Examples of Mori dream surfaces of general type with $p_g=0$

We provide examples of minimal surfaces of general type with $p_g=0$ and $K^2=2,3,\dots,8,9$ which are Mori dream spaces. On these examples we also give explicit description of their effective cones with all negative curves. We also present non-minimal surfaces of general type with $p_g=0$ that are not Mori dream surfaces. This is a joint work with Kyoung-Seog Lee.