Search Results (65)

High-order numerical methods are essential for achieving predictive fidelity in modern computational fluid dynamics, yet many existing schemes face significant trade-offs between accuracy, robustness, and computational efficiency. This study introduces the Compact-Corrected MUSCL (CCMUSCL) scheme, a novel framework that enhances the traditional MUSCL approach by incorporating localized information from high-order, compact finite-difference formulas. Unlike classical compact schemes that require solving global linear systems, this method applies corrections locally to the MUSCL flux. This strategy allows the scheme to maintain spectral-like resolution while preserving the robustness and locality of the original MUSCL framework. The performance of CCMUSCL is evaluated using a series of rigorous 1D and 2D benchmark cases. Numerical results demonstrate that CCMUSCL achieves accuracy comparable to or exceeding that of traditional high-order WENO schemes, particularly in resolving intricate, small-scale flow structures and sharp discontinuities. Furthermore, efficiency analysis reveals that CCMUSCL is significantly more cost-effective than WENO, requiring substantially fewer arithmetic operations in 1D and offering an even more pronounced reduction in operations for 3D flux evaluations. By offering a tunable balance between robustness and accuracy through the use of the van Albada limiter as a localized indicator, the CCMUSCL scheme provides a highly efficient and flexible alternative for large-scale high-speed flow simulations. Full article

This article proposes a novel conservative ConRKDG method for one-dimensional hyperbolic conservation laws with applications in computational fluid dynamics simulations. A DG local solution is reconstructed over each element based on the sub-cell solution averages with a newly proposed set of shape functions. In this virtue, the conservation property of the problem is naturally imposed for the numerical DG solution. In addition, the availability of finite-volume sub-cell solution averages without any DG-to-FV transformation or vice versa facilitates a direct and robust technique for detecting troubled elements, in which the unlimited DG local solution is deemed unstable. A new WENO-type smoothness measurement based on sub-cell solution averages is introduced to assess whether a DG local solution is admissible or unstable, thereby determining whether an element is good or troubled. For the latter case, a secondary finite-volume WENO method is invoked in an a posteriori phase to recalculate the sub-cell averages to sustain numerical stability by essentially suppressing non-physical spurious oscillations in the vicinity of shocks or discontinuities at troubled elements. The performance of the ConRKDG method with different secondary finite-volume WENO methods is compared for both problems with smooth solutions and those with shocks and discontinuities. Full article

In this study, a third-order meshless method is presented through adopting WENO-Z reconstruction as a substitute for traditional linear reconstruction. In order to achieve a third-order reconstruction of WENO-Z, the required three-point stencils are created by introducing ghost points on the lines through each pair of the central and satellite points of the meshless cloud. The flow variables of the ghost point are evaluated by a proposed interpolation technique, in which only available information associated with the cloud is utilized. Based on each resultant stencil of the ghost-central-satellite points, the WENO-Z is then implemented for computing the variables at the midpoints between the central and satellite points of the cloud. In this way, the resulting meshless method could be expected to be of third-order accuracy while obtaining an oscillation-free property. A series of typical model cases, including linear advection of sinusoid wave, convection of an isentropic vortex, and two well-known shock-tube problems, are selected to be simulated for validation. The expected third-order of accuracy and inherit ability of shock capturing are achieved regardless of whether the meshless points distributed are regular or irregular. In addition, a set of subsonic, transonic, and supersonic flows over aerodynamic bodies like single-and multi-element airfoils are also demonstrated for the compressible Euler equations, and obtained numerical results compare well with the reference data in the literature. Full article

This study presents a novel fifth-order unequal-sized trigonometric weighted essentially non-oscillatory (US-TWENO) scheme and a novel hybrid US-TWENO (HUS-TWENO) scheme with a novel troubled cell indicator in a finite difference framework to address hyperbolic conservation laws on structured grids. Firstly, we propose three unequal-degree reconstruction polynomials in the new trigonometric polynomial space to devise a novel fifth-order US-TWENO scheme. Then, we devise a novel troubled cell indicator capable of accurately identifying troubled cells containing strong discontinuities: the existence of extreme points of the trigonometric polynomials within the smallest interval (the target cell itself) is determined by whether the estimated minimum and maximum values of their derivative trigonometric polynomials have opposite signs. To the best of our knowledge, this is the first troubled cell indicator devised specifically within the target cell interval. The HUS-TWENO scheme is improved, offering greater efficiency, lower dissipation, and higher resolution. Numerical experiments demonstrate the effectiveness of the HUS-TWENO scheme. Full article

To investigate the aerodynamic characteristics of the subsonic transport standard model (DLR-F4 wing–body configuration), this study uses the Spalart–Allmaras Detached Eddy Simulation (SA-DES) turbulence model as the core, coupling it with fifth-order WENO/WCNSs and HLLC approximate Riemann solver for numerical simulations under different angles of attack (AOA). Through comparative simulations, effects of grid density, turbulence models (URANS/DES), and spatial discretization schemes (second-order CDS, fifth-order WENO-JS/WCNS-JS) on accuracy are analyzed, focusing on grid convergence and numerical scheme dissipation in separated flows. The results show medium-density grid results are stable, balancing accuracy and efficiency. Under high AOA, DES outperforms URANS in capturing separated vortex structures, effectively reproducing small-scale vortices in the wing–body junction. High-order WCNS performs best in predicting wing-tip vortices and wake turbulence due to lower dissipation. WCNS-JS/WCNS-T (different weight functions) affect lift/drag coefficient errors: WCNS-JS has smaller lift prediction errors, while WCNS-T better reduces dissipation and maintains wing-tip vortex integrity. This study provides key references for high-accuracy simulations of complex separated flows, supporting efficiency improvement and accuracy optimization in aerospace vehicle aerodynamic design. Full article

Rochia nilotica is a tropical Pacific gastropod inhabiting shallow coral reef habitats and supporting important marine resources in Pacific island nations. In this study, we analyzed specimens collected from Weno Island, Chuuk Atoll, Federation States of Micronesia (FSM), using an integrative approach that combined morphological characteristics, molecular phylogenetics (COX1 and 16S rRNA), and complete mitochondrial genome analysis. While the Chuuk population exhibited morphological features consistent with R. nilotica, molecular data revealed substantial genetic divergence. Phylogenetic analyses based on the complete mitochondrial genome (17,664 bp) clustered the Chuuk specimen with Rochia virgata. Phylogenies inferred from concatenated COX1 and 16S rRNA gene sequences yielded congruent topologies, placing the Chuuk lineage within the Rochia clade but clearly separated from other R. nilotica populations in New Caledonia and Mo’orea Island, French Polynesia. This genetic divergence is likely driven by the long-term geographic isolation of Chuuk Atoll. The lagoon’s fringing reefs descend rapidly into waters exceeding 4000 m, which may act as a barrier to restricting larval dispersal. Combined with the extremely short planktonic larval duration of R. nilotica (approximately four days), such environmental isolation may promote the formation of a distinct gene pool. Despite morphological uniformity, the observed genetic divergence suggests that the Chuuk population may represent a cryptic species. Our study provides a complete mitochondrial genome and offers robust phylogenetic framework that provides an understanding of species boundaries within Rochia. These findings underscore the importance of integrating genomic and morphological data for accurate species identification and have implications for conservation and sustainable aquaculture practices in geographically isolated reef ecosystems. Full article

This paper presents an efficient and high-order WENO-based Upwind Rotated Lattice Boltzmann Flux Solver (WENO-URLBFS) on graphics processing units (GPUs) for simulating three-dimensional (3D) compressible flow problems. The proposed approach extends the baseline Rotated Lattice Boltzmann Flux Solver (RLBFS) by redefining the interface tangential velocity based on the theoretical solution of the Euler equations. This improvement, combined with a weighted decomposition of the numerical fluxes in two mutually perpendicular directions, effectively reduces numerical dissipation and enhances solution stability. To achieve high-order accuracy, the WENO interpolation is applied in the characteristic space to reconstruct physical quantities on both sides of the interface. The density perturbation test is employed to assess the accuracy of the scheme, which demonstrates 5th- and 7th-order convergence as expected. In addition, this test case is also employed to confirm the consistency between the CPU serial and GPU parallel implementations of the WENO-URLBFS scheme and to assess the acceleration performance across different grid resolutions, yielding a maximum speedup factor of 1208.27. The low-dissipation property of the scheme is further assessed through the inviscid Taylor–Green vortex problem. Finally, a series of challenging three-dimensional benchmark cases demonstrate that the present scheme achieves high accuracy, low dissipation, and excellent computational efficiency in simulating strongly compressible flows with complex features such as strong shock waves and discontinuities. Full article

Predicting wildland fire spread requires numerical schemes that can resolve sharp gradients at the fireline while remaining stable and efficient on practical grids. We develop a compact high-order finite-difference scheme for Hamilton–Jacobi level-set formulations of wildfire propagation, based on the anisotropic spread law of Mallet and co-authors. The spatial discretization employs a compact finite-difference derivative scheme to achieve spectral-like resolution with narrow stencils, improving accuracy and boundary robustness compared with wide-stencil ENO/WENO reconstructions. To control high-frequency artifacts intrinsic to non-dissipative compact schemes, an implicit high-order low-pass filter is incorporated and activated after each Runge–Kutta stage. Convergence is verified on the eikonal expanding-circle benchmark, where the method attains the expected high-order spatial accuracy as the grid is refined. The proposed scheme is then applied to wind-driven wildfire simulations governed by Mallet’s non-convex Hamiltonian, including a single ignition under moderate and strong wind. A complex topology test case is also considered, involving two ignitions that merge into a single front with the evolution of an internal unburnt island. The results demonstrate that the proposed method accurately reproduces fireline evolution even on coarse grids, achieving accuracy comparable to fifth-order WENO while maintaining superior fidelity in complex fireline topologies, where it better resolves multi-front interactions and topological changes in the fireline. This makes the method an efficient, accurate alternative for level-set wildfire modeling and readily integrable into existing frameworks. Full article

In this paper, we propose the MUSWENO scheme, a novel mapped weighted essentially non-oscillatory (WENO) method that employs unequal-sized stencils, for solving nonlinear degenerate parabolic equations. The new mapping function and nonlinear weights are proposed to reduce the difference between the linear weights and nonlinear weights. Smaller numerical errors and fifth-order accuracy are obtained. Compared with traditional WENO schemes, this new scheme offers the advantage that linear weights can be any positive numbers on the condition that their summation is one, eliminating the need to handle cases with negative linear weights. Another advantage is that we can reconstruct a polynomial over the large stencil, while many classical high-order WENO reconstructions only reconstruct the values at the boundary points or discrete quadrature points. Extensive examples have verified the good representations of this scheme. Full article

Inertial confinement fusion (ICF) stands as one of the approaches to achieve controlled thermonuclear fusion, capable of supplying humans with abundant, economical, and safe energy. In this study, the high-order hybrid compact–WENO scheme is employed to simulate Rayleigh–Taylor instability (RTI) phenomena, one of the challenges hindering the realization of ICF, and to investigate the interaction of RTI phenomena in a multi-layer fluid system. To ensure a more reasonable comparison, the corresponding initial and boundary conditions for three-layer and four-layer fluids are derived based on the same Atwood number. Numerical results show that with the development of RTI phenomena, the interaction between interfaces can be gradually observed. The number of fluid layers exhibits an inhibitory effect on the development of RTI phenomena. When a pair of spike and bubble at two adjacent interfaces reach the same height, the evolution of the spike–bubble gap changes significantly. Full article

In this study, we introduce a novel 2-step compact scheme-based high-order correction method for computational fluid dynamics (CFD). Unlike traditional single-formula-based schemes, our proposed approach refines flux function values by leveraging results from high-order compact schemes on the same stencils, provided a certain smoothness condition is met. By applying this method, we achieve a more stable and efficient compact corrected Weighted Essentially Non-Oscillatory (WENO) scheme. The results demonstrate significant improvements across all enhanced schemes, particularly in capturing shock waves sharply and maintaining stability in complex scenarios, such as two interacting blast waves, as validated through 1D benchmark tests. In addition, error analysis is also provided for the two different correction configurations based on WENO. Full article

Micro-vortex generators (MVGs) are widely utilized as passive devices to control flow separation in supersonic boundary layers by generating ring-like vortices that mitigate shock-induced effects. This study employs large eddy simulation (LES) to investigate the flow structures in a supersonic boundary layer (Mach 2.5, Re = 5760) controlled by two MVGs installed in tandem, with spacings varying from 11.75 h to 18.75 h (h = MVG height), alongside a single-MVG reference case. A fifth-order WENO scheme and third-order TVD Runge–Kutta method were used to solve the unfiltered Navier–Stokes equations, with the Liutex method applied to visualize vortex structures. Results reveal that tandem MVGs produce complex vortex interactions, with spanwise and streamwise vortices merging extensively, leading to a significant reduction in vortex intensity due to mutual cancellation. A momentum deficit forms behind the second MVG, weakening that from the first, while the boundary layer energy thickness doubles compared to the single-MVG case, indicating increased energy loss. Streamwise vorticity distributions and instantaneous streamlines highlight intensified interactions with closer spacings, yet this complexity diminishes overall flow control effectiveness. Contrary to expectations, the tandem configuration does not enhance boundary layer control but instead weakens it, as evidenced by reduced vortex strength and amplified energy dissipation. These findings underscore a critical trade-off in tandem MVG deployment, suggesting that while vortex interactions enrich flow complexity, they may compromise the intended control benefits in supersonic flows, with implications for optimizing MVG arrangements in practical applications. Full article

This paper addresses fundamental challenges in numerical approximation methods, focusing on balancing accuracy with shape-preserving properties. We present novel approaches that combine traditional spline methods with modern numerical techniques, extending existing quasi-interpolation techniques based on B-splines. Our methods maintain computational efficiency while better handling discontinuities, achieving $C^1$ and $C^2$ reconstructions and preserving essential shape properties. We demonstrate theoretical frameworks showing optimal approximation order $O\left(h^{d+1}\right)$, $d=2,3$, with local reconstruction. Numerical experiments confirm significant improvements in accuracy and smoothness near discontinuities compared to existing methods, particularly in image processing and shock-capturing applications. Full article

This paper develops a numerical simulation method for polymer-flooding reservoirs using the high-order Weighted Essentially Non-Oscillatory (WENO) scheme. The research begins by leveraging the WENO method to obtain high-order approximations of the saturation and polymer concentration functions and formulates a sequential solution strategy for the hyperbolic mass conservation equations of the water phase and polymer component in these reservoirs. Three numerical tests compare the WENO scheme with the traditional first-order upwind difference method. The results show that the WENO scheme has higher computational accuracy, especially in predicting fronts, which improves the prediction of water cut and polymer production concentration. Under the same accuracy, the WENO method requires fewer grids and has much higher computational efficiency. A sensitivity analysis of the polymer solution viscosity parameters verifies that the WENO method can accurately simulate reservoir production behavior, providing an efficient and accurate reservoir simulation alternative. Full article

The dispersion and dissipation properties of a numerical scheme are critical in simulating flow fields involving a wide range of length scales. In this study, we highlight the common oversight of focusing merely on controlling dispersion error without considering the importance of appropriate dispersion and scalability in computational efficiency. This study demonstrates that adjusting dispersion to match the local flow field near discontinuities is more effective in suppressing oscillations than simply minimizing dispersion. This proposed high-order finite difference scheme with adaptive dispersion minimized dissipation (ADMD) achieves adaptive controllable dispersion near flow field discontinuities, known as the ADMD scheme. This scheme, derived as a fourth-order finite difference scheme with seven points based on Taylor expansion, comprises a basic central component, additional dissipation component, and dispersion component. By exploring the effect of dispersion on numerical oscillations and the importance of adjusting dispersion according to the local flow field, a discontinuity detection function was established to enable the dispersion properties to adapt to the local flow field. Drawing inspiration from flow field smoothing in the weighted essentially non-oscillatory (WENO) scheme, efforts were made to minimize scheme dissipation. The main benefits of the ADMD scheme over several WENO-type schemes are robustness and efficiency, as the ADMD scheme saves at least 40–90% CPU time compared to the same-order WENO-type schemes for some numerical examples. Additionally, the numerical scheme proves advantageous in terms of simulating the decaying isotropic turbulence problem of three-dimensional compressible turbulence. Full article