How to replicate sessions between two web applications on the same tomcat?

I have two web applications (simply called app1 and app2 in the following) on the same tomcat, and sometimes app1 will be re-deployed.
Is there a way to replicate the session from app1 to app2 when app1 is down, and recover it back when app1 comes back?
I have tried surveying keywords like "session migration" and "clustering".
But it seems that they are used in the situation of putting the web applications on different tomcat servers.
I don't know how to try it in the same tomcat server with different web applications...

Thanks!