At this stage it is assumed you have created a GRASS project in UTM projection and imported the DEM for your area in that project.
Create a new GRASS project in the same database as your UTM project.
Let's assume the name is AREA_LL and mapset PERMANENT.
The projection needs to be Lat/Lon, the area boundaries are not important.
The resolution can also by any for now.
The datum should wgs84 and parameter should be 1.
Once you have entered the AREA_LL project, import the elevation spheroid as below;
"r.in.ascii input=~arsf/dems/geoid-spheroid/ww15mgh.grd output=wwgsg"
Now you can exit AREA_LL, go back to your UTM project
Import/Re-project the elevation spheroid as below;
"r.proj -n input=wwgsg location=AREA_LL mapset=PERMANENT output=wwgsgUTM"
Now elevate the DEM by adding the spheroid;
"r.mapcalculator amap=yourDEMmap bmap=wwgsgUTM formula=A+B outfile=yourelevatedDEMmap help=-"