arXiv subjects

Wenpei Long

Publications and source records attributed to Wenpei Long.

14 recordsLinked to original sources

arXiv2026

A unified gas-kinetic wave-particle method for multiscale gas-mixture flow with an elementary chemical reaction

Hypersonic flows in the near space often couple continuum-rarefied multiscale effect with finite-rate chemistry. This paper extends the UGKWP method to multiscale gas mixture flows with a single elementary reaction. In the UGKWP method, hydrodynamic waves are employed to describe near-equilibrium distribution functions, and numerical particles are used for the evolution of nonequilibrium ones. The adaptive conversion between waves and particles, guided by the characteristic integral solution, together with the introduction of dt into the flux as an observation scale, has enabled the UGKWP method to succeed in many multiscale problems involving complex physics. In this work, rather than relying on a comprehensive reactive kinetic model for the entire distribution function, chemical source terms are first evaluated at the macroscopic level and then incorporated into the wave-particle update, while free-transport particles are kept chemically inactive in the monatomic setting considered here. This approach leverages the modeling advantages of wave-particle decoupling, facilitating extension to more complex chemical reactions. Moreover, an approximate extension of an advanced multispecies kinetic model is developed in this work for multispecies effect with species number larger than two. The present UGKWP method is assessed for the Zeldovich-type reaction O2+N=NO+O through hypersonic cylinder flows over a wide Knudsen number range, covering chemically inert, forward exothermic, forward endothermic and dE=0 conditions, and through shock structures with hot upstream/downstream equilibrium states. Agreement with DSMC is obtained for gas mixture flow fields, species mole fractions and wall quantities. A three-dimensional side jet flow over a blunt cone is further simulated to demonstrate the three-dimensional capability of the present code.

physics.comp-ph↗

arXiv2026

An asymptotic-preserving adjoint unified gas kinetic scheme for sensitivity analysis

High-dimensional sensitivity analysis and uncertainty quantification for multiscale gas dynamics, spanning the continuum to rarefied regimes, require computationally efficient and mathematically consistent gradient evaluation. This paper develops a discrete adjoint method for the unified gas-kinetic scheme (UGKS) based on a dual-consistent formulation. The adjoint system is derived directly from the discrete microscopic velocity-distribution equation coupled with the macroscopic-moment compatibility conditions. To resolve the stiff cross-scale coupling, we propose an asymptotic-preserving (AP) adjoint formulation constructed via macroscopic-moment projection and microscopic lifting. Under this framework, the AP adjoint formulation eliminates the stiff collision coupling and removes the collision-time step restriction in the continuum regime. Numerically, a memory-efficient residual-evaluation algorithm that mirrors the forward UGKS cell-vertex data structure is implemented to bypass the memory bottleneck in velocity space. Furthermore, a macroscopic--microscopic predictor--corrector implicit marching scheme is designed to accelerate convergence without solving a globally coupled system. The accuracy, consistency, and robustness of the proposed AP-adjoint scheme are rigorously verified against an independent linearized UGKS solver across a wide range of Knudsen numbers, including lid-driven cavity heat conduction, microchannel thermal creep flow, and hypersonic flow past a circular cylinder.

math.NA↗

arXiv2026

Rigorously justified local time stepping in the unified gas-kinetic wave-particle method for steady multiscale flow simulation

Local time stepping (LTS) can accelerate convergence to steady states in kinetic simulations with large variations in the local time steps across the computational domain. When neighboring cells advance with unequal time steps, the time-averaged particle flux must be balanced across their common interface. For particle-based or hybrid wave-particle methods under finite volume method (FVM) framework, we rigorously establish a sufficient condition for time-averaged interfacial particle-flux balance: fixed positive local time steps together with proportional particle-mass scaling. When a particle crosses from cell $L$ to cell $R$, its mass is scaled by $\Delta t_R/\Delta t_L$. In the unified gas-kinetic wave-particle (UGKWP) implementation, the same ratio is applied to the remaining free-transport time of the crossing particle. LTS also affects the wave-particle decomposition and the time integration of the wave fluxes in UGKWP. The wave-particle decomposition in cell $i$ is determined by the local ratio $\Delta t_i/\tau_i$, which better reflects the local relation between the observation scale and relaxation time for multiscale cases. The equilibrium and analytic free transport wave fluxes are integrated over and normalized by the corresponding cell-side time steps to obtain the interfacial time-averaged wave fluxes. The UGKWP-LTS method is used to simulate the hypersonic flow past a cylinder at $\mathrm{Kn}=0.01$ and $0.1$, and a flat plate at $\mathrm{Kn}=0.0169$. In all three cases, the surface quantities obtained with UGKWP-LTS agree well with the reference data. Relative to global time stepping (GTS), UGKWP-LTS achieves step-count speedups of $6.6\times$, $3.8\times$, and $20\times$ for the three cases, respectively. The corresponding wall-clock speedups are $7.1\times$, $4.5\times$, and approximately $21\times$.

physics.flu-dyn↗

arXiv2026

A second-order unified gas-kinetic wave-particle method with enhanced mesh independence for hypersonic flows

Benefiting from the direct modeling of physical laws in a discretized space and the automatic decomposition of the gas distribution function into hydrodynamic waves and particles, the UGKWP method offers significant advantages for multiscale flows such as hypersonic flows, plasma transport, and radiation transport. In this study, the particle sampling accuracy in the UGKWP method is improved from first order to second order, so that the second-order spatial and temporal accuracy is preserved across the full scheme. Specifically, the modifications include second-order particle sampling based on local macroscopic gradients, a weighted least-squares gradient reconstruction that incorporates wall values, a revised Venkatakrishnan limiter for highly stretched cells, and conservation corrections after particle sampling. Moreover, the first-order Chapman--Enskog term is considered in the free-transport part of the hydrodynamic wave flux, enabling better recovery of the GKS in the near-continuum regime. Based on these improvements, the mesh-independence behavior of the UGKWP method is notably enhanced, which is more consistent with the performance of the UGKS, validated by a detailed hypersonic cylinder flow test case. Furthermore, systematic comparisons with the single-scale DSMC method are performed for two-dimensional hypersonic flow over a cylinder and three-dimensional flow over a blunt cone. Wall pressure, shear stress, and heat flux coefficients (CP, CF, and CQ) are examined in the cylinder case, while the overall aerodynamic coefficients (CL, CD, and L/D) are assessed in the cone case. The multiscale UGKWP method exhibits significantly better mesh-independence performance than DSMC for mesh-sensitive quantities such as CF, CQ, CD, and L/D, which are critical for aerodynamic and thermal protection design of near-space hypersonic vehicles.

physics.flu-dyn↗

arXiv2026

Surrogate-Based Aerodynamic Shape Optimization in Multiscale Flows via the Implicit Unified Gas-Kinetic Scheme

While hypersonic glide vehicles such as the HTV-2 continue to be a focal point in aerospace research, their aerodynamic characteristics in complex near-space environments are not yet fully understood. Because traditional continuum assumptions fail to accurately capture multiscale flow features across varying rarefied altitudes, this study investigates the aerodynamic shape optimization of an HTV-2-type aircraft across multiple flow regimes. An automated optimization framework is developed by coupling surrogate-based optimization (SBO) with the implicit unified gas-kinetic scheme (IUGKS). To ensure relevance to practical engineering requirements, both volumetric and center-of-pressure constraints are incorporated into the optimization process. The resulting optimized configurations are subsequently validated through high-fidelity computations, detailed flow-field evaluations, and global sensitivity analyses. Under volumetric constraints, the optimized lift-to-drag ratio ($L/D$) increases significantly at altitudes ranging from 70 km to 100 km. The optimal aerodynamic strategy is shown to shift with altitude: at 70 km, reducing the windward radius ($R_1$) weakens the oblique shock wave, whereas at highly rarefied altitudes, reducing the leeward radius ($R_3$) enhances the expansion wave. Correspondingly, sensitivity analyses confirm that as flow rarefaction increases, aerodynamic dominance shifts toward $R_3$. Furthermore, reducing the wingtip bluntness ($R_2$)yields consistent aerodynamic benefits across the entire flight envelope, ultimately driving the optimized geometries toward a flatter and more slender profile.

physics.flu-dyn↗

arXiv2026

On the Applicability of the Gas-Kinetic Scheme with Kinetic Boundary Conditions for Near-Continuum Hypersonic Flows

Rarefied gas effects are of critical importance for the aerodynamic performance of hypersonic vehicles operating at high altitudes. In these scenarios, conventional computational fluid dynamics (CFD) solvers break down as the linear constitutive relations underlying the Navier-Stokes equations cease to be valid. Based on direct modeling, the unified gas-kinetic scheme (UGKS) and the unified gas-kinetic wave-particle (UGKWP) method successfully capture non-equilibrium physics across all Knudsen numbers, yet they incur substantially higher computational costs than continuum solvers. Within the same kinetic framework, the gas-kinetic scheme (GKS) employs the Chapman-Enskog expansion for near-equilibrium flow physics and adopts the same kinetic boundary conditions as UGKS and UGKWP. This formulation naturally permits velocity slip and temperature jump, thereby extending the applicability of GKS into the slip and transitional regimes. By utilizing this natural kinetic slip boundary condition, the GKS provides a more physically faithful representation of non-equilibrium wall interactions than conventional CFD solvers equipped with Maxwell-type slip conditions, ultimately yielding more accurate aerodynamic predictions. To determine the applicability of the GKS in near-continuum flow regimes, we first examine a simple circular cylinder geometry, comparing surface quantities and distribution functions in detail. Furthermore, we investigate a 9{\deg}blunted cone, a 70{\deg} blunted cone with a cylindrical sting, and the Apollo 6 command module. This analysis focuses on integrated aerodynamic predictions, which are validated against experimental data, Direct Simulation Monte Carlo (DSMC) simulations, and other kinetic methods.

physics.flu-dyn↗

arXiv2026

A unified gas-kinetic wave-particle method for multiscale binary-species gas mixtures

This paper presents a unified gas-kinetic wave-particle (UGKWP) method for simulating multiscale binary-species gas mixtures. Benefiting from direct modeling in a discretized space, the UGKWP method enables the automatic decomposition of the gas distribution function into analytical hydrodynamic waves and discrete particles, which respectively describe its near-equilibrium and non-equilibrium parts. This approach offers significant advantages for simulating various multiscale physical phenomena, such as hypersonic flows, plasma transport, and radiation transport. In this study, we employ the model proposed by Groppi et al. [EPL, 96 (2011) 64002] to calculate the macroscopic velocity and temperature of the local target equilibrium distribution function, thereby recovering the correct viscosity and diffusion coefficients in the continuum flow regime. To address the heat conduction coefficient, the Shakhov model is incorporated to correct the Prandtl number. Diffusion effects are accounted for not only in the source term via an operator-splitting method, but also in the flux evolution through the characteristic integral solution, while strictly maintaining consistency between the wave and particle descriptions. Furthermore, the microscopic model for high-speed particles is improved by utilizing a physically corrected collision time to determine their free-transport time. Through a series of numerical tests spanning the continuum to rarefied regimes, the proposed UGKWP method is shown to accurately capture the differences in velocity and temperature between different species. Notably, for hypersonic flows, the predicted wall pressure, shear stress, and heat flux coefficients agree well with DSMC results.

physics.flu-dyn↗

arXiv2026

Unified Gas-Kinetic Scheme for Unsteady Multiscale Flows with Moving Boundaries

Simulating multiscale flows with moving boundaries, such as hypersonic multi-body separation and flows in micro-electro-mechanical systems (MEMS), requires robust numerical methods that couple mesh deformation with complex flow physics. This paper presents a hybrid overlapping moving-mesh technique developed within the unified gas-kinetic scheme (UGKS). To mitigate the Courant-Friedrichs-Lewy (CFL) constraint, we extend the implicit unsteady UGKS solver to support moving meshes, incorporating memory-efficient data handling and parallel computing optimizations to maximize computational efficiency. Validated against hypersonic multi-body separation and thermal rarefied MEMS flows, the proposed scheme accurately resolves complex, dynamic multiscale phenomena. The results confirm that this robust and efficient method provides a highly reliable tool for modeling dynamic flow interactions in complex geometric configurations.

physics.flu-dyn↗

arXiv2025

Adaptive criterion and modification of wave-particle decomposition in UGKWP method for high-speed flow simulation

Benefitting from the direct modeling of physical laws in a discretized space and the automatic decomposition of hydrodynamic waves and particles, the unified gas-kinetic wave-particle (UGKWP) method offers notable advantages in various multiscale physics, such as hypersonic flow, plasma transport and radiation transport. Aiming at achieving a more suitable and efficient wave-particle decomposition in high-speed flow simulation and enhancing the performance in the drastic scale variation region, in this work, the scale adaptive criterion is studied and the flux evolution of UGKWP method is modified. Specifically, besides the perspective of time which is naturally considered in the time-dependent distribution function of UGKWP method, two more criteria from views of space and gradient are utilized to identify the local scale, and to reduce the computational consumption of particles on describing the near-equilibrium microscopic gas distribution function. Moreover, corresponding to the coefficients in the time integration flux of unified gas-kinetic scheme (UGKS), the evolution of hydrodynamic wave is modified to be more consistent with particles, which is essential when the scale changes intensely in different cells. A variety of test cases are conducted to validate the performance of the adaptive UGKWP method, including hypersonic flows around a cylinder at multiple inflow Knudsen numbers, hypersonic flow over a slender cavity, side-jet impingement on hypersonic flow and three-dimensional hypersonic flows over a $70^{\circ}$ blunted cone with a cylindrical sting.

physics.comp-ph↗

arXiv2024

A Gas-Kinetic Scheme for Maxwell Equations

The Gas-Kinetic Scheme (GKS), widely used in computational fluid dynamics for simulating hypersonic and other complicated flow phenomena, is extended in this work to electromagnetic problems by solving Maxwell's equations. In contrast to the classical GKS formulation, the proposed scheme employs a discrete rather than a continuous velocity space. By evaluating a time-accurate numerical flux at cell interfaces, the proposed scheme attains second-order accuracy within a single step. Its kinetic formulation provides an inherently multidimensional framework, while the finite-volume formulation ensures straightforward extension to unstructured meshes. Through the incorporation of a collision process, the scheme exhibits lower numerical dissipation than classical flux-vector splitting (FVS) methods. Furthermore, the kinetic decomposition enables direct implementation of non-reflecting boundary conditions. The proposed scheme is validated against several benchmark problems and compared with established methods, including the Finite-Difference Time-Domain (FDTD) method and FVS. A lattice Boltzmann method (LBM) implementation is also included for comparative analysis. Finally, the technique is applied to simulate electromagnetic wave propagation in a realistic aircraft configuration, demonstrating its ability to model complex geometries.

math.NA↗

arXiv2024

An efficiency and memory-saving programming paradigm for the unified gas-kinetic scheme

In recent years, non-equilibrium flows have gained significant attention in aerospace engineering and micro-electro-mechanical systems. The unified gas-kinetic scheme (UGKS) follows the methodology of direct modeling to couple particle collisions and free transport during gas evolution. However, like other discrete-velocity-based methods, the UGKS faces challenges related to high memory requirements and computational costs, such as the possible consumption of $1.32$ TB of memory when using $512$ cores for the simulations of the hypersonic flow around an X38-like space vehicle. This paper introduces a new UGKS programming paradigm for unstructured grids, focusing on reducing memory usage and improving parallel efficiency. By optimizing the computational sequence, the current method enables each cell in physical space to store only the distribution function for the discretized velocity space, eliminating the need to retain the entire velocity space for slopes and residuals. Additionally, the parallel communication is enhanced through the use of non-blocking MPI. Numerical experiments demonstrate that the new strategy in the programming effectively simulates non-equilibrium problems while achieving high computational efficiency and low memory consumption. For the hypersonic flow around an X38-like space vehicle, the simulation, which utilizes $1,058,685$ physical mesh cells and $4,548$ discrete velocity space mesh cells, requires only $168.12$ GB of memory when executed on $512$ CPU cores. This indicates that memory consumption in the UGKS is much reduced. This new programming paradigm can serve as a reference for discrete velocity methods for solving kinetic equations.

physics.comp-ph↗

arXiv2024

An implicit adaptive unified gas-kinetic scheme for steady-state solutions of non-equilibrium flows

Nonequilibrium flows have been frequently encountered in various aerospace engineering applications. To understand nonequilibrium physics, multiscale effects, and the dynamics in these applications, an effective and reliable multiscale scheme for all flow regimes is required. Following the direct modeling methodology, the adaptive unified gas-kinetic scheme employs discrete velocity space (DVS) to accurately capture the non-equilibrium physics, recovering the original unified gas-kinetic scheme (UGKS), and adaptively employs continuous distribution functions based on the Chapman-Enskog expansion to achieve better efficiency. Different regions are dynamically coupled at the cell interface through the fluxes from the discrete and continuous gas distribution functions, thereby avoiding any buffer zone between them. In the current study, an implicit adaptive unified gas-kinetic scheme (IAUGKS) is constructed to further enhance the efficiency of steady-state solutions. The current scheme employs implicit macroscopic governing equations and couples them with implicit microscopic governing equations within the non-equilibrium region, resulting in high convergence efficiency in all flow regimes. A series of numerical tests were conducted for high Mach number flows around diverse geometries such as a cylinder, a sphere, an X-38-like vehicle, and a space station. The current scheme can capture the non-equilibrium physics and provide accurate predictions of surface quantities. In comparison with the original UGKS, the velocity space adaptation, unstructured DVS, and implicit iteration significantly improve the efficiency by one or two orders of magnitude. Given its exceptional efficiency and accuracy, the IAUGKS serves as an effective tool for nonequilibrium flow simulations.

physics.flu-dyn↗

arXiv2023

Adaptive unified gas-kinetic scheme for diatomic gases with rotational and vibrational nonequilibrium

Multiscale non-equilibrium physics at large variations of local Knudsen number are encountered in applications of aerospace engineering and micro-electro-mechanical systems, such as high-speed flying vehicles and low pressure of the encapsulation. An accurate description of flow physics in all flow regimes within a single computation requires a genuinely multiscale method. The adaptive unified gas-kinetic scheme (AUGKS) is developed for such multiscale flow simulation. The AUGKS applies discretized velocity space to accurately capture the non-equilibrium physics in the multiscale UGKS, and adaptively employs continuous distribution functions following Chapman-Enskog expansion to efficiently recover near-equilibrium flow region in GKS. The UGKS and GKS are dynamically connected at the cell interface through the fluxes from the discretized and continuous gas distribution functions, which avoids any buffer zone between them. In this study, the AUGKS method with rotation and vibration non-equilibrium is developed. The real gas effect in different flow regimes has been captured. To capture aerodynamic heating accurately, the heat flux modifications are also included. Unstructured discrete particle velocity space is adopted to further improve the computational performance. Numerical tests, including Sod tube, normal shock structure, high-speed flow around the two-dimensional cylinder and three-dimensional sphere and space vehicles, and an unsteady nozzle plume flow from the continuum flow to the background vacuum, have been conducted to validate the current scheme. In comparison with the original UGKS, the current scheme speeds up the computation, reduces the memory requirement, and maintains the equivalent accuracy for multiscale flow simulation, which provides an effective tool for non-equilibrium flow simulations, especially for the flows at low and medium speed.

physics.flu-dyn↗

arXiv2023

Nonequilibrium flow simulations using unified gas-kinetic wave-particle method

Nonequilibrium flows are common in aerospace engineering, and numerical simulations are vital in understanding non-equilibrium flow dynamics in spacecraft flight. The unified gas-kinetic wave-particle (UGKWP) method has been developed for multi-scale flow simulation, which models the coupled particle transport and collision within a numerical time in the flux evaluation across a cell interface. The UGKWP balances precision and efficiency in multiscale flow simulations, particularly in high-speed flow. In this study, the UGKWP method is used to simulate supersonic flow around a sphere, hypersonic flow around a space vehicle, nozzle plume into a vacuum, and side-jet impingement on hypersonic flow. The UGKWP accurately renders the Navier-Stokes solution within the nozzle, extending to free molecular flow in the external environment, all within a singular computation. Complicated structures in flow interaction have been captured by the UGKWP method. All simulation results have been verified through experimental measurements or Direct Simulation Monte Carlo (DSMC) methods. The UGKWP method requires only 60 GiB of memory to simulate a three-dimensional space vehicle with 560593 cells under different flow conditions, making it efficient and accurate for aerospace engineering applications.

physics.flu-dyn↗