ=550. This well-known benchmark has been intensively studied by the turbulence community. DNS and LES of the flow have been performed by numerous authors. Therefore, various quantities are available to assess the accuracy of the LES approach, such as averaged velocity and velocity fluctuations profiles and kinetic energy spectra.

Participants are expected to perform the computations for a set of structured grids which will be provided on request. Additional computations on unstructured meshes are also welcome. The assessment criteria include spatially and temporally averaged wall normal variations of the velocity and its correlations.

The participants are expected to use the meshes - structured, unstructed, and 2D extruded - provided by the test case leader in order to ensure similar grid spacing near the wall for all participants. These will be generated/provided on request as a function of the interpolation used by the discretisation method.

**NOTE: This test case is slightly different from the previous edition.**- Read more about WS2 LES of the plane channel at Ret=550
- Log in to post comments