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Summary Adaptive Mesh Refinement (AMR) shows attractive properties in automatically refining the flow region of interest, and with AMR better prediction can be obtained with much less labour work and cost compared to manually re-meshing or the global mesh refinement. Cartesian AMR is well established; however, AMR on hybrid unstructured mesh which is heavily employed in the high-Reynolds number flow simulation, is less matured and existing methods may result in degraded mesh quality, which mostly happens in the boundary layer or near the sharp geometric features. User intervention or additional constraints, such as freezing all boundary layer elements or refining the whole boundary layer, are required to assist the refinement process. In this work, a novel AMR strategy is developed to handle existing difficulties. In the new method, high-order unstructured elements are first generated based on the baseline mesh; then the refinement is conducted in the parametric space; at last the mesh suitable for the solver is output. Generating refined elements in the parametric space with high-order elements is the key of this method and this helps to guarantee both the accuracy and robustness. With the current method, three-dimensional hybrid unstructured mesh of huge size and complex geometry can be automatically refined, without user intervention nor additional constraints. With test cases including the two-dimensional airfoil and three-dimensional full aircraft, the current AMR method proves to be accurate, simple and robust. This article is protected by copyright. All rights reserved.

Summary A multi-block curvilinear mesh-based adaptive mesh refinement (AMR) method is developed to satisfy the competing objectives of improving accuracy and reducing cost. Body-fitted curvilinear mesh-based AMR is used to capture flow details of various length scales. A series of efforts are made to guarantee the accuracy and robustness of the AMR system. A physics-based refinement function is proposed, which is proved to be able to detect both shock wave and vortical flow. The curvilinear mesh is refined with cubic interpolation, which guarantees the aspect ratio and smoothness. Furthermore, to enable its application in complex configurations, a sub-block-based refinement strategy is developed to avoid generating invalid mesh, which is the consequence of non-smooth mesh lines or singular geometry features. A newfound problem of smaller wall distance, which negatively affects the stability and is never reported in the literature, is also discussed in detail, and an improved strategy is proposed. Together with the high-accuracy numerical scheme, a multi-block curvilinear mesh-based AMR system is developed. With a series of test cases, the current method is verified to be accurate and robust and be able to automatically capture the flow details at great cost saving compared with the global refinement. Copyright © 2015 John Wiley & Sons, Ltd.

SUMMARY In this paper, a simple and efficient improvement to the famous Swanson–Turkel matrix dissipation model for the central scheme is proposed. In the new matrix dissipation model, the accuracy is improved by eliminating the second-difference dissipation added to the characteristic fields representing the vorticity waves. This strategy is proposed based on analyzing the flow-physics about shock-vortex interaction using the Rankine–Hugoniot jump condition. In this paper, the behavior of central scheme for rotational flow is also theoretically and numerically analyzed. Results show a newfound problem of the original scalar and matrix dissipation models, in which for rotational flow excessive second-difference dissipation is added due to the pressure-based shock sensor. With current new matrix dissipation model improved accuracy is obtained at minimal cost overhead, especially, in the highly vortical region where the second-difference dissipation is reduced. At the same time, it preserves the excellent shock capturing capability and convergence speed of original method. Numerical properties of this new matrix dissipation model are validated with a series of numerical experiments and results comparison with original model verifies improved performance of current method. Copyright © 2013 John Wiley & Sons, Ltd.

SUMMARY In this paper, the efficient application of high-order weighted essentially nonoscillatory (WENO) reconstruction to the subsonic and transonic engineering problems is studied. On the basis of the physical considerations, two techniques are proposed to enhance the accuracy and efficiency of the WENO reconstruction. First, it is observed that the WENO scheme using characteristic variable has better accuracy and convergence speed than the scheme using primitive variable. For engineering problems with shock of moderate amplitude, on the basis of the Rankine–Hugoniot conditions, a simplified characteristic-variable-based WENO is developed. The simplified version significantly reduces the cost overhead without sacrificing the shock-capturing capability. Second, in this work, it is found for viscous case that it is better to include the viscous effect. On the basis of a simple analysis, the viscous correction to the parameter e in the WENO reconstruction is proposed. Numerical results indicate, with the proposed simplified characteristic-variable-based reconstruction and the viscous correction, that the nonlinear WENO interpolation is sharply activated in the region of shock jump, whereas in the shockless area, the WENO interpolation weights are tuned towards the designed optimal value for better accuracy. Compared with the original characteristic-variable-based WENO, the current implementation has similar accuracy and reduced cost. At the same time, compared with the primitive variable-based WENO, better accuracy and convergence speed are obtained at marginal cost overhead. Several practical cases are calculated to demonstrate the accuracy and efficiency of the current methodology. Copyright © 2012 John Wiley & Sons, Ltd.

The present paper investigates the implicit solution of time spectral model for periodic unsteady flows. In the time spectral model, the physical time derivative is approximated using spectral method. The robustness issues associated with implicit solution of time spectral model are analyzed and validated by numerical results. It is found that spectral approximation of the time derivative weakens the diagonal dominance property of the Jacobian matrix, resulting in the deterioration of stability and convergence speed. In this paper we propose to solve the coupled governing equations implicitly using multigrid preconditioned generalized minimal residual (GMRES) method, which demonstrates favorable convergence speed. Also it is demonstrated that the current method is insensitive to the variations of frequency and number of harmonics. Comparison of computation results with dual time step unsteady computation validates the high efficiency of the current method. Copyright © 2009 John Wiley & Sons, Ltd.