Abstract: In this article, cache blocking is implemented for the Navier Stokes equations with anti-aliasing support on mixed grids in PyFR for CPUs. In particular, cache blocking is used as an alternative to kernel fusion to eliminate unnecessary data movements between kernels at the main memory level. Specifically, kernels that exchange data are grouped together, and these groups are then executed on small sub-regions of the domain that fit in per-core private data cache. Additionally, cache blocking is also used to efficiently implement a tensor product factorisation of the interpolation operators associated with anti-aliasing. By using cache blocking, the intermediate results between application of the sparse factors are stored in per-core private data cache, and a significant amount of data movement from main memory is avoided. In order to assess the performance gains a theoretical model is developed, and the implementation is benchmarked using a compressible 3D Taylor-Green vortex test case on both hexahedral and prismatic grids, with third-, fourth-, and fifth-order solution polynomials. The expected performance gains based on the theoretical model range from 1.99 to 2.83, and the speedups obtained in practice range from 1.51 to 3.91 compared to PyFR v1.11.0.

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Abstract: Mars has a lower atmospheric density than Earth, and the speed of sound is lower due to its atmospheric composition and lower surface temperature. Consequently, Martian rotor blades operate in a low-Reynolds-number compressible regime that is atypical for terrestrial helicopters. Nonconventional airfoils with sharp edges and flat surfaces have shown improved performance under such conditions, and second-order-accurate Reynolds-averaged Navier-Stokes (RANS) and unsteady RANS (URANS) solvers have been combined with genetic algorithms to optimize them. However, flow over such airfoils is characterized by unsteady roll-up of coherent vortices that subsequently break down/transition. Accordingly, RANS/URANS solvers have limited predictive capability, especially at higher angles of attack where the aforementioned physics are more acute. To overcome this limitation, we undertake optimization using high-order direct numerical simulations (DNS). Specifically, a triangular airfoil is optimized using DNS. Multi-objective optimization is performed to maximize lift and minimize drag, yielding a Pareto front. Various quantities, including lift spectra and pressure distributions, are analyzed for airfoils on the Pareto front to elucidate flow physics that yield optimal performance. The optimized airfoils that form the Pareto front achieve up to a 48% increase in lift or a 28% reduction in drag compared to a reference triangular airfoil studied in the Mars Wind Tunnel at Tohoku University. The work constitutes the first use of DNS for aerodynamic shape optimization.

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Summary: Next-generation Entry, Descent, and Landing (EDL) systems for Titan and Mars must safely slow down increasingly large payloads. One particular challenge occurs during the transonic phase of descent, where the spacecraft is subject to aerodynamic instabilities that can cause uncontrolled oscillations, posing a significant risk of mission failure. This project will further develop the GPU-accelerated computational fluid dynamics flow solver PyFR - implementing improved shock capturing approaches and a full 6-DOF free-flight capability - and use it to study dynamic stability in the transonic phase of descent. The work will be undertaken in collaboration with Texas A&M University and NASA Ames.

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