Numerical simulation of accretion discs in close binary systems and discovery of spiral shocks

The history of hydrodynamic numerical simulations for accretion disks in close binary systems is reviewed, in which emphasis is placed, in particular, on the facts that spiral shock waves were numerically found in 1986 by researchers including one of the present authors and that spiral structure was discovered in IP Pegasi in 1997 by Steeghs et al. The results of our two and three-dimensional numerical simulations in recent years are then summarized, with comparison being made with observations.