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Numerics testing: solving Euler flows using a Navier-Stokes solver
Problem description
Inviscid incompressible flow around a cylinder and an ellipse.
Physics and modelling
Potential flow, laminar incompressible flow with zero viscosity.

Potential flow problems can be solved accurately using potentialFoam, available in the standard release. However, it is in principle possible to solvethe same problem using a Navier-Stokes solver and setting the viscosity to zero. In this case, every discretisation issue will be clearly visible (most pressure-velocity segregated CFD codes blow up the moment you set the viscosity to zero) The objective of the exercise is to examine the accuracy of discretisation in OpenFOAM, both visually and in absolute terms (this is possible as the analytical value of lift and drag for both geometries is zero). We shall list the lift and drag values both for Upwind Differencing (UD) for reference and the best discretisation available in OpenFOAM. In both cases, the “numerical drag” for second-order discretisation is about 2% of the one for the first order scheme. Also, the solution shows that the navier-Stokes solver causes no distortion of the flow field.

Flow around a cylinder


Discretisaton Drag [N/m width]


1st order (UD) 297.28
2nd order (Gamma2V) 6.73


Flow around an ellipse


Discretisaton Drag [N/m width]


1st order (UD) 1105.28
2nd order (Gamma2V) 180.46


OpenFOAM solver
potentialFoam, icoFoam.


Inviscid flow around a cylinder
Figure 1: Inviscid flow around a cylinder



Inviscid flow around an ellipse
Figure 2: Inviscid flow around an ellipse


Author
Simulation by Nabla Ltd.