Multi-dimensional Optimal Order Detection techniques for Arbitrary Lagrangian Eulerian (schemes) for compressible flows PhD

This exciting research seeks to evolve the forefront of computational fluid dynamics (CFD) methods for compressible flows in the emerging Exascale High-Performance Computing (HPC) landscape. The aim is to achieve high-order of accuracy but also to obtain physically meaningful results that can advance the landscape of engineering simulations.

The choice of the best numerical method, governing equations, and framework is far from obvious and unique. Employing a MOOD-style algorithm that continuously scrutinises every facet of the numerical solution, ensuring adherence to both physical and numerical admissible criteria. This algorithm unlocks several possibilities and enables high-accuracy and computational efficiency across single- and multi-physics simulations.

However for Arbitrary Lagrangian Eulerian (ALE) frameworks, conservation errors, dissipation errors in regions of low-mesh quality, and carbuncle are just some of the issues that persist. The primary goal of this project is to advance the MOOD techniques for ALE frameworks by establishing new metrics that can accurately capture conservation errors during mesh deformation, bypassing/minimising the carbuncle phenomenon, establishing new physical and numerical admissible detection criteria for ALE, evaluate any potential benefits of high-order methods in the ALE context, and advance an available open source CFD software with the newly formulated algorithms/methods/frameworks.

Cranfield University’s Computational Engineering Sciences Centre and Advanced Numerical Methods Group will host this project, benefiting from a proven track record in pioneering and implementing cutting-edge methodologies across the entire spectrum of computational fluid dynamics and close collaborations with other research groups around the globe. AWE will serve as the industry sponsor for this project, providing valuable support by computational physics specialists.

The results of this project will contribute to an improved understanding of the possibilities and limitations of high-order MOOD methods for ALE schemes of compressible flows. The developed tools and methods will be implemented in massively parallel open-source CFD software and demonstrate best practices for method/equations/formulation selection for emerging architectures of Exascale High Performance Computing (HPC) facilities.

The student involved in this project will acquire valuable skills through several experiences including attending modules from our MSc in CFD, attending workshops for Exascale HPC in national facilities, visiting several European research groups that the centre is in close collaboration for enhancing the depth and breadth of their research methods and growing their network, and close collaboration with our partner, AWE. The student will be supported to present in international conferences, and workshops and further enrich their skillset.