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Module Development Konstantinos G. Kyprianidis 3.5 LISIS In this section, details are given on the development of LISIS, a numerical meth- ods library for use by the developed engine performance code, as well as HERMES and HEPHAESTUS. The library was developed with the purpose of improving the computational speed and stability of these codes, as well as to eliminate the numerical noise problems hindering VITAL TERA2020 optimisation capability. As part of this research effort, an improved gradient-based algorithm for solving non-linear equation systems is proposed. 3.5.1 General objectives The general objectives set during the development of the LISIS library are: • Provide a generic interface to the library in order to be used by different codes without modifications. • Improve computational speed compared to existing implementations within VITAL TERA2020. • Reduce the frequency of non-convergence cases compared to existing im- plementations within VITAL TERA2020. • Eliminate the numerical noise problems hindering VITAL TERA2020 op- timisation capability. 3.5.2 Code development For engine performance steady state simulations an algebraic equation system may be formed (see for example Fawke and Saravanumuttoo [151]) and is typ- ically solved using a gradient-based root-finding method. Non gradient-based methods may also be employed for solving non-linear equations; their success will largely depend on the particulars of the system they are applied to. Per- haps the simplest gradient-based method available for solving multidimensional problems is the Newton-Raphson method [152]; it uses the Jacobian matrix to 66PDF Image | Multi-disciplinary conceptual design of future jet engine systems
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