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We study the accretion processes on a black hole by a numerical simulation. We use a grid‐based finite difference code for this purpose. We scan the parameter space spanned by the specific energy and the angular momentum and compare the time‐dependent solutions with those obtained from theoretical considerations. We found several important results. (a) The time‐dependent flow behaves close to a constant height model flow in the pre‐shock region and a flow with vertical equilibrium in the post‐shock region. (c) The infall time‐scale in the post‐shock region is several times higher than the free‐fall time‐scale. (b) There are two discontinuities in the flow, one being just outside of the inner sonic point. Turbulence plays a major role in determining the locations of these discontinuities. (d) The two discontinuities oscillate with two different frequencies and behave as a coupled harmonic oscillator. A Fourier analysis of the variation of the outer shock location indicates higher power at the lower frequency and lower power at the higher frequency. The opposite is true when the analysis of the inner shock is made. These behaviours will have implications in the spectral and timing properties of black hole candidates.

Hydrodynamic simulations of oscillating shock waves in a sub‐Keplerian accretion flow around black holes