Field Programmable Gate Arrays generate algorithmic specific architectures that improve the codes' FLOP per watt ratio. Such devices are re-gaining interest due to the rise of new tools that facilitate their programming, such as OmpSs. The computational fluid dynamics community is always investigating new architectures that can improve its algorithms' performance. Commonly, those algorithms have a low arithmetic intensity and only reach a small percentage of the peak performance. The sparse matrix-vector multiplication is one of the most time-consuming operations on unstructured simulations. The matrix's sparsity pattern determines the indirect memory accesses of the multiplying vector. This data path is hard to predict, making traditional implementations fail. In this work, we present an FPGA architecture that maximizes the vector's re-usability by introducing a cache-like architecture. The cache is implemented as a circular list that maintains the BRAM vector components while needed. Following this strategy, up to 16 times of acceleration is obtained compared to a naive implementation of the algorithm.