in that case the shock front will oscillate (Figs. 2c, 2f). If the angular momentum piling results in too strong centrifugal barrier, it could drive the shock out of the computation domain.

It may be noted that we are simulating the inner part of the disc, the inner few $\times~10r_g$ of the disc. And, therefore the injection parameters are similar to the inner boundary conditions of an accretion disc. Since matter entering a black hole has angular momentum, typically $1 \lsim \lambda \lsim 2$, our chosen angular momentum are also of the same order. However, at the outer edge angular momentum may reach very high value depending on $\alpha$. For example, with injection parameters $r_{\rm inj} = 50.4$, $v_{\rm inj} = - 0.06436$, $a_{\rm inj} = 0.06328$, and ${\lambda}_{\rm inj} = 1.63$, one can integrate the effective one dimensional equations of motion to estimate the angular momentum at the outer boundary and it is typically around $45~r_gc$ at $r_{\rm out} \sim 4000~r_g$.

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![image](fig3.eps){width="90.00000%"}

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From Figs. 2c-2e, it is clear that the shock can experience persistent oscillation for some critical viscosity and injection parameters. But the shock front is a surface and that too not a rigid one. Therefore, 