Thank you for your efforts and time to my post!

I was aware of the example mentioned, it was very helpful, while I am not very sure if I face the same problem. Because I suppose since u and v in my case are the results the model solved, and Fx is not loaded from other models where mesh or interpolation methods could be different, therefore they might have to be in the same dimension with other variables. Please correct me if I am wrong.

I attach my model here for your information, since it is a very general model that can be used in others' cases as well. and the logic is elaborated in the following.

two-fluid model**It is a classic two-fluid model, where two phase fluids interpenetrate one another (i.e. smoke in air, suspended particles in water, etc. if someone is interested, i suppose this logic can be extended to 3 phases as well). one of the two fluids is under external force in a certain region. this force will drive this fluid to move. and the relative movement between two fluids will induce the other fluid to move by friction. My interest is the evolution of the concentration of the two phases.**the equations i used are two NS, with one convection-diffusion. therefore there are 7 variables to be solved in total in a 2D geometry: velocities and pressure for each fluid, and the concentration for one of the fluids. The equations are edited accordingly (please refer to my model). one of the main editions is that in the mass conservation, the concentration has to be included, as if each fluid is compressible

**in each grid**.

besides, the two NS are coupled by the stokes drag force. the force is a function of relative velocity (u1-u2 and v1-v2) and concentration phi.

**Here come the questions: what might be the variable that is not in the same dimension with others? And can I generate a m. file so that I can check the dimension of each variable in matlab?**Thanks again to everyone that reads here. I wish this is helpful to you.