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Numerical simulation of complex computational fluid dynamics problems evolving in time plays an important role in scientific and engineering applications. Accurate behavior of dynamical systems can be understood using large scale simulations which traditionally requires expensive super-computing facilities. In the paper a Field Programmable Gate Array (FPGA) based framework is described to accelerate simulation of complex physical spatio-temporal phenomena. Simulating complicated geometries requires unstructured spatial discretization which results in irregular memory access patterns severely limiting computing performance. Data locality is improved by mesh node renumbering technique which results in a sequential memory access pattern. Additionally storing a small window of cell-centered state values in the on-chip memory of the FPGA can increase data reuse and decrease memory bandwidth requirements. Generation of the floating-point data path and control structure of the arithmetic unit containing dozens of operators is a very challenging task when the goal is high operating frequency. Efficiency and use of the framework is described by a case study solving the Euler equations on an unstructured mesh using finite volume technique. On the currently available largest FPGA the generated architecture contains three processing elements working in parallel providing 75 times speedup compared to a high performance microprocessor.