Making linearized methods in fluid mechanics available to a broader audience with FEniCS

In fluid mechanics research, linearizing the governing equations around a base state has yielded significant insight in flow unsteadiness, as for example turbulence. The principles of these linearized methods go back to the 19th century to illustrious names, such as Helmholtz, Rayleigh, Kelvin and Reynolds. Despite over a century of successful application of the linearized Navier–Stokes equations in research to understand countless different forms of flow unsteadiness, its full potential for application in academia and especially industry up to today remains not exhausted by far: Although research groups around the globe successfully develop and apply in-house codes to address various unsteady flow configurations using the linearized equations, no common coding-platform exists that enables these groups to share their expertise and benefit from each other's developments, both in modelling and coding. As a consequence, the hurdle of applying such tools to a new configuration is high, which makes the method—despite its potential—unattractive to researchers which are new to this field and fluid mechanics engineers. With our solver FELiCS (Finite-Element Linearized Combustion Solver, not to be confused with FEniCS), our goal is to fill this gap, and make the rich toolbox of linearized methods available to a broader audience. Our code uses the FEniCS package in order to discretize the governing equations in space, which together with the python environment, and efficient toolboxes, such as SLEPc and ARPACK is the ideal framework for our purposes. Currently, the code is applied to various configurations, such as investigating turbulence in jet flows, hydrodynamic instabilities, such as eg the cylinder vortex street, and laminar and turbulent combustion dynamics. Our talk will give an overview of linearized methods in fluid mechanics as well as current and potential application fields.