Abstract: In this study we generate optimal Runge-Kutta (RK) schemes for converging the Artificial Compressibility Method (ACM) using dual time-stepping with high-order unstructured spatial discretizations. We present optimal RK schemes with between s=2 and s=7 stages for Spectral Difference (SD) and Discontinuous Galerkin (DG) discretizations obtained using the Flux Reconstruction (FR) approach with solution polynomial degrees of k=1 to k=8. These schemes are optimal in the context of linear advection with predicted speedup factors in excess of 1.80x relative to a classical RK44 scheme. Speedup factors of between 1.89x and 2.11x are then observed for incompressible Implicit Large Eddy Simulation (ILES) of turbulent flow over an SD7003 airfoil. Finally, we demonstrate the utility of the schemes for incompressible ILES of a turbulent jet, achieving good agreement with experimental data. The results demonstrate that the optimized RK schemes are suitable for simulating turbulent flows and can achieve significant speedup factors when converging the ACM using dual time-stepping with high-order unstructured spatial discretizations.

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Abstract: Quantification of 3D intravascular flow is valuable for studying arterial wall diseases but currently there is a lack of effective clinical tools for this purpose. Divergence Free Interpolation (DFI) using Radial Basis Function (RBF) is an emerging approach for full field flow reconstruction using experimental sparse flow field samples. Previous DFI reconstructs full field flow from scattered 3D velocity input obtained using Phase Contrast MRI with low temporal resolution. In this study, a new DFI algorithm is proposed to reconstruct full field flow from scattered 2D in-plane velocity vectors obtained using ultrafast contrast enhanced ultrasound (>1000 fps) and particle imaging velocimetry (Ultrasound PIV, or UIV). The full 3D flow field is represented by a sum of weighted divergence free RBFs in space. Due to the acquired velocity vectors being only in 2D and hence the problem being ill-conditioned, a regularized solution of the RBF weighting is achieved through Singular Value Decomposition (SVD) and the L-curve method. The effectiveness of the algorithm is demonstrated via numerical experiments for Poiseuille flow and helical flow with added noise, and it is shown that an accuracy of up to 95.6% can be achieved for Poiseuille flow (with 5% input noise). Experimental feasibility is also demonstrated by reconstructing full-field 3D flow from experimental 2D UIV measurements in a carotid bifurcation phantom. The method is typically faster for a range of problems compared to computational fluid dynamics, and has been demonstrated to be effective for the three flow cases.

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Summary: A PhD Studentship is currently available. The project, will involve addition of 'in-situ' visualisation, processing, and analysis technology to PyFR, an open-source high-order massively-parallel CFD platform, as well as its application to solve a range of challenging unsteady flow problems. Candidates should hold, or expect to obtain, an undergraduate degree in a numerate discipline. Previous programming experience is important (ideally Python, C++ and CUDA).

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