Abstract: The scale-resolving simulation of high speed compressible flow through direct numerical simulation (DNS) or large eddy simulation (LES) requires shock-capturing schemes to be more accurate for resolving broadband turbulence and robust for capturing strong shock waves. In this work, we develop a new paradigm of dissipation-adjustable, shock capturing scheme to resolve multi-scale flow structures in high speed compressible flow. The new scheme employs a polynomial of n-degree and non-polynomial THINC (Tangent of Hyperbola for INterface Capturing) functions of m-level steepness as reconstruction candidates. These reconstruction candidates are denoted as . From these candidates, the piecewise reconstruction function is selected through the boundary variation diminishing (BVD) algorithm. Unlike other shock-capturing techniques, the BVD algorithm effectively suppresses numerical oscillations without introducing excess numerical dissipation. Then, an adjustable dissipation (AD) algorithm is designed for scale-resolving simulations. This novel paradigm of shock-capturing scheme is named as . The proposed scheme has following desirable properties. First, it can capture large-scale discontinuous structures such as strong shock waves without obvious non-physical oscillations while resolving sharp contact, material interface and shear layer. Secondly, the numerical dissipation property of can be effectively adjusted between n+1 order upwind-biased scheme and non-dissipative n+2 order central scheme through a simple tunable parameter ?. Thirdly, with the scheme can recover to n+2 order non-dissipative central interpolation for smooth solution over all wavenumber, which is preferable for solving small-scale structures in DNS as well as resolvable-scale in explicit LES. Finally, the under-resolved small-scale can be solved with the dissipation adjustable algorithm through the so-called implicit LES (ILES) approach. Through simulating benchmark tests involving multi-scale flow structures and comparing with other central-upwind schemes, the superiority of the proposed scheme is evident. For instance, the simulation results of the supersonic planar jet show that schemes can achieve competitive results as schemes which utilize a higher degree of reconstruction polynomial. Thus, in comparison with the previous work, the proposed schemes have the benefit of a more compact stencil and lower cost. In summary, this work provides an alternative scheme for solving multi-scale problems in high speed compressible flows.

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Abstract: Martian conditions present various challenges when designing rotorcraft. Specifically, the thin atmosphere and low sound speed require Martian rotor blades to operate in a low-Reynolds-number (1000-10,000) compressible regime, for which conventional airfoils are not designed. Here, we use PyFR to undertake high-order direct numerical simulations (DNS) of flow over a triangular airfoil at a Mach number of 0.15 and Reynolds number of 3000. Initially, spanwise periodic DNS are undertaken. Extending the domain-span-to-chord ratio from 0.3 to 0.6 leads to better agreement with wind-tunnel data at higher angles of attack, when the flow is separated. This is because smaller domain spans artificially suppress three-dimensional breakdown of coherent structures above the suction surface of the airfoil. Subsequently, full-span DNS in a virtual wind tunnel are undertaken, including all wind-tunnel walls. These capture blockage and wall boundary-layer effects, leading to better agreement with wind-tunnel data for all angles of attack compared to spanwise periodic DNS. The results are important in terms of understanding discrepancies between previous spanwise periodic DNS and wind-tunnel data. They also demonstrate the utility of high-order DNS as a tool for accurately resolving flow over triangular airfoils under Martian conditions.

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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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