hp-Adaptive discretization

A key challenge when simulating complex flow phenomena is a temporal and spacial variation in the require resolution. In turbulent flow problems, the appearance of boundary layers, shear layers or complex wake flows and the associated decay of flow structures along a wide range of scales impose a very high resolution requirement. Further, in the transsonic and supersonic regime, as well as in the presence of phase interfaces, discontinuous solution features like shocks or material interfaces need to be captured and localized.
To tackle these challenges, we developed a hybrid hp-adaptive Discontinuous Galerkin/Finite Volume operator. It exploits the high-order convergence and scale resolving capabilities of the efficient Discontinuous Galerkin Spectral Element Method (DGSEM) with the robust Finite Volume (FV) method, well suited for shock and interface capturing. Based on a error and smoothness indicator, we employ a p-adaptive DGSEM operator in smooth areas, while discontinuous solution features are treated with a second order TVD FV operator on a h-refined sub-cell grid.
While this hybrid, adaptive discretization strategy allows for an efficient localization of the degrees of freedom, it entails significant load variations among processor the units in parallel computations. Using a dynamic load balancing scheme that repartitions the domain along a space filling curve, we can maintain favorable scaling properties and thus profit from the vast computational resources of todays massively parallel high performance architectures.

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Multiphase flow simulation

Multi-phase flows are omnipresent in nature and relevant for many technical applications like the fuel injection systems of rocket or airplane engines. With the multiphase extension of FLEXI, we are at the forefront of studying complex multiphase problems like phase transition under extreme conditions, high speed multi-component jet-flows and droplet grouping. Key challenges in the field of multi-phase flow dynamics are the thermodynamic and numerical modelling of the interface and the work with complex real material equations of state (EOS).
The multi-phase FLEXI provides implementations of both a diffuse interface approach to simulate complex mixing and jet flows and a sharp-interface method to study the dynamics of individual droplets. In the sharp-interface context, interface modeling is achieved with the solution of an interfacial Riemann problem, that allows the incorporation of local thermodynamic phase transition models. A key building block of the multiphase code framework is an EOS-module, that supports a wide range of real material EOS from simple cubic material laws to multi-parameter eos. Affordable EOS-evaluation is facilitated with an efficient tabulation approach.

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AI-Integrated CFD

Aritificial Intelligence (AI) and especially Machine learning (ML) have emerged as powerful tools in Computational Fluid Dynamics (CFD) that promise to accelerate the pace of innovation and discovery in fluid dynamics. ML models can be utilized in CFD as surrogates for physical models, for uncertainty optimization or to detect and extract flow patterns within highly complex turbulent flow fields. Hence, the application of ML models allows to reduce the computational cost while maintaining or even improving the accuracy of complex high-fidelity simulations.
As computational requirements and capabilities continue to advance in both fields, integrating AI and CFD efficiently is challenging due to their differences in the applied software and hardware. To address this, FLEXI incorporates ML models efficiently using for instance our TensorFlow-Fortran-Bridge that allows to deploy trained AI models in large-scale simulations with FLEXI. Moreover, the Relexi Framework can be used to train AI models with Reinforcement Learning using CFD simulations with FLEXI as the training environment to derive novel surrogate models or for applications in active low control. These approaches have been applied successfully for a wide variety of different applications ranging from shock localization and capturing methods to advanced to advanced data-driven turbulence models. With this, FLEXI yields the foundation for a novel class of intelligent, optimizable flow solvers.

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