arXiv subjects

Junzhe Cao

Publications and source records attributed to Junzhe Cao.

At least 19 recordsLinked to original sources

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 $Δt_R/Δt_L$. 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 $Δt_i/τ_i$, 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 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

PhysAgent: A Multi-Agent Framework for Reliable Remote Heart Rate Estimation

Remote photoplethysmography (rPPG) enables non-contact heart-rate estimation from facial videos, but its weak physiological signal is easily corrupted by motion, illumination changes, occlusion, skin-appearance variation, and device noise. Existing rPPG methods typically rely on a single model to directly predict heart rate or recover pulse waveforms, while different strong estimators may produce conflicting yet individually plausible candidates for the same video. To resolve these conflicts, we propose PhysAgent, an inference-time multi-agent candidate-verification framework. Unlike direct prediction approaches, PhysAgent neither trains a new base rPPG model nor asks Multimodal Large Language Models (MLLMs) to output heart rate directly. In contrast, it treats outputs from multiple base estimators as physiological hypotheses to be verified and uses a lightweight 4B MLLM, Qwen3-VL-4B, to drive multi-agent reasoning over video conditions, signal reliability, and candidate disagreement. A deterministic physiological verifier checks the fusion proposal, and a reproducible numerical fusion process produces the final heart rate. Experimental results on multiple public rPPG benchmarks show that PhysAgent improves fusion stability and reliability across different datasets and source-domain settings, while avoiding the irreproducibility and physiological inconsistency of direct MLLM prediction or unconstrained ensemble fusion. The code will be released soon.

cs.CV↗

arXiv2026

A Low-Storage Implicit Dual-Time Finite-Volume Framework for Radio-Frequency Capacitively Coupled Plasma Fluid Simulations

Radio-frequency (RF) capacitively coupled plasmas (CCPs) are widely utilized in semiconductor manufacturing. Efficiently and accurately solving the underlying fluid governing equations to resolve the complex multi-physics fields is crucial for optimizing plasma reactor designs and process control. To overcome the severe numerical stiffness and prohibitive time-step constraints inherent in low-temperature plasma modeling, we present a robust, low-storage implicit dual-time finite-volume framework for RF CCP simulations, establishing a highly efficient and memory-friendly pathway for the predictive modeling of multi-dimensional low-temperature plasmas. In this approach, the physical time advancement is strictly decoupled from explicit stability limits through a backward-difference formula (BDF), while the resulting nonlinear system is efficiently solved using pseudo-time iterations. A localized block-implicit relaxation method is employed to handle the stiff transport and chemical source terms at the cell level, effectively circumventing the massive memory overhead typical of conventional fully implicit solvers. Concurrently, a semi-implicit treatment of Poisson's equation is integrated to accelerate the electrostatic coupling. The framework is first verified against a standard one-dimensional argon discharge benchmark, demonstrating that a highly accurate periodic state can be achieved with satisfactory computational efficiency through the optimal selection of the physical time step, pseudo-CFL number, and inner iteration step. To further demonstrate the multidimensional applicability of the proposed method, the solver is extended to genuine two-dimensional configurations. The numerical results show the multi-dimensional distortion of the electrostatic potential and localized electron heating zones induced by the transverse boundaries.

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°blunted cone, a 70° 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

Intervention-Based Self-Supervised Learning: A Causal Probe Paradigm for Remote Photoplethysmography

Remote Photoplethysmography (rPPG) enables convenient non-contact physiological measurement. Existing Self-Supervised Learning (SSL) methods commonly fall into a correlation trap: they tend to learn the most dominant periodic signals in the data, such as high-energy motion or illumination noise, rather than the faint, true rPPG signal, leading to poor model generalization. To address this, we propose a new SSL paradigm, Physiological Causal Probing (PCP), which treats the latent rPPG signal as the underlying physical source and the resulting pixel chrominance variations as its visual manifestation. Its core idea is to shift from passive correlation learning to active, precise intervention: it intervenes on the video based on a proposed rPPG hypothesis, and verifies whether the post-intervention changes match physical expectations. We propose the Interv-rPPG framework to implement PCP: an rPPG extractor named PhysMambaFormer hypothesizes the rPPG signal, while a Controllable Physiological Signal Editor conducts precise chrominance-domain interventions on videos based on this hypothesis. Interv-rPPG validates the physical realism of the hypothesis through `Falsifiability via Nulling' and `Axiomatic Equivariance'. Our editor achieves precise editing of the rPPG signal by intervening in the low-frequency chrominance components of the video. Our method improves both in-domain and cross-domain performance on challenging datasets such as VIPL-HR and MMPD. Furthermore, it surpasses the supervised baseline in complex cross-dataset settings, while remaining competitive on clean datasets where the intervention mechanism may introduce slight residual chrominance noise. Extensive experiments, including diagnostic analysis of nuisance sensitivity, demonstrate that the PCP paradigm effectively resists motion and illumination artifacts.

cs.CV↗

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↗

arXiv2026

SVC 2026: the Second Multimodal Deception Detection Challenge and the First Domain Generalized Remote Physiological Measurement Challenge

Subtle visual signals, although difficult to perceive with the naked eye, contain important information that can reveal hidden patterns in visual data. These signals play a key role in many applications, including biometric security, multimedia forensics, medical diagnosis, industrial inspection, and affective computing. With the rapid development of computer vision and representation learning techniques, detecting and interpreting such subtle signals has become an emerging research direction. However, existing studies often focus on specific tasks or modalities, and models still face challenges in robustness, representation ability, and generalization when handling subtle and weak signals in real-world environments. To promote research in this area, we organize the Subtle visual Challenge, which aims to learn robust representations for subtle visual signals. The challenge includes two tasks: cross-domain multimodal deception detection and remote photoplethysmography (rPPG) estimation. We hope that this challenge will encourage the development of more robust and generalizable models for subtle visual understanding, and further advance research in computer vision and multimodal learning. A total of 22 teams submitted their final results to this workshop competition, and the corresponding baseline models have been released on the \href{https://sites.google.com/view/svc-cvpr26}{MMDD2026 platform}\footnote{https://sites.google.com/view/svc-cvpr26}

cs.CV↗

arXiv2026

PhysNeXt: Next-Generation Dual-Branch Structured Attention Fusion Network for Remote Photoplethysmography Measurement

Remote photoplethysmography (rPPG) enables contactless measurement of heart rate and other vital signs by analyzing subtle color variations in facial skin induced by cardiac pulsation. Current rPPG methods are mainly based on either end-to-end modeling from raw videos or intermediate spatial-temporal map (STMap) representations. The former preserves complete spatiotemporal information and can capture subtle heartbeat-related signals, but it also introduces substantial noise from motion artifacts and illumination variations. The latter stacks the temporal color changes of multiple facial regions of interest into compact two-dimensional representations, significantly reducing data volume and computational complexity, although some high-frequency details may be lost. To effectively integrate the mutual strengths, we propose PhysNeXt, a dual-input deep learning framework that jointly exploits video frames and STMap representations. By incorporating a spatio-temporal difference modeling unit, a cross-modal interaction module, and a structured attention-based decoder, PhysNeXt collaboratively enhances the robustness of pulse signal extraction. Experimental results demonstrate that PhysNeXt achieves more stable and fine-grained rPPG signal recovery under challenging conditions, validating the effectiveness of joint modeling of video and STMap representations. The codes will be released.

cs.CV↗

arXiv2026

PHASE-Net: Physics-Grounded Harmonic Attention System for Efficient Remote Photoplethysmography Measurement

Remote photoplethysmography (rPPG) measurement enables non-contact physiological monitoring but suffers from accuracy degradation under head motion and illumination changes. Existing deep learning methods are mostly heuristic and lack theoretical grounding, limiting robustness and interpretability. In this work, we propose a physics-informed rPPG paradigm derived from the Navier-Stokes equations of hemodynamics, showing that the pulse signal follows a second-order dynamical system whose discrete solution naturally leads to a causal convolution, justifying the use of a Temporal Convolutional Network (TCN). Based on this principle, we design the PHASE-Net, a lightweight model with three key components: 1) Zero-FLOPs Axial Swapper module to swap or transpose a few spatial channels to mix distant facial regions, boosting cross-region feature interaction without changing temporal order; 2) Adaptive Spatial Filter to learn a soft spatial mask per frame to highlight signal-rich areas and suppress noise for cleaner feature maps; and 3) Gated TCN, a causal dilated TCN with gating that models long-range temporal dynamics for accurate pulse recovery. Extensive experiments demonstrate that PHASE-Net achieves state-of-the-art performance and strong efficiency, offering a theoretically grounded and deployment-ready rPPG solution. The source code is available at https://github.com/Alex036225/PhaseNet.

cs.CV↗

arXiv2025

The study of coherent Rayleigh-Brillouin scattering in multiple flow regimes using unified gas-kinetic scheme

Coherent Rayleigh-Brillouin scattering (CRBS) holds great promise for the characterization of gas properties and the investigation of gas kinetic processes. The CRBS spectrum exhibits a strong dependence on the Knudsen number (Kn), revealing its inherently multiscale nature. In the unified gas-kinetic scheme (UGKS), collisions are intrinsically coupled with free transport during flux construction, endowing the method with distinct multiscale capabilities. Specifically, the UGKS reduces to a Boltzmann solver when the relaxation time is greater than or equal to the time step, and to the gas-kinetic scheme (GKS)-a Navier-Stokes solver-when the relaxation time is much smaller than the time step, thereby accommodating flow regimes without constraints on the molecular mean free path or collision time. In this study, the UGKS is extended to simulate CRBS phenomena, with the governing equation formulated based on the BGK-Shakhov model. Detailed derivations are provided. To account for the additional perturbation source term, a second-order accurate numerical algorithm is developed using the Strang splitting method within the UGKS framework. The proposed model is validated against argon CRBS experiments, demonstrating excellent agreement. Building on this validated framework, the impact of incident signal intensity on CRBS spectra across a range of Knudsen numbers is systematically examined, accompanied by an in-depth analysis of the underlying physical mechanisms. This work broadens the applicability of CFD-based CRBS simulations and provides a reliable numerical foundation for exploring high-intensity, multiscale gas-kinetic phenomena in future research.

physics.flu-dyn↗

arXiv2025

SVC 2025: the First Multimodal Deception Detection Challenge

Deception detection is a critical task in real-world applications such as security screening, fraud prevention, and credibility assessment. While deep learning methods have shown promise in surpassing human-level performance, their effectiveness often depends on the availability of high-quality and diverse deception samples. Existing research predominantly focuses on single-domain scenarios, overlooking the significant performance degradation caused by domain shifts. To address this gap, we present the SVC 2025 Multimodal Deception Detection Challenge, a new benchmark designed to evaluate cross-domain generalization in audio-visual deception detection. Participants are required to develop models that not only perform well within individual domains but also generalize across multiple heterogeneous datasets. By leveraging multimodal data, including audio, video, and text, this challenge encourages the design of models capable of capturing subtle and implicit deceptive cues. Through this benchmark, we aim to foster the development of more adaptable, explainable, and practically deployable deception detection systems, advancing the broader field of multimodal learning. By the conclusion of the workshop competition, a total of 21 teams had submitted their final results. https://sites.google.com/view/svc-mm25 for more information.

cs.CV↗

arXiv2025

A simplified unified wave-particle method for diatomic gases with rotational and vibrational non-equilibrium

The hypersonic flow around near-space vehicles constitutes a multi-scale flow problem. Due to insufficient molecular collisions to achieve equilibrium, rarefied gas effects are present in the flow field. Thus, numerical methods capable of accurately resolving multi-scale flows are required. Furthermore, high-temperature gas effects in hypersonic flows mean vibrational excitation of polyatomic molecules. Consequently, numerical methods accounting for non-equilibrium in rotational and vibrational internal energy modes are required. This study derives a quantified model-competition (QMC) mechanism for diatomic gases with rotational and vibrational non-equilibrium, starting from integral solutions of kinetic model equations with rotational and vibrational energy. The QMC mechanism categorize collisional and free-transport particles in cell, applying computational weighting based on their local scale regimes. We developed a simplified unified wave-particle (SUWP) method for diatomic gases based on QMC mechanism. For the macroscopic of the method, a three-temperature model accounting for rotational and vibrational energy is incorporated into both the kinetic inviscid flux scheme and {Navier-Stokes} solvers. For the microscopic of the method, a collisionless DSMC solver is employed to resolve non-equilibrium flow physics. This work validates the proposed SUWP method with rotational and vibrational non-equilibrium through benchmark cases, including shock tube, shock structures, flow past a cylinder, Apollo 6 command module and space station Mir. Compared to the DSMC and deterministic methods, the SUWP method exhibits favorable computational efficiency while maintaining accuracy.

physics.flu-dyn↗

arXiv2025

A hybrid numerical algorithm based on the stochastic particle Shakhov and DSMC method

The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and continuum/near-continuum regimes, which calls for larger time steps and coarser spatial grids for efficient numerical simulation. However, the mesh sizes and time steps in DSMC are constrained by the single-scale nature of the Boltzmann equation and the explicit treatment of collision term following operator splitting. To overcome the resulting computational inefficiency, the Time-Relaxed Monte Carlo (TRMC) method introduces a suitable time discretization of the Boltzmann equation, allowing for significantly larger time steps. Besides, domain decomposition methods leverage the complementary strengths of continuum and particle-based approaches, facilitating the efficient simulation of multi-scale gas flows. However, in TRMC method, the physically accurate high-order terms are truncated and approximated through convergence to a local Maxwellian distribution. Meanwhile, the continuum breakdown criteria employed in hybrid methods are either empirical or semi-empirical. Recently, a timescale-based decomposition of the Boltzmann equation has been proposed to enable a more rational coupling between DSMC and Navier-Stokes. Inspired by this strategy, a novel hybrid particle method is proposed to couple the stochastic particle Shakhov with DSMC, in which the collision operator is decomposed into two sub-steps based on local observation timescale and the relaxation time. The validity and accuracy of the proposed method are demonstrated through a series of benchmark cases, including 1-D sod shock tube, 2-D hypersonic flow around cylinder and jet expansion into the vacuum, 3-D hypersonic flows around sphere and X-38 like vehicle in near-continuum flow regimes.

physics.comp-ph↗