On the research

The first image shows a streamline plot of constant wind. There is no polar outflow, however, there is a circumbinary disk. Fluid parcels start in polar region just fall onto the disk. The disk looks stable as the red streamline means the fluid parcel position in later time.

The second image shows a streamline plot of dense shell wind. The disk is not stable as there is no limit circle around it. There is no red lines in the streamline indicating that the fluid parcel just run away.

Below shows a polytropic wind with gamma=1.35 . The wind start at 0.5 AU, 1500 K with 20km/s. It drops to about 300 K at 10 AU. This simulation is done with my 1D spherical Riemann Solver.

Heat can be transported by conduction, convection and radiation. High order Riemann solver can handle convection very well. Conduction is not important in the exterior region of star but important in interior (very deep, can be estimated). Radiation is the most important heat transfer mechanism in low density region, for Local Thermal Equilibrium (LTE) situation, Monte Carlo (MC) method is the best both for multi-dimension and 1D. In non-LTE situation, people sometimes use particular cooling function, for example, hydrogen cooling or any other molecular cooling, there are also MC model for non-LTE but I need to research more.

In general, MC method is universal in simulating radiative transfer.

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