Generalised high-order Eulerian Smoothed Particle Hydrodynamics for internal flows applied to flow-induced vibration and nuclear tube banks

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Computational fluid dynamics or CFD is mature with several general-purpose commercial codes available based on the finite-volume or finite-element (mesh-based) approaches with various options for turbulence modelling. The success of CFD in industrial design has however encouraged increasing demands to be made in terms of the resolution of the flow and finer grain physics, requiring ever increasing resources to be employed, both in terms of computation and manpower. Notable successes are in nuclear reactors, turbo-machinery, combustion chambers, heat exchangers, marine turbines, vehicle aerodynamics, aeronautics, offshore engineering amongst many others. Commercial enterprise tends to focus on two key aspects for improving the efficiency and accuracy of simulations in increasingly complex and demanding practical problems: performance on massively parallel computing and optimal mesh generation. State-of-the-art in commercial CFD suggests meshes may comprise several hundred million cells, over a billion for a nuclear reactor simulation (CD-Adapco, 2016), and runs with massively parallel computing (often with thousands of processors) taking days or weeks. Implementation of High-Order (HO) methods has received comparatively less attention, but can offer flexibility and gains in efficiency and accuracy beyond what can be achieved through optimal meshing and parallelisation alone. HO methods are known to be beneficial, even necessary, in unsteady vortex-dominated and turbulent flow modelling where many problems remain beyond the reach of state-of-the-art second-order CFD even on supercomputers. Important open-source codes from academia are making headway in increasing uptake of HO methods, but optimal implementation within complex 3-D geometries (that may contain arbitrarily moving boundaries) and adaptivity remain challenging problems in a high-order framework. We propose to address these problems through an alternative numerical method that is attractive in its simplicity, amenable to high-order spatial approximations in complex domains while retaining a natural affinity for parallelisation on emerging architectures. We provide this improvement in capability by abandoning the mesh and using particles, which, in Lagrangian form, have been used widely for the modelling of highly distorted flows involving interfaces and multi-physics. The investigators have been active in the development of smoothed particle hydrodynamics (SPH) particularly in divergence-free incompressible form and in developing algorithms for energy efficient hardware. Recently an Eulerian form has been tested by the investigators with high order Gaussian interpolating kernels (up to 6th order) demonstrating spatial convergence to machine accuracy in model periodic problems. In viscous transient flow with second-order time stepping, the accuracy obtained is similar to spectral methods. This new approach opens up considerable opportunities particularly for internal flows. One downside of this approach is that several billion particles will be required for complex systems, and the floating point operations per second (FLOPS) per particle in SPH are typically an order of magnitude greater than the finite volume/hp-element equivalent. This is compensated by the SPH formulation being ideally suited for parallel processing due to its locally interpolative (meshless) nature and ease of implementation on emerging hardware including most GPUs.