A320 CREW HAD #2 ENG FAILURE NEAR PHX.

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ON ARR INTO PHOENIX; AT FLT LEVEL 350; APPROX 160 DEGS NM NE OF PHX ON THE BUNTR ARR; WE GOT AN ECAM CAUTION ENG 2 COMPRESSOR VANE. THE ECAM ADVISED US TO AVOID THRUST CHANGES. WE HAD BEEN CLRED TO DSND TO FL290; SO NOT CHANGING THRUST WAS CERTAINLY NOT AN OPTION; AND YET THE ECAM DID NOT SPECIFICALLY TELL US TO SHUT IT DOWN. WE DID A GRADUAL DSCNT DOWN TO FL290. AS WE LEVELED OFF; THE ENG #2 N2 WENT UP TO ABOUT 99%; AND THE EGT FLUCTUATED; BUT THE ENG SEEMED TO STABILIZE ABOUT EVEN WITH #1 ENG. WE CONTINUED ON FOR A COUPLE OF MORE MINS; KEEPING A CONSTANT EYE ON THE ENG PARAMETERS; WHEN SUDDENLY THE EGT SPIKED; THE N2 WENT UP ABOVE 100%+; AND AFTER A COUPLE OF BUMPS; WHICH I SUSPECT WERE COMPRESSOR STALLS; THE ENG STALLED COMPLETELY. AT THAT POINT; WE FOLLOWED THE ECAM PROCS; WHICH INCLUDED THE ENG SHUT DOWN PROC. CONSIDERING THAT THERE HAD BEEN NO FIRE; AND THAT NONE WAS INDICATED; THE DECISION WAS MADE TO NOT USE THE FIRE EXTINGUISHERS. WE ALSO DECIDED THAT BECAUSE OF THE WAY THE ENG SHUTDOWN AND THE UNSTABLE PARAMETERS INDICATED PRIOR TO SHUTDOWN; RESTARTING THE ENG; AT LEAST AT THIS POINT; WAS PROBABLY NOT A GOOD IDEA. WE CALLED MAINT AND DISPATCH; AND ADVISED THEM THAT WE WOULD BE COMING HOME ON 1 ENG. WE THEN BRIEFED THE FLT ATTENDANTS THAT WE WOULD BE MAKING A PRECAUTIONARY LNDG IN PHOENIX IN ABOUT 20 MINS. AFTER TALKING TO THE PAX; WE REVIEWED EVERYTHING WE HAD DONE UP TO THIS POINT; AND SATISFIED THAT WE HAD DONE ALL THAT WE COULD WITH THE ENG; WE PREPARED FOR A SINGLE ENG LNDG. THE FO BRIEFED THE VISUAL APCH; AND WE SET THE ACFT UP FOR A FLAPS 3 LNDG; USING MEDIUM AUTOBRAKE. A NORMAL APCH PROFILE AND LNDG WAS MADE TO RWY 26 IN PHX. PAX WERE ADVISED THAT THE SIT WAS UNDER CTL; AND THAT WE WOULD BE TAXIING TO THE GATE. BRAKE TEMPS WERE MONITORED; AND BRAKE FANS WERE TURNED ON AS WE TAXIED TO THE GATE; WHERE WE SHUT THE ACFT DOWN AND HANDED IT OVER TO MAINT. PAX WERE DEPLANED THROUGH THE JETWAY; AND CREW MEMBERS WERE DEBRIEFED; AND WE ALL WENT ON OUR WAY.