There are multiple easy ways.
Just touch web.xml of any webapp.
touch /usr/share/tomcat/webapps/<WEBAPP-NAME>/WEB-INF/web.xml
You can also update a particular jar file in WEB-INF/lib and then touch web.xml, rather than building whole war file and deploying it again.
Delete webapps/YOUR_WEB_APP directory, Tomcat will start deploying war within 5 seconds (assuming your war file still exists in webapps folder).
Generally overwriting war file with new version gets redeployed by tomcat automatically. If not, you can touch web.xml as explained above.
Copy over an already exploded "directory" to your webapps folder