# Algorithmic Differentiation of Different Algorithms for the Same Problem: A Case Study.

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## Abstract

Large-scale numerical simulation is one of the basic blocks in computational science and engineering. Researchers in academia and industry rely on highly complex simulation codes that are able to simulate even the most complicated physical phenomena. Several approaches are possible in order to validate the results of a numerical simulation, such as examining the results obtained from different simulation packages. In addition one could analyze the impact of certain input parameters on the solution. Such sensitivities of the computed solution can be obtained by automatic differentiation, a technique for computing truncation error-free derivatives of functions given in the form of a computer program. For a standard flow problem, we examine the results obtained from the two simulation packages FLUENT and SEPRAN, and we compare the derivatives which are computed by automatic differentiation. We show that, although the two packages employ fundamentally different algorithms, the results obtained, i.e., the velocity fields and their respective sensitivities, are comparable.