It just happens to be very complicated. You're right in that it's a mixture of E&M, thermodynamics, and fluid mechanics. Whether it becomes computationally prohibitive to model is something I am unsure of, but may be possible with some simplifying assumptions.
Edit: after a bit more research, I found a paper where, if I follow correctly, they are laying out a framework for creating such a model: http://arxiv.org/abs/1004.1611
It just happens to be very complicated. You're right in that it's a mixture of E&M, thermodynamics, and fluid mechanics. Whether it becomes computationally prohibitive to model is something I am unsure of, but may be possible with some simplifying assumptions.
Edit: after a bit more research, I found a paper where, if I follow correctly, they are laying out a framework for creating such a model: http://arxiv.org/abs/1004.1611