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- BL2 - Laminar shock-boundary layer interaction
- BL3 - Heaving & pitching airfoil
- BR1 - RANS of Joukowski airfoil
- BS1 - Taylor-Green vortex, Re=1600
- BS2 - LES channel flow Ret=590

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# Test cases

## AR1 - RANS of the Common Research Model (5th AIAA Drag Prediction Workshop)

The common research model (CRM) is a wing-body configuration which was extensively studied with state-of-the-art CFD codes in the fifth drag prediction workshop (DPW-5 - http://aaac.larc.nasa.gov/tsab/cfdlarc/aiaa-dpw/Workshop5/workshop5.html).

The CRM is considered under transonic cruise conditions. The flow is assumed to be steady-state and fully turbulent. Computations are to be performed in a target lift mode, i.e., given a specified lift coefficient, the corresponding angle of attack has to be determined. The objective of the simulations is to obtain mesh-converged drag and moment coefficient values as well as pressure distributions in sections along the wing span.

In previous editions of the workshop on high order CFD methods, only second order DG results have been provided, thus a higher order contribution or at least some mixed order (e.g. in the form of hp-adaptive results) is highly welcome. Meshes will be provided upon request.

## AR2 - RANS of the transonic turbulent flow in a 3D channel with a swept bump

The objective of the present test case is to analyze the field resulting from a 3D shock wave /boundary layer interaction occurring in a 3D channel with a swept bump. In this case, the interactions taking place with the boundary layers of the four walls can lead to the formation of several separations which are at the origin of vortical structures cause of intense secondary flows.

Participants are expected to perform grid refinement studies or hp-adaptive computations using a RANS model of choice. The target quantities of interest are the static pressure distribution on the walls, the turbulent kinetic energy profiles and the mean stream-wise velocity profiles in longitudinal planes. Meshes will be provided at request.

## AS1 - DNS/LES of the infinite cylinder at Re=3900

This test case concerns the flow over an infinitely long cylinder at a Reynolds number of 3900, which is simulated using a spanwise periodic mesh. This test case is aimed at characterizing the accuracy and efficiency of high order solvers for the prediction of complex unsteady multi-scale problems under low Reynolds number conditions.

An infinitely smooth initial condition with a bias in the spanwise and vertical direction is imposed. Two flow regimes are of interest for the results:

**Deterministic phase**. The unsteady solution at a predefined time t1, before any chaos or turbulence starts, will be used to assess the spatial and time accuracy of the flow solver. The bias is designed to ensure that the non-symmetric flow is not a consequence of round-off or truncation errors. Since this period is expected to be relatively small, hp-refinements or adaptations can be employed to obtain accurate Cl and Cd (error < 0.01 count) values to assess solution spatial and temporal accuracy;**Turbulent flow**. After the flow reaches a statistically periodic state at t2, averaged quantities and Reynolds stresses are computed until a given time t3 for comparison purposes.

Three meshes with different resolutions are provided; participants may use hp-adaptation in the first phase.

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## AS2 - Spanwise periodic DNS/LES of transitional turbine cascades

This test case concerns the spanwise periodic DNS or LES of the transitional and separated flow on the T106A and T106C subsonic turbine cascades. These are well-known test cases for assessing transition models for low Reynolds numbers. The first test case concerns the T106A at Re=60.000, while the T106C is computed at Re=80.000. As the inlet turbulence is very low, both flows feature laminar separation and transition in the reattachment zone or in the wake.

Participants should run both cases on either a suite of block-structured or unstructured hexahedral meshes, which will be generated and provided on request.

## BI1 - Inviscid vortex transport

The test case concerns the long term transport of a vortex by a uniform base flow over a quadrangular, doubly periodic domain. This problem is aimed at testing a high-order method’s capability to preserve vorticity in an unsteady inviscid flow. Accurate transport of vortexes at all speeds (including Mach << 1) is very important for Large-Eddy and Detached-Eddy simulations, possibly the workhorse of future industrial CFD simulations, as well as for aeronautics/rotorcraft applications.

This test case has been part of the workshop since the beginning, so participants are requested to use at least the meshes from the previous workshops.

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## BI2 - Inviscid flow over a bump

This test case concerns the subsonic flow over a smooth Gaussian bump in a channel. This problem is aimed at testing high-order methods for the computation of internal flow with a high-order curved boundary representation. In this subsonic flow problem, the geometry is smooth, and so is the flow.

The entropy should be a constant in the flow field. The L2 norm of the entropy error is then used as the indicator of solution accuracy since the analytical solution is unknown. The convergence rate can be expected to be P+1, where P is order of the discrete polynomial approximation.

Mandatory grid convergence studies should be run on a sequence of structured meshes, which will be provided upon request. The resolution sequence will be adapted to the method. Additional computations on unstructured meshes are expected if the method permits.

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## BI3 - Inviscid bow shock

The detached bow shock upstream of a 2D simple blunt body in inviscid conditions is studied. This case is designed to isolate testing of the shock-capturing properties of schemes. This case is computationally expedient, being steady, two-dimensional, inviscid flow, with well-defined boundary conditions.

The geometry is a flat center section, with two constant radius sections top and bottom. While the flow is symmetric top and bottom, a full domain is computed to support potentially spurious behavior. The aft section of the body is not included to avoid developing an unsteady wake. Two sets of structured meshes are provided. For finite volume type codes, straightsided meshes in CGNS are provided, whereas for finite element like methods, a series in gmsh format is provided, derefined as a function of the order of accuracy N. Participants can additionally provide results on unstructured meshes.

The assessment criteria include the conservation of total enthalpy as well as the comparison of stagnation pressure with respect to theory.

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## BL1 - 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. Participants are required to use a sequence of provided grids, as they have been demonstrated to be able to provide the optimal convergence rate in drag. A low Reynolds number of 1,000 is employed to emphasise the viscous terms. For an adjoint consistent discretization, the optimal convergence rate is 2P. Otherwise, the convergence rate can be expected to be P+1.

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## BL2 - Laminar shock-boundary layer interaction

This test case considers the interaction between an incident oblique shock wave impinging a laminar boundary layer developing over a flat plate. The interaction produces a separation of the

flow and a subsequent recirculation bubble. The free stream Mach number is 2.15 and the lengthwise Reynolds number at the shock impingement location is 105. In this configuration, the flow remains 2D and stationary.Participants are required to perform a grid/order convergence study, demonstrating convergence of the drag coefficient of the full plate, as well as the separation and reattachment point locations. Furthermore the pressure and friction coefficient along the plate will be compared. Computations should be run on a predefined mesh sequence, which will be provided on request. Additional unstructured mesh computations will also be considered.

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## BL3 - Heaving and pitching airfoil

This problem is aimed at testing the accuracy and performance of high-order flow solvers for problems with deforming domains. A NACA 0012 airfoil is undergoing a smooth flapping-type motion, starting from rest at zero angle of attack and ending at a position one chord length higher. The metrics used to assess the accuracy of the solution are the total energy (i.e. integrated power) extracted from the flow during the motion and the vertical impulse imparted on the airfoil by the flow (integrated vertical force). The viscosity is constant and the Reynolds number with respect to the chord length is Re=1000.

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