We present a model checking approach for verifying the correctness of concurrency in numerical models. The forms of concurrency we address are from (1) coupled modeling where distinct components, e.g., ocean, wave, and atmospheric, exchange interface conditions during runtime, and (2) multi-instance modeling where local variations of the same numerical model are executed concurrently to minimize common (and therefore redundant) computations. We present general guidelines for representing these forms of concurrency in an abstract verification model and then apply them to an adaptive ocean circulation model that determines the geographic extent and severity of coastal floods. The ocean model employs multi-instance concurrency: a collection of engineering design and failure scenarios are concurrently simulated using patches, regions of a grid that grow and shrink based on the hydrodynamic changes induced by each scenario. We show how concurrency inherent in the simulation model can be represented in a verification model to ensure correctness and to automatically generate safe synchronization arrangements.