Anti-Aliasing of Flux Reconstruction Schemes in ... - WCCM 2016

Anti-Aliasing of Flux Reconstruction Schemes in Rotating Curved Elements Jin Seok Park / Peter E Vincent Imperial College London South Kensington Campus London SW7 2AZ, UK High-order methods for unstructured grids offer the promise of increased simulation accuracy in the vicinity of complex engineering geometries. The flux reconstruction (FR) approach provides a unifying framework for various unstructured high-order methods [1], including nodal discontinuous Galerkin (DG) and spectral difference (SD) schemes. Moreover, FR methods coupled with explicit time-marching schemes exhibit a significant degree of temporal/spatial locality, which is favourable when considering recent hardware architectures, such as Graphical Processing Units (GPUs). Rotating frames with sliding mesh interfaces are used widely to simulate flow over turbo-machinery and rotorcraft. In the present study we investigate aliasing errors arising from rotation of high-order curved elements via an arbitrary Lagrangian and Eulerian (ALE) approach. Such elements can occur at curved sliding interfaces, for example. Figure 1 shows propagation of a two-dimensional Gaussian density/pressure pulse (governed by the compressible Euler equations). Specifically, the initial conditions were defined as (ρ, u, v, p) = (1, 0.2, 0, 1/γ) + (ρr, 0, 0, pr), ρr = pr = εexp(αr) , (1) , where ε = 0.0002, α = log(2)/9 and r = (x2 + y2). The computational domain was r ≤ 40. The domain r ≤ 20 was rotating with an angular velocity ω = π/8, and a sliding interface was located at r = 20. Curved elements were present along the sliding interface, as well as along a static interface at r = 4.5. Figure 1a shows the normalized pressure perturbation (without anti-aliasing) at t = 16. It can be seen that aliasing errors, generated by the rotating curved elements at the sliding and static interfaces, pollute the solution. The nature of the aforementioned aliasing errors are identified, and strategies for their removal via antialiasing are proposed. In particular we anti-alias the transformed flux within each element and the transformed common normal flux on the surface of each element. Results in Figure 1b show a clear improvement in solution accuracy once these strategies are applied. 40 30

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Figure 1: Distribution of pr/ε at t = 16 without anti-aliasing (a). Distribution of pr/ε along the x axis at t = 16 with and without anti-aliasing (b).

Keywords(optional): high-order flux reconstruction, unstructured grids, anti-aliasing References(optional) [1]H. T. Huynh. A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. In 18th AIAA Computational Fluid Dynamics Conference, Miami, FL, 2007.