I am wondering which kind of circuit is that and what is does when +-Vin is applied on the input. The output of the circuit is cathode of D26/R30/C52 node. Thank you.
It's a precision half wave rectifier.
It can be considerably improved by connecting another diode with cathode to the op-amp output and anode to the inverting input. This stops the output slewing towards the negative rail when the input is positive.
Note that the output impedance is not symmetrical. It's low for positive going output but 10k otherwise. This can cause unexpected problems if unbuffered.
A possible better solution is a full wave precision rectifier using 2 op-amps.
This is a full-wave precision rectifier. When a negative voltage is applied to the input it acts as an inverting amplifier, so Vout = -Vin. When a positive voltage is applied, the op-amp rails near the negative supply rail and the positive voltage finds it's way to the output, Vout = +Vin (if loading is minimal on the output).
The op-amp output has to slew all the way from near the negative rail to +0.6V at the negative-going zero crossings so it's not going to be great at high frequency. The capacitor also doesn't help with high frequency response but it may help with stability. Op-amps which are railed don't necessarily come out of saturation, and start slewing, as quickly as one might hope- and any measure of that is often omitted from the datasheet information, particularly if it is bad.
Also, some op-amps behave differently in this configuration because of protection diodes between the inverting and non-inverting inputs, so current flows through R31.
Edit: See below for simulation of this working.