Search

This paper introduces a novel hybrid numerical method, SAUSM, designed for accurate and robust simulation of compressible flows governed by the Euler equations. While the AUSM + scheme provides proper resolution of smooth flow features, it is susceptible to anomalies, particularly the carbuncle phenomenon near strong shock discontinuities. Conversely, the AUFS scheme offers inherent stability in capturing shocks; however, it lacks the accuracy of AUSM + in smooth regions. The proposed SAUSM method combines AUSM + and AUFS through an adaptive weighting function, facilitating a seamless transition between the schemes. This approach preserves the accuracy of AUSM + in smooth regions while ensuring robust shock-capturing capabilities near discontinuities. The effectiveness of the SAUSM method is rigorously demonstrated through a comprehensive suite of progressively complex test cases. Numerical experiments demonstrate SAUSM's proficiency in resolving intense shock patterns and discontinuities without introducing anomalies. In the selected test cases, SAUSM agrees with reference solutions and effectively mitigates anomalies observed in AUSM + , including kinked Mach stems. In the challenging test case involving hypersonic blunt body flow over a cylinder, SAUSM adapts dissipation effectively by utilizing its adaptive weighting function to generate smooth pressure distributions, thereby eliminating the carbuncle instability linked to AUSM + when applied to a high aspect ratio grid. The consistent formulation of flux splitting and the adaptive weighting in SAUSM prevent excessive dissipation away from discontinuities, thus preserving accuracy comparable to that of exact Riemann solvers. Consequently, SAUSM emerges as a promising and innovative approach to accurately and robustly simulate a wide range of compressible Euler flows. The comprehensive results obtained from the validation tests firmly establish SAUSM as a highly effective general-purpose technique for computational fluid dynamics in academic research. [ABSTRACT FROM AUTHOR]

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics. [ABSTRACT FROM AUTHOR]

A Rotated Lattice Boltzmann Flux Solver (RLBFS) with improved stability is proposed in this paper for the effective simulation of compressible flows with intense shock waves at high Mach numbers. Unlike the conventional LBFS or conventional Riemann solvers, which evaluate its mass, momentum and energy fluxes in the normal direction of each cell interface, the present RLBFS decomposes the outer normal direction of the cell interface into two perpendicular directions of the velocity difference and their counterparts. The fluxes in these two directions are respectively evaluated by the LBFS and the final fluxes at each interface are obtained by weighted summations of the two obtained fluxes. The matrix-based stability theory is applied to analyze the proposed solver by simulating the strong normal shock problem from Mach number 1.5 to 10. It reveals that the RLBFS has a smaller negative eigenvalue than the original LBFS, indicating that the RLBFS is more stable. The numerical accuracy of the RLBFS is evaluated by simulating the advection of density perturbation. The performance of the RLBFS is further demonstrated by simulating seven more compressible flows, including the transonic flow over RAE2822 airfoil, odd-even grid perturbation problem, a Mach 3 wind tunnel with a step, supersonic corner flow, double Mach reflection of a strong shock, shock-boundary layer interaction and hypersonic viscous flow around a blunt body. The obtained results agree well with the published data, showing that the RLBFS can effectively avoid the phenomenon of shock instability and thus has a potential for simulating practical compressible flows with intense shock waves at high Mach numbers. • A rotated lattice Boltzmann flux solver with improved stability is proposed. • A matrix-based stability theory is used to analyze the RLBFS and the LBFS. • Theoretical analysis show that the RLBFS is more stable than LBFS. • Numerical examples show the reliability and capability of the RLBFS. [ABSTRACT FROM AUTHOR]

An adaptive mesh refinement–rotated lattice Boltzmann flux solver (AMR-RLBFS) is presented to simulate two and three-dimensional compressible flows with complex shock structures. In the method, the RLBFS, which has a strong shock-capturing capability and can effectively eliminate the shock instability phenomenon, is applied to solve the flow filed by reconstructing the fluxes at each cell interface adaptively with the mesoscopic lattice Boltzmann model. To locally and dynamically improve the resolution of intricate shock structures and optimize the required computational resources, a block-structured adaptive mesh refinement (AMR) technique is introduced. The validity and effectiveness of the proposed method are confirmed through a range of two and three-dimensional numerical cases, including the shock tube problem, the four-wave Riemann problem, explosion within a rectangular box, and the vorticity induced by a shock. The results obtained using the AMR-RLBFS exhibit excellent agreement with published data and demonstrate high accuracy in capturing complex shock structures. The computational efficiency of the AMR-RLBFS can be also improved significantly compared to the RLBFS on uniform grids. Furthermore, the numerical outcomes underscore the capability of the AMR-RLBFS to eliminate shock instability effects while efficiently capturing a broader spectrum of small-scale vertical structures. These findings highlight the ability of AMR-RLBFS to improve the computational efficiency and capture intricate shock structures effectively, making it a valuable tool for studying a wide range of compressible flows from aerodynamics to astrophysics.

• Numerous applications in various compressible flow field investigations. • The technique's filtering quality shows less prominent elements of a flow that are difficult to observe in the actual visualization records. • Showing the evolution of flow features as a function of location and time by sequences of streaks obtained at different positions of the flow field. • Inherent uncertainties in the measurements with this technique are highlighted. This paper discusses a digital version of the traditional streak imaging technique combined with different flow visualization methods. The basic characteristics of the technique, its advantages and its shortcomings are presented alongside a number of applications in fluid mechanics. Streak images are useful to track and quantify the propagation or development of distinct flow features as a function of time. In addition, the appearance of a new trace, or the change of grey scale (or color in the case of polychrome visualizations), can be used to graphically reveal the location and instant of the onset of certain flow phenomena. In addition, the method also has a filtering quality that allows one to show less prominent elements of a flow that may be difficult to observe in the actual visualization records. A sequence of streaks obtained at different positions of the flow field can be used to track the evolution of flow features as a function of location and time. Some features of the digital technique are highlighted via a direct comparison with results from the literature. [ABSTRACT FROM AUTHOR]

HLLC is one kind of schemes which resolve shock, contact, and rarefaction waves exactly and has high value of application in compressible fluid simulation. HLL scheme cannot deal with the contact and shear waves accurately, thus it has much more dissipation compared with the HLLC scheme. However, numerical tests have illustrated that HLLC scheme may suffer from shock instability phenomena in the vicinity of strong shock waves while it performs well in low speed and subsonic flow. HLL-HLLC scheme which is suitable for a larger range of flow is proposed through mathematical analyses of HLLC and HLL scheme. The new proposed scheme indicates the property of HLLC which has low order dissipation in low speed flow and can overcome the shortcoming of shock instability phenomena in high speed flow. The effectiveness and robustness of the proposed scheme free from shock instability phenomena is demonstrated through three numerical simulations: hypersonic flow on double wedge configuration, supersonic flow over backward-facing step and hypersonic flow over blunt body. [ABSTRACT FROM AUTHOR]

Due to its high resolution for discontinuities and high efficiency, the HLLEM scheme is a popular numerical method to calculate the conservative hyperbolic systems. When capturing multidimensional strong shock waves, however, it will encounter different forms of numerical oscillations, such as the odd-even decoupling and carbuncle phenomenon, which is a great hindrance to its application in hypersonic flow problems. In this paper the numerical shock instability of the HLLEM scheme is investigated from a mathematical perspective and a corresponding cure is proposed. A special linearized small perturbation analysis shows that perturbations evolved in the streamwise direction will be attenuated while the density and shear velocity perturbations evolved in the transverse direction will not be attenuated and thus induce the occurrence of instability. In order to suppress the numerical oscillation in capturing strong shock waves, a function based on the pressure ratio at the cell interface is defined to control the dissipation of the HLLEM flux. And a BVD (boundary variation diminishing) algorithm is implemented to pick the smallest density jump from all combinations among reconstructed density values to reduce the numerical dissipation, thus the contact resolving capability of the HLLEM scheme is further improved. The higher resolution for contact discontinuities and better stability for shock waves brought by the current strategies are demonstrated through solving a series of one- and two-dimensional benchmark test problems. • The shock instability of the HLLEM solver is studied in depth. • The shock instability is eliminated by the antidiffusion controlling technique with a shock indicator function. • The resolution of the HLLEM solver for contact discontinuities is improved by a BVD algorithm. • Numerical results demonstrate that the strategies adopted provide higher resolution and better shock stability. [ABSTRACT FROM AUTHOR]