Context : Eccentric accretion disks in superoutbursting cataclysmic and other binary systems .

Aims : We study the development of finite eccentricity in accretion disks in close binary systems using a grid-based numerical scheme .
We perform detailed parameter studies to explore the dependence on viscosity , disk aspect ratio , the inclusion of a mass-transfer stream and the role of the boundary conditions .

Methods : Using a two-dimensional grid-based scheme we study the instability of accretion disks in close binary systems that causes them to attain a quasi-steady state with finite eccentricity .
Mass ratios 0.05 \leq q \leq 0.3 appropriate to superoutbursting cataclysmic binary systems are considered .

Results : Our grid-based scheme enables us to study the development of eccentric disks for disk aspect ratio h in the range 0.01 - 0.06 and dimensionless kinematic viscosity \nu in the range 3.3 \times 10 ^ { -6 } -10 ^ { -4 } . Previous studies using particle-based methods were limited to the largest values for these parameters on account of their diffusive nature .
Instability to the formation of a precessing eccentric disk that attains a quasi-steady state with mean eccentricity in the range 0.3 - 0.5 occurs readily .
The shortest growth times are \sim 15 binary orbits for the largest viscosities and the instability mechanism is for the most part consistent with the mode-coupling mechanism associated with the 3:1 resonance proposed by Lubow .
However , the results are sensitive to the treatment of the inner boundary and to the incorporation of the mass-transfer stream .
In the presence of a stream we found a critical viscosity below which the disk remains circular .

Conclusions : Eccentric disks readily develop in close binary systems with 0.05 \leq q \leq 0.3. Incorporation of a mass-transfer stream tends to impart stability for small enough viscosity ( or , equivalently , mass-transfer rate through the disk ) and to assist in obtaining a prograde precession rate that is in agreement with observations .
For the larger q the location of the 3:1 resonance is pushed outwards towards the Roche lobe where higher-order mode couplings and nonlinearity occur .
It is likely that three-dimensional simulations that properly resolve the disk ’ s vertical structure are required to make significant progress in this case .