Data-Driven Turbulence Modeling: Discovering Turbulence Models using Sparse Symbolic Regression

Computational Fluid Dynamics (CFD) is the main tool to use in industry and engineering problems including turbulent flows. Turbulence modeling relies on solving the Navier-Stokes equations. Solving these equations directly takes a lot of time and computational power. More affordable methods solve the Reynolds Averaged Navier-Stokes (RANS)...

Domain Decomposition Helmholtz Solvers: Obtaining Wave Number Independence

Wave phenomena play an important role in many different applications such as MRI scans, seismology and acoustics [41, 49, 47]. At the core of such applications lies the Helmholtz equation, which represents the time-independent version of the wave equation. Simulating a Helmholtz problem numerically with accurate numerical solutions for large...

Machine learning for cardiovascular modelling: Predicting time-dependent, aortic blood flow

The increase in complexity of mathematical models in an attempt to approximate reality and desire to have near real-time results have emphasized the need for fast numerical simulations. Especially in areas where classic numerical methods struggle to produce valid solutions in reasonable computational time due to their<br/>complex behaviour on...

Predicting the optimal CFL number for pseudo time-stepping: with machine learning in the COMSOL CFD module

Commercial finite element software like COMSOL is build to be user-friendly. For example, the user does not have to find weak formulations, or discretise the partial differential equations by hand. One of the more difficult parts of using finite element software is deciding which solver method and solver parameters to choose, as the performance...

Reduced Order Models for Fluid Flow With Generative Adversarial Networks

The goal of this work is to evaluate the aptness of generative adversarial networks (GANs) for use as surrogate reduced order fluid models. In contrast to previously published work, the focus is placed on analyzing the specific effect of adversarial training, by comparing GAN outcomes with those from an identical generator network trained...

Surrogate models for the characterization of hydrodynamic loads on perforated monopiles

Perforated monopiles show promise in providing a better alternative to the commonly used jacket-like substructures used in intermediate water depths in the range of 30 to 120 m. By introducing perforations near the vicinity of the splash zone the wave loads on the monopile can be mitigated and the fatigue damage reduced, which is the main...

Analytical approach to hollow core Photonic Crystal Fiber for gas sensing

Interference of light can be used to determine the concentration of a gas, called gas sensing. The absorption of the light by the gas molecules is measured based on the phase change of the light. In this report, a hollow core photonic crystal fiber is treated. The gas sample is inserted into the hollow core. Photonic crystal fibers possess the...

Error Estimates for Finite Element Simulations Using Neural Networks

In this work residual error estimates are constructed using Neural Networks for Finite Element Method. These can be used to do adaptive mesh refinement. Two neural networks are developed the Multilayer Perceptron and the Transformer model. The error estimates are made for 1d poisson equations but the idea will generalise to higher dimensions as...