Long ago, I needed to install the EXPRESS version of MSSQL 2008 (oh i am using MSSQL 2014 nowadays) and that version dictates to get installed with a named instance, but i needed to have it as default instance to run it properly under Tomcat. I have the following ROOT.xml of Catalina tomcat and the followings snippets are the solution:
With the default instance:
With the named instance, you need to specify the instance: