Physics-informed neural networks for highly compressible flows: assessing and enhancing shock-capturing capabilities

While physics-informed neural networks have been shown to accurately solve a wide range of fluid dynamics problems, their effectivity on highly compressible flows is so far limited. In particular, they struggle with transonic and supersonic problems that involve discontinuities such as shocks. While there have been multiple efforts to alleviate...

Mimetic isogeometric modeling and discretization of compressible Euler flows

This thesis poses a new geometric formulation for compressible Euler flows. A partial decomposition of this model into Roe variables is applied; this turns mass density, momentum and kinetic energy into product quantities of the Roe variables. Lie derivative advection operators of weak forms constructed with this decomposed model naturally...

Hamiltonian Discontinuous Galerkin Finite Element Method for Internal Gravity Waves: An exactly energy conserving discretization

A DGFEM discretization has been developed for the Hamiltonian dynamics of stratified incompressible linear fluid flow. The developed discretization can handle the numerical challenges posed by wave attractors: the three dimensionality of the domain, the focusing of wave energy and the incompressibility of the flow. The discretization is...

Spatially mass-, kinetic energy- and helicity-preserving mimetic discretization of 3D incompressible Euler flows

Based on the recently developed mimetic spectral element method, we propose an effective numerical scheme for solving three-dimensional periodic incompressible Euler flows, which spatially preserves mass, kinetic energy and helicity. Preserving multiple integral invariants numerically will significantly contribute to the stability and accuracy...

Structure Preserving Isogeometric Analysis for Computational Fluid Dynamics

Double degree. Supervision of the thesis also at: Faculty Applied Mathematics, Department Numerical Analysis, Programme M.Sc. Applied Mathematics. Structure-preserving discretization techniques preserve fundamental structure of operators and operands found in partial differential equations. Classical discretization techniques sometimes neglect...

Isogeometric Analysis for Compressible Flows with Application in Turbomachinery

Computer-aided design (CAD) and finite element analysis (FEA) tools are extensively used in industrial design processes. The idea of isogeometric analysis (IGA) is to bring those worlds closer together. Combining them significantly increases the efficiency of the design and development processes. The general idea of the IGA approach is to use...

Multi-fidelity Method for Aerodynamic Optimisation of Axial Compressor Blades

In turbomachinery optimisation problems, run time is often a critical factor due to high dimensionality of the design search space. This work explores the use of the multi-fidelity method to speed up an aerodynamic optimisation algorithm applied to axial compressor blades. A rotor blade is optimised in a two-stage blade geometry for maximum...

The Lagrangian Mimetic Spectral Element Method: Solving (non-)Linear Advection Problems with a Mimetic Method

Advection is at the heart of fluid dynamics and is responsible for many interesting phenomena. Unfortunately, it is also the source of the non-linearity of fluid dynamics. As such, its numerical treatment is challenging and often suboptimal. One way to more effectively deal with advection is by using a Lagrangian formulation instead of the...