Nice mausoleum wall!
For a completely basic/fast secure, I'd likely use either rebar or stakes driven in the ground behind it, then running very small holes at the very bottom where they won't be seen easily and securing to the post/stake with fishing line or zip ties. But if you have VERY windy conditions, then that won't work as well.
Next option I'd try would be to glue along the bottom length a wood 1x2 and then screw through the front into the wood and attach THAT to stakes driven into the ground. The wood 1x2 would provide stability and weight to the bottom and allow you to attach things easier to further stabilize it. If the wall is in sections, I'd just cut the 1x2 into slightly smaller than the width of each section, glue down using something like liquid nails and then use a self tapping screw to go through the front into the wood strip and previously placed stake.
Or if you completely can't deal with cutting wood (I couldn't for a while as power tools were outside my comfort zone for years), my workaround was getting cheapy wooden stakes and just pounding them into the ground along the front and back, leaving about 2 foot or so above ground. I would make sure they were painted to match whatever surface they were meant to be holding, and then wedging the wall/structure between them. You want the space between them to be really tight so it pinches the wall in there - any gaps and the wall isn't really being helped that much, so it may take a few tries to get the angle of the stakes and the snugness needed. It works surprisingly well if the top is secured, so this may be the easiest/quickest option to try. If you look closely at the photo below, you can see my stakes holding up the circus tent walls in the red stripey areas. There are corresponding stakes on the back of the wall too. These held up really well in stormy conditions, so it may work for you.
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Foamcore sheets are quite difficult to stabilize against really windy conditions if you don't have them glued down to a more stable surface like plywood sheets, but hopefully you can figure out something that will work.
