Even if flow is inviscid, recirculation will be introduced due to artificial viscosity (from numerical schemes and spatial discretization) which in turn will create vorticities. So there will be "separation" behind objects.
Solving the potential equation will yield the results you expect as irrotationality of the flow is assumed. Since you have a simple case, to get an idea of what the flow field would look like you can initialize using hybrid initialization which does that; solves Laplace's equation to obtain the velocity field.
Otherwise you can limit this artificial viscosity by further refining the grid and using higher order discretizations, which might still not completely give you what you want.
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