The role of residuals in determining if simulation results are to be trusted should not be misunderstood. Reaching steady residuals means that the solution has converged to a value. Whether this value is correct or not can ultimately be concluded by monitoring the solution field.
There are a number of factors that could cause large pressure residuals. You could perform a convergence study to determine if results are reliable. In case of this simulation, consider the following:
- Mesh quality could impose a lower limit on residual values. Even though your mesh looks good, convergence of the solution by refining the mesh should be studied. Specifically consider boundary vicinity and regions of high gradient.
- Linear solvers have an impact on convergence behavior. You could try a different solver for pressure to see if residuals change.
- Absolute and relative residuals must be considered carefully. We have had a discussion on this here. As demonstrated, residuals must be chosen in accordance with all variables. In your case, relative pressure residual could be reconsidered.
This list is in fact longer. You could reconsider the choice of the turbulence model, turbulence wall treatment, numerical schemes, etc. However, be aware that the residual value in itself is not the issue, e.g. one could under-relax to get smaller residuals, but this does not improve the solution. Whatever you do, convergence of the solution field is the deciding factor.