Maybe, you have to use optimal mesh which the results don't change significantly  with increasing mesh. Good luck.

Does this difference shown in every physical quantities or just one or a few? I once run a simple lubrication flow and found the similar phenomenon as yours. But only in streamline/velocity, not in pressure. Soon figure out that the triangular mesh not suitable for this problem if I need to see stream line

Hi Samane, There are many ways to get convergence. I would suggest you to first solve a reference problem. Verify your results with published results. Use both triangular and brick mesh to check for convergence. usually problem comes when you get high gradients in some regions. You can also try adaptive mesh refinement option given in study step which works only with triangular mesh elements. This is will generate additional mesh elements in high gradient regions automatically and you will get improved solution with each iteration of adaptive mesh refinement . This way you can be sure about the solution obtained.  

It's always better to use AMR with varying the initial mesh sizes and then use the finner one to perform simulation. In some cases u cant find best solution when mesh size stops to effect the solution. In those cases u mention ur DOF solved for along with number of elements, maximum mesh size and time step in the paper to ensure reviewers that u have used enough discretization.