Wireless Mesh Networks (WMNs) are ad-hoc networks where no infrastructure exists and where some of the participating nodes can also act as routers to forward traffic on behalf of others. WMNs have been proposed for various applications and can greatly vary in terms of size (from a handful of nodes to thousands) and complexity (static or mobile nodes, scarce or dense etc.). Efficient and robust IP routing is essential for these networks and its performance can greatly affect all other network performance metrics such as throughput, delay, packet delivery ratio etc. A lot of routing algorithms have been proposed ever since the advent of WMNs and research is still ongoing on the topic. All of the proposed solutions are based on the principle of distributed routing where routers exchange signalization messages in order to discover the network topology. In the present paper we propose a centralized routing based on the relatively recent paradigm of Software Defined Networking (SDN). We have used NS3 to simulate a dynamic mesh network where a subset of nodes are mobile and a source host generates traffic destined to a sink host. We evaluated four common network performance metrics namely packet delivery ratio, packet drop ratio due to route unavailability, average throughput and signalling overhead. By making appropriate assumptions, we compared our solution with three of the most widely used routing protocols for WMNs namely DSDV, AODV and OLSR. Our simulations demonstrate that, under certain conditions, our solution outperforms the aforementioned distributed routing algorithms and can improve network performance.