305, 333–359 (2016)Īntoniadis, A.F., Drikakis, D., Farmakis, P.S., Fu, L., Kokkinakis, I., Nogueira, X., Silva, P.A., Skote, M., Titarev, V., Tsoutsanis, P.: UCNS3D: an open-source high-order finite-volume unstructured CFD solver. 126, 202–228 (1996)įu, L., Hu, X.Y., Adams, N.A.: A family of high-order targeted ENO schemes for compressible-fluid simulations. Jiang, G.S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. Liu, X.D., Osher, S., Chan, T.: Weighted essentially non-oscillatory schemes. Harten, A.: High resolution schemes for hyperbolic conservation laws. Jameson, A.: Analysis and design of numerical schemes for gas dynamics, 1: artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence. Von, N.J., Richtmyer, R.: A method for the numerical calculation of hydrodynamic shocks. Griffin, K.P., Fu, L., Moin, P.: Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer. 51, 82–126 (2009)įu, L., Karp, M., Bose, S.T., Moin, P., Urzay, J.: Shock-induced heating and transition to turbulence in a hypersonic boundary layer. Shu, C.-W.: High order weighted essentially nonoscillatory schemes for convection dominated problems. Pirozzoli, S.: Numerical methods for high-speed flows. A set of benchmark simulations demonstrate the performance of the new FMRENO schemes for handling complex fluid problems with a wide range of length scales. Compared to the standard weighted/targeted essentially non-oscillatory (W/TENO) schemes, the computational efficiency is dramatically enhanced by avoiding the expensive evaluations of the classical smoothness indicators. Moreover, the new FMRENO schemes feature low numerical dissipation for resolving the broadband physical fluctuations by adaptively choosing the candidate stencil with better spectra or higher accuracy order based on the local flow regularity. With this new framework, the desirable high-order accuracy is restored in the smooth regions while the sharp shock-capturing capability is achieved by selecting the targeted stencil satisfying the MP criterion most. If all the candidate stencils are judged to be nonsmooth, the targeted stencil that violates the MP criterion the least is deployed as the final reconstruction instead. Third, a multi-resolution stencil selection strategy, which prioritizes the stencils with better spectral property or higher-order accuracy meanwhile satisfying the MP criterion, is proposed. A candidate stencil, with which the reconstructed cell interface flux locates within the MP lower and upper bounds, is regarded to be smooth. Second, the monotonicity-preserving (MP) limiter is introduced as the regularity criterion of the candidate stencils. A set of candidate stencils ranging from high- to low-order (from large to small stencils) is constructed in a hierarchical manner. First, a new candidate stencil arrangement is developed for a multi-resolution representation of the local flow scales. In this paper, a new class of high-order fast multi-resolution essentially non-oscillatory (FMRENO) schemes is proposed with an emphasis on both the performance and the computational efficiency.
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