It turns out "advanced" is a bit of a conundrum.
1. Sometimes different simulators are very good (or the best) at different things. Something good for computational fluid dynamics (CFD) may not be the best thing for figuring out energy transfer.
2. Commonly different simulations have different ways of implementing things. This is not quite my sub-area of simulation, but I did work on a short (approx 1/2 time for 1 year) project some time ago that modeled mass and energy transfer. (A package called CTH - out of Sandia, IIR.) Anyway, you can set up problems in one of two fundamentally different ways - you can model elements of matter moving about, or you can model fixed position cells and the matter that passes between them. These can often give the comparable results, but not always.
3. Different simulations can look at reality from different levels. Some simulations model some model gravitation really well, some model mass-energy transfer, some model magnetism. (I imagine there are simulators that are really good with QM effects, but I don't have any experience at that.)
What might be useful is for you to figure out what you would like to do and then look for specific packages that can address that particular interest. Generally, the free packages are not going to have very good support, are not going to have a good interface, and may not have really good sample input data.
However, there is a freeware package that I have only used a little bit called ROOT ( root.cern.ch ) that is easy to install and easy to program. Also, when I had trouble I emailed the general group and the main author answered me within hours. Be forewarned: just because you have this package, it doesn't mean you can avoid learning a lot of math and computer science as well.
ROOT is a programming language that is a subset of C++, but it's interpreted, making devolopment a little quicker than is common. It requires Cygwin ( a linux emulator) if you want to run it under windows. (It's also VERY slow for 3D graphs if you're in emulation.) I would guess it runs a LOT quicker directly under Linux.
It's not so much a simulator itself, as a programming environment with predefined classes that allow you to build in the functionality you need.
good luck
