ovs-ofctl add-flow <switch1> "arp,actions=flood"
ovs-ofctl add-flow <switch1>
"in_port=1,ip,nw_dst=172.16.2.1,actions=output:2"
ovs-ofctl add-flow <switch1>
"in_port=2,ip,nw_dst=172.16.1.1,actions=output:1"

ovs-ofctl add-flow <switch2> "arp, actions=flood"
ovs-ofctl add-flow <switch2>
"in_port=2,ip,nw_dst=172.16.2.1,actions=output:1"
ovs-ofctl add-flow <switch2>
"in_port=1,ip,nw_dst=172.16.1.1,actions=output:2"

Assuming the switches use port 1 towards the containers, and port 2 to
connect to each other.

Then, ARP will work easily, and your hosts will know the MAC address of
each of them.
Pinging will also work according to the IP addresses!

Again, in case they are in different IP range, then other rules are
necessary, but I recommend to play first within Layer 2, then migrate
your use case to Layer 3 - as it is a little bit more complicated.