arXiv subjects

Xing Ji

Publications and source records attributed to Xing Ji.

At least 19 recordsLinked to original sources

arXiv2026

High-order compact ALE gas-kinetic scheme on three-dimensional unstructured meshes

In this paper, a compact high-order gas-kinetic scheme (HGKS) is developed for compressible arbitrary Lagrangian-Eulerian (ALE) computations on three-dimensional unstructured meshes. To achieve high-order spatial accuracy, a large number of matrix inversions are required for spatial reconstruction. In ALE computations, the mesh moves and the geometric information must be recalculated at each time step, which reduces computational efficiency. To improve efficiency, a memory-reduction reconstruction strategy is employed to construct a quadratic polynomial on unstructured meshes. By differentiating the candidate polynomial, the quadratic terms are obtained by the least-squares method using the average gradient values of the cell itself and its neighboring cells. The linear terms of the polynomial are also determined by the least-squares method. On three-dimensional unstructured meshes, a $3\times3$ coefficient matrix must be stored, and four least-squares procedures are required to construct a quadratic polynomial. To suppress numerical oscillations in flows with discontinuities, generalized essentially non-oscillatory (GENO) reconstruction and a gradient compression factor are adopted. To accelerate the computation, a multi-GPU accelerated code is implemented using Compute Unified Device Architecture (CUDA) and Message Passing Interface (MPI). The current scheme is fully explicit, and the acceleration framework can be developed based on cell-level parallelism. Numerical examples are presented to evaluate the accuracy and robustness of the scheme, including flows with strong discontinuities, pitching wings, and helicopter rotors. Numerical results confirm the excellent performance of the compact ALE scheme on unstructured meshes.

math-ph↗

arXiv2026

A semi-implicit unified gas-kinetic wave-particle method with energy-conserving electromagnetic coupling for multiscale plasmas

In multiscale plasmas, kinetic regions coexist with collision-dominated, strongly magnetized and quasi-neutral ones. In these regions, the collision time, the cyclotron period and the plasma period, respectively, are far shorter than the flow time scales. Schemes that treat the collisions and the field coupling explicitly must take time steps below these times and below the light-crossing time of a cell. This paper presents a semi-implicit unified gas-kinetic wave-particle (UGKWP) method for the multispecies Vlasov-Maxwell system with Bhatnagar-Gross-Krook collisions. The electric field follows from a reformulated Maxwell equation, a single linear system with a unique solution for any time step. Its current response is built from the implicit-midpoint velocity map, which then pushes the particles and the hydrodynamic wave alike. The field step conserves the discrete total energy exactly and remains stable without resolving the cyclotron period, the plasma period or the light-crossing time, so that the time step follows from the flow and sound speeds. A Gauss's law correction adjusts the electric field and the joint charge of particles and wave while conserving the mass, momentum and energy of every charged species. The method reproduces whistler waves and electron plasma waves from Landau damping to collision-dominated oscillations. It agrees with particle-in-cell, two-fluid and magnetohydrodynamic references in a Brio-Wu problem from weak to strong collisionality and magnetization, the Orszag-Tang vortex and collisionless magnetic reconnection. It needs far less CPU time than either the UGKWP method with an explicit solver for the perfectly hyperbolic Maxwell equations or a deterministic multiscale kinetic scheme. In collisional plasmas, it also needs less CPU time than an implicit particle-in-cell method with the same collision operator, increasingly so as collisions strengthen.

physics.plasm-ph↗

arXiv2026

A GPU-efficient local ADER finite-difference method for compressible-flow DNS

Algorithm design tailored to graphics processing units (GPUs) can substantially improve the efficiency of computational fluid dynamics (CFD) simulations. Efforts to adapt CFD solvers to GPUs often focus on spatial discretization, while time advancement commonly relies on multistage Runge--Kutta (RK) methods. However, these RK methods require repeated residual evaluations and full-domain operations, increasing the cost of compressible-flow direct numerical simulation (DNS). To reduce this overhead, we develop a local arbitrary high-order derivatives (ADER) finite-difference method that couples a compact ten-point quadratic predictor to a conservative central corrector through operator matching. With two quadrature nodes, one Picard correction, and selective dissipation, smooth convective tests recover third-order convergence under fixed-CFL refinement and near-seventh-order spatial behavior when background spatial error dominates. Temporal states remain kernel-local, and halo communication overlaps interior computation. Tests of smooth advection, periodic turbulence, and wall-bounded flows assess accuracy and flow statistics. On a $302^3$-node viscous Taylor--Green benchmark without heat conduction, throughput reaches 230.87 million node updates per second on one V100 GPU in double precision, 1.944 times that of spatially matched three-stage Runge--Kutta integration. Weak-scaling efficiency reaches 99.44\% from 4 to 32 V100 GPUs at 1.812 billion nodes.

physics.comp-ph↗

arXiv2026

A polar-harmonic unified gas-kinetic scheme for magnetized ion dynamics from cyclotron kinetics to the Hall-Pedersen constitutive limit

Magnetized ion transport in weakly ionized plasmas ranges from gyroangle-dependent kinetics to Hall-Pedersen drift-diffusion as collisionality and magnetization vary. We develop a polar-harmonic unified gas-kinetic scheme (PH-UGKS) for the ion Vlasov-BGK equation in a uniform magnetic field. The scheme evolves the full ion distribution by coupling a conservative density update to exponential evolution of its nonequilibrium component. Exact collision-rotation integration in gyroangle Fourier space is combined with a time-averaged kinetic flux that incorporates spatial transport and electric acceleration, together with a compact Hall-Pedersen correction to the density flux. The scheme conserves ion number, and analysis establishes second-order temporal consistency and asymptotic preservation of the Hall-Pedersen density limit at fixed magnetization. Numerical tests reproduce ion Bernstein dispersion and Dory-Guest-Harris growth rates and resolve changes in the gyroharmonic spectrum as the collision-to-gyrofrequency ratio varies. The driven ion-flux response agrees with an independent characteristic-Volterra reference, including finite-frequency departures from the instantaneous Hall-Pedersen relation. In collisional tests, accurate responses are obtained with time steps far larger than both the collision time and the gyroperiod. Fixed-resolution density tests confirm convergence to the corresponding Hall-Pedersen discretization. The same kinetic formulation thus connects kinetic response and macroscopic transport without switching to a fluid solver or subcycling microscopic time scales.

physics.plasm-ph↗

arXiv2026

A GPGPU-Oriented Full Phase-Space Parallel Unified Gas-Kinetic Scheme with Velocity-Block Pipelining

The deterministic unified gas-kinetic scheme (UGKS) provides a multiscale framework for nonequilibrium gas dynamics, but its high-dimensional phase-space discretization leads to severe memory pressure and communication overhead, especially on large unstructured meshes. This paper presents a GPGPU-oriented UGKS with velocity-block pipelining and full phase-space MPI decomposition. In the proposed formulation, the discrete velocity space is partitioned into fixed-size velocity blocks for accelerator execution, while MPI ranks are organized into coupled physical-space and velocity-space communicators. As a result, each rank stores and advances only a local physical subdomain together with a contiguous subset of velocity blocks, and macroscopic moments are recovered through lightweight reductions over the velocity-space communicator. To improve concurrency and reduce exposed communication cost, a triple-buffered pipeline is further developed to overlap microscopic reconstruction, physical-halo exchange, nonequilibrium flux evaluation, and the first-stage distribution update during the local velocity-block sweep. The implementation targets SIMT-based GPGPU accelerators through a portable device-runtime abstraction. Numerical experiments demonstrate that the $P_v=8$ configuration achieves a $33.4$--$35.4\times$ strong-scaling speedup on 64 nodes, while an Orion-like capsule simulation reaches approximately $1.33\times10^{11}$ phase-space degrees of freedom on 4096 GPGPU accelerators. These results indicate that the proposed method preserves the original UGKS flux construction and two-stage time discretization, while substantially reducing microscopic storage per rank and improving the scalability of large unstructured phase-space simulations.

physics.comp-ph↗

arXiv2026

A single-stage high-order compact gas-kinetic scheme in arbitrary Lagrangian-Eulerian formulation

This study presents the development of a compact gas-kinetic scheme using an arbitrary Lagrangian-Eulerian (ALE) formulation for structured meshes. Unlike the Eulerian formulation, the ALE approach effectively tracks flow discontinuities, such as shock waves and contact discontinuities. However, mesh motion alters the geometry and increases computational costs. To address this, two key strategies were introduced to reduce costs and enhance accuracy. The first strategy is to use the gas-kinetic scheme to construct a third-order gas-kinetic flux, rather than the Runge-Kutta method to achieve high-order time accuracy, which allows a single reconstruction and flux calculation per time step. This approach enables direct updates of both cell-averaged flow variables and their gradients using a time-accurate flux function, facilitating compact reconstruction. Second, the significant computational expense is spent on reconstruction, which requires recalculating the reconstruction matrix at each time step due to mesh changes. A simplified fourth-order compact reconstruction using a small matrix was used to mitigate this cost. The combination of fourth-order spatial reconstruction and third-order time-accurate flux evolution ensures both high resolution and computational efficiency in the ALE framework. The tests shows that the current reconstruction is 2.4x to 3.0x faster than the previous reconstruction. Additionally, a generalized ENO(GENO) method for handling discontinuities enhances the scheme's robustness. The numerical test cases, such as the Riemann problem, Sedov problem, Noh problem, and Saltzmann problem, demonstrated the robustness and accuracy of our method.

physics.comp-ph↗

arXiv2026

A Three-Dimensional Two-Temperature Gas-Kinetic Scheme with Generalized Kinetic Boundary Condition for Hypersonic SBLI

Accurate prediction of aerothermal loads in hypersonic flows is critical yet challenging due to the coupling of Shock-Wave/Boundary-Layer Interactions (SBLI) and thermal non-equilibrium. This work presents the development of a three-dimensional two-temperature Gas-Kinetic Scheme (3D 2T-GKS) on unstructured meshes. The scheme resolves translational-rotational and vibrational energy modes within a unified kinetic framework. A key innovation is the integration of a Generalized Kinetic Boundary Condition (GKBC), which physically decouples the thermal accommodation of vibrational energy from the translational-rotational mode, thereby offering a more accurate model for gas-surface interactions. Additionally, a Discontinuity Feedback Factor (DFF) is employed to capture strong shock waves with reduced numerical dissipation compared to classical limiters. The method is rigorously validated against standard experimental benchmarks, including the sharp double-cone and hollow cylinder-flare configurations. Numerical results demonstrate that the proposed solver, augmented by the GKBC, accurately captures complex wave structures, separation topologies, and surface heat flux distributions. These findings confirm the robustness and fidelity of the 3D 2T-GKS for simulating complex hypersonic non-equilibrium flows.

physics.flu-dyn↗

arXiv2026

The stability priority of spatial-temporal coupled compact element methods over decoupled compact element methods

With the increasing industrial demands, two families of high-order numerical schemes are widely used within the computational fluid dynamics community. One is the method of line, which relies on Runge-Kutta (RK) time-stepping applied to a semi-discrete, spatio-temporally decoupled formulation. The other is the family of Lax-Wendroff (LW) type method, which are inherently spatial-temporal coupled and are constructed within a multi-stage multi-derivative (MSMD) framework. This paper, for the first time, conducted a comparative Fourier stability analysis of RK and LW method to distinguish the dispersion and dissipation effects of numerical schemes respectively. Through rigorous theoretical derivation and consistent numerical validation, we draw the following conclusions: While explicit RK line methods are straightforward like Discontinuous Galerkin (DG) method and flux reconstruction (FR) method, they employ from a decoupling of spatial and temporal accuracy, thus discarding flow field evolution information and requiring small time steps. In contrast, spatial-temporal coupled compact methods, such as the gas-kinetic scheme (GKS) and the generalized Riemann problem (GRP) solver, utilize initial-value information from space far more effectively for time evolution. Even with just one additional order of spatial-temporal coupled information, they show better stability compared to RK methods. This provides new insights for CFD algorithm design, emphasizing the need for consistency between the dependence in the physical domain and that in numerical domain.

math-ph↗

arXiv2026

A two-temperature gas-kinetic scheme for hypersonic nonequilibrium flow computations

Accurate aerodynamic and aerothermodynamic predictions are crucial for numerous hypersonic applications. This paper proposes a gas-kinetic scheme (GKS) coupled with a two-temperature kinetic model, which distinguishes between the translational-rotational and vibrational modes of temperature. Compared with one-temperature model and the translational-rotational multi-temperature model, the proposed model provides a more physically accurate simulation of real gas effects when vibrational energy modes of air are excited. On the other hand, it is computationally simpler than multi-temperature model with independent translational, rotational and vibrational modes. The scheme is implemented on both structured and unstructured grids. To further improve the robustness for strong shock and rarefaction waves, the discontinuity feedback factor is employed instead of traditional limiters. Numerical verifications are conducted on one-dimensional shock structure, two-dimensional (2D) hypersonic flow over a cylinder, 2D hypersonic flow over a wedge and 2D Edney Type IV shock/shock interaction. Compared with experimental data, the reference results from direct simulation Monte Carlo (DSMC) method and Navier--Stokes (NS) solvers, the present method demonstrates accurate prediction of the thermally non-equilibrium shock wave structures and hypersonic flow fields.

physics.flu-dyn↗

arXiv2025

A Geometric Multigrid-Accelerated Compact Gas-Kinetic Scheme for Fast Convergence in High-Speed Flows on GPUs

Implicit methods and GPU parallelization are two distinct yet powerful strategies for accelerating high-order CFD algorithms. However, few studies have successfully integrated both approaches within high-speed flow solvers. The core challenge lies in preserving the robustness of implicit algorithms in the presence of strong discontinuities, while simultaneously enabling massive thread parallelism under the constraints of limited GPU memory. To address this, we propose a GPU-optimized, geometric multigrid-accelerated, high-order compact gas kinetic scheme (CGKS) that incorporates three key innovations: (1) a multi-color lower-upper symmetric Gauss-Seidel scheme that eliminates thread conflicts and preserves memory efficiency, serving as an implicit smoother on coarse grids; (2) a discontinuity-adaptive relaxation technique and a multigrid prolongation process, based on a discontinuous feedback factor, which dynamically stabilize shock regions without compromising convergence in smooth zones; and (3) a three-layer V-cycle geometric parallel multigrid strategy specifically tailored for unstructured meshes. Extensive tests on multi-dimensional subsonic to hypersonic flows demonstrate that our GPU-based high-performance solver achieves one to two orders of magnitude faster convergence compared to previous explicit solvers. More importantly, it preserves the shock-capturing robustness of the explicit CGKS and exhibits strong scalability on GPU architectures. This work presents a unified framework that synergistically leverages implicit acceleration and GPU optimization for high-speed flow simulations, effectively overcoming traditional trade-offs between parallelism, memory constraints, and numerical stability in high-order methods.

math.NA↗

arXiv2025

Very High-order Compact Gas-kinetic Scheme With Discontinuity Feedback Factor

This paper presents a robust and efficient very high-order scheme for compressible flow simulation, addressing critical limitations of existing high-order methods. The proposed scheme combines the compact gas-kinetic scheme (CGKS) with an adaptive stencil extension reconstruction with discontinuity feedback factor (ASE-DFF), achieving significant improvements in both robustness and computational efficiency. Traditional weighted essentially non-oscillatory (WENO) schemes suffer from reduced robustness at higher order and require costly smoothness indicators for large stencils. Meanwhile, compact methods based on Discontinuous Galerkin (DG) and Flux Reconstruction (FR) struggle with poor time-marching efficiency. In contrast, the ASE-DFF-CGKS introduces two key innovations: (1) a unified framework enabling arbitrarily high-order compact gas-kinetic scheme without sacrificing large CFL number, and (2) a discontinuity feedback factor that eliminates the need for expensive smoothness indicator calculations while essentially keeping first-order robustness near discontinuities. The scheme's advantages are demonstrated through benchmark simulations. It maintains a CFL number above 0.5 for up to 9th-order case, unlike conventional compact methods that restrict a CFL less than 0.05. Also it delivers high-resolution results for flow involving strong shock and rarefaction wave. This work provides a practically impactful solution for high-fidelity compressible flow simulation, balancing computational efficiency, high-order accuracy and robustness in challenging flow regimes.

physics.comp-ph↗

arXiv2025

An efficient and robust high-order compact ALE gas-kinetic scheme for unstructured meshes

For the arbitrary-Lagrangian-Eulerian (ALE) calculations, the geometric information needs to be calculated at each time step due to the movement of mesh. To achieve the high-order spatial accuracy, a large number of matrix inversions are needed, which affect the efficiency of computation dramatically. In this paper, an efficient and robust high-order compact ALE gas-kinetic scheme is developed for the compressible moving grids and moving boundary problems. The memory-reduction reconstruction is used to construct a quadratic polynomial on the target cell, where both structured and unstructured meshes can be used. Taking derivatives of the candidate polynomial, the quadratic terms can be obtained by the least square method using the average gradient values of the cell itself and its adjacent cells. Moving the quadratic terms to right-hand side of the constrains for cell averaged value, the linear terms of the polynomial can be determined by the least square method as well. The gradient compression factor is adopted to suppress the spurious oscillations near discontinuities. Combined with the two-stage fourth-order time discretization, a high-order compact gas-kinetic scheme is developed for ALE computation. In the process of mesh movement, the inversions of lower order matrix are needed for the least square method, which makes a 7x speedup and improves the efficiency greatly. In the computation, the grid velocity can be given by the mesh adaptation method and the cell centered Lagrangian nodal solver. Numerical examples are presented to evaluate the accuracy, efficiency, robustness and the preservation of geometric conservation law of the current scheme.

physics.comp-ph↗

arXiv2025

An implicit gas-kinetic scheme for internal and external flows

The gas-kinetic scheme(GKS) is a promising computational fluid dynamics (CFD) method for solving the Navier-Stokes equations. It is based on the analytical solution of the BGK equation, which enables accurate and robust simulations. While GKS has demonstrated excellent properties (e.g., unified treatment of inviscid and viscous fluxes, inherent adaptive dissipation control), its application to classical engineering problems, such as aerodynamic flows and fluid machinery, remains underdeveloped compared to conventional CFD methods. This study bridges this gap by advancing GKS capabilities for real-world engineering challenges. First, the GKS is extended to a rotating coordinate frame, enabling efficient simulations of internal flows in turbomachinery. Second, the computational inefficiency of explicit GKS is addressed through an implicit time discretization using the generalized minimal residual method. The Jacobian matrices for inviscid/viscous fluxes are approximated using the first-order kinetic flux vector splitting scheme and the thin shear layer approximation to enhance robustness and computational efficiency further. Third, the shear-stress transport turbulence model is coupled to expand GKS's applicability to industrial turbulent flows. Numerical tests, including internal compressor rotor flow and external flow over a 3-D wingbody, validate the proposed method's accuracy and efficiency. Via our implicit scheme, the force coefficients of the 3-D wing-body flow with about five million mesh elements can converge after 500 steps. This work represents a practical advancement of GKS, demonstrating its potential to compete with established CFD solvers in high-Reynolds-number external and internal turbulent flows.

physics.flu-dyn↗

arXiv2025

UGKWP and IUGKP methods for Multi-Scale Phonon Transport with Dispersion and Polarization

This paper presents two novel methods for solving multi-scale phonon transport problems with dispersion and polarization effects: the unified gas-kinetic wave-particle (UGKWP) method and the implicit unified gas-kinetic particle (IUGKP) method. Both approaches are based on solving multiple groups of BGK equations at discrete frequency points. The UGKWP method constructs multiscale macroscopic fluxes at cell interfaces through the integral solution of the unsteady BGK equation and efficiently captures non-equilibrium transport using statistical particles. Its wave-particle adaptive framework ensures computational efficiency across different regimes: in the diffusive limit, it matches the cost of explicit diffusion equation solutions, while in the ballistic limit, it performs comparably to pure particle methods. The IUGKP method, specifically designed for steady-state problems, determines the particle evolution scale based on the physical mean free path. This approach enables rapid convergence at both large and small Knudsen numbers, with the latter facilitated by a newly constructed macroscopic prediction equation. Both methods incorporate an adaptive frequency-space sampling technique that maintains particle counts per cell comparable to single-frequency methods, significantly improving computational efficiency and memory usage. The accuracy and efficiency of both methods are validated through various numerical tests, including large-scale three-dimensional conduction heat transfer simulations. Results demonstrate their effectiveness in handling complex phonon transport phenomena across multiple scales.

physics.comp-ph↗

arXiv2025

Implicit unified gas kinetic particle method for steady-state solution of multiscale phonon transport

This paper presents a highly efficient implicit unified gas-kinetic particle (IUGKP) method for obtaining steady-state solutions of multi-scale phonon transport. The method adapts and reinterprets the integral solution of the BGK equation for time-independent solutions. The distribution function at a given point is determined solely by the surrounding equilibrium states, where the corresponding macroscopic quantities are computed through a weighted sum of equilibrium distribution functions from neighboring spatial positions. From a particle perspective, changes in macroscopic quantities within a cell result from particle transport across cell interfaces. These particles are sampled according to the equilibrium state of their original cells, accounting for their mean free path as the traveling distance. The IUGKP method evolves the solution according to the physical relaxation time scale, achieving high efficiency in large Knudsen number regimes. To accelerate convergence for small Knudsen numbers, an inexact Newton iteration method is implemented, incorporating macroscopic equations for convergence acceleration in the near-diffusive limit. The method also addresses spatial-temporal inconsistency caused by relaxation time variations in physical space through the null-collision concept. Numerical tests demonstrate the method's excellent performance in accelerating multi-scale phonon transport solutions, achieving speedups of one to two orders of magnitude. The IUGKP method proves to be an efficient and accurate computational tool for simulating multiscale non-equilibrium heat transfer, offering significant advantages over traditional methods in both numerical performance and physical applicability.

physics.comp-ph↗

arXiv2025

Unified gas-kinetic wave-particle method for multi-scale phonon transport

Over the past 7 decades, the classical Monte Carlo method has played a huge role in the fields of rarefied gas flow and micro/nano scale heat transfer, but it also has shortcomings: the time step and cell size are limited by the relaxation time and mean free path, making it difficult to efficiently simulate multi-scale heat and mass transfer problems from the ballistic to diffusion limit. To overcome this drawback, a unified gas-kinetic wave-particle (UGKWP) method is developed for solving the phonon Boltzmann transport equation (BTE) in all regimes covering both ballistic and diffusive limits. This method is built upon the space-time coupled evolution model of the phonon BTE, which provides the framework for constructing a multi-scale flux at the cell interfaces. At the same time, in order to capture non-equilibrium transport efficiently, the multi-scale flux comprises two distinct components: a deterministic part for capturing the near-equilibrium or diffusive transport and a statistical particle part for recovering non-equilibrium or ballistic transport phenomena. The UGKWP method exhibits remarkable multi-scale adaptability and versatility, seamlessly bridging the gap between the diffusive and ballistic transport phenomena. In the diffusive limit, the present method naturally converges to the Fourier's law, with the diminishing particle contribution, whereas in the ballistic limit, the non-equilibrium flux is fully described by the free-streaming particles. This inherent adaptability not only allows for precise capturing of both equilibrium and non-equilibrium heat transfer processes but also guarantees that the model adheres strictly to the underlying physical laws in each phonon transport regime.

physics.comp-ph↗

arXiv2025

Treatment of Wall Boundary Conditions in High-Order Compact Gas-Kinetic Schemes

The boundary layer represents a fundamental structure in fluid dynamics, where accurate boundary discretization significantly enhances computational efficiency. This paper presents a third-order boundary discretization for compact gas-kinetic scheme (GKS). Wide stencils and curved boundaries pose challenges in the boundary treatment for high-order schemes, particularly for temporal accuracy. By utilizing a time-dependent gas distribution function, the GKS simultaneously evaluates fluxes and updates flow variables at cell interfaces, enabling the concurrent update of cell-averaged flow variables and their gradients within the third-order compact scheme. The proposed one-sided discretization achieves third-order spatial accuracy on boundary cells by utilizing updated flow variables and gradients in the discretization for non-slip wall boundary conditions. High-order temporal accuracy on boundary cells is achieved through the GKS time-dependent flux implementation with multi-stage multi-derivative methodology. Additionally, we develop exact no-penetration conditions for both adiabatic and isothermal wall boundaries, with extensions to curved mesh geometries to fully exploit the advantages of high-order schemes. Comparative analysis between the proposed one-sided third-order boundary scheme, third-order boundary scheme with ghost cells, and second-order boundary scheme demonstrates significant performance differences for the third-order compact GKS. Results indicate that lower-order boundary cell treatments yield substantially inferior results, while the proposed third-order treatment demonstrates superior performance, particularly on coarse grid configurations.

math.NA↗

arXiv2024

An Adaptive Reconstruction Method for Arbitrary High-Order Accuracy Using Discontinuity Feedback

This paper introduces an effcient class of adaptive stencil extension reconstruction methods based on a discontinuity feedback factor, addressing the challenges of weak robustness and high computational cost in high-order schemes, particularly those of 7th-order or above. Two key innovations are presented: The accuracy order adaptively increases from the lowest level based on local stencil smoothness, contrasting with conventional methods like Weighted Essentially Non-Oscillatory (WENO) and Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL)limiters, which typically reduce order from the highest level. The Discontinuity Feedback Factor (DF) serves a dual purpose: detecting sub-cell discontinuity strength and explicitly incorporating into the reconstruction process as a local smoothness measure. This approach eliminates the need for computationally expensive smoothness indicators often required in very high-order schemes, such as 9th-order schemes, and can be easily generalized to arbitrary high-order schemes. Rigorous test cases, including a Mach 20000 jet, demonstrate the exceptional robustness of this approach.

math.NA↗