In some aspects, techniques and systems for modeling fluid flow are described. A flow model represents intersecting flow paths for well system fluid. The flow paths intersect at a flow path intersection. A band matrix and an intersection table are generated based on the flow model. The band matrix represents fluid flow within the respective flow paths, and the intersection table represents fluid flow between the flow paths at the flow path intersection. The flow model can be operated using the band matrix and the intersection table, for example, to calculate fluid flow variables at various locations along the flow paths.