arXiv subjects

Yajun Zhu

Publications and source records attributed to Yajun Zhu.

At least 19 recordsLinked to original sources

arXiv2026

An Implicit Discrete Adjoint Gas-Kinetic Scheme for Aerodynamic Shape Optimization across all Mach Number Regimes

The gas-kinetic scheme (GKS) integrates the characteristics of flux difference scheme (FDS) and flux vector splitting (FVS) scheme, providing high accuracy in smooth regions and strong robustness near discontinuities across all Mach regimes. Leveraging these properties, an implicit discrete adjoint GKS is developed for aerodynamic shape optimization over a wide range of Mach numbers. The adjoint solver is constructed using the source-transformation-based algorithmic differentiation tool Tapenade. To enhance computational efficiency, both the flow and adjoint GKS equations are solved using an implicit time-marching strategy, also known as the Lower-Upper Symmetric Gauss-Seidel (LU-SGS) method. The effectiveness of the implicit formulation is demonstrated through comparisons with the explicit approach. To accurately impose solid wall boundary conditions, particularly in hypersonic regimes, kinetic boundary conditions and their adjoint counterparts are formulated for both adiabatic no-slip and isothermal walls. Four benchmark test cases covering subsonic, transonic, supersonic, and hypersonic flows are used to verify the effectiveness of the developed adjoint-based design optimization system.

physics.flu-dyn↗

arXiv2026

A Hybrid Gas-Kinetic Scheme and Discrete Velocity Method for Continuum and Rarefied Flows

The gas-kinetic scheme (GKS) provides high computational efficiency and accuracy for continuum flow simulations but is unable to reliably capture rarefaction effects. In contrast, although the discrete velocity method (DVM) is better suited for rarefied flows, it exhibits reduced accuracy and slow convergence when applied to continuum regimes. To overcome these limitations, this work proposes a hybrid GKS-DVM method that integrates the strengths of both approaches. The hybrid approach balances the equilibrium distribution function in GKS with the upwind-reconstructed non-equilibrium distribution function in DVM through a numerical collision time. This balancing strategy ensures to recover Navier-Stokes solutions in the continuum limit (asymptotic preserving), while naturally capturing free molecular flows in the rarefied limit. Moreover, the introduction of a numerical collision time significantly enhances robustness in shock capturing for continuum flow applications. To further reduce computational cost of the hybrid approach, several adaptive strategies based on the local Knudsen number and Mach number have been proposed. The effectiveness and accuracy of the proposed hybrid method are systematically assessed through four representative test cases: a flat-plate boundary layer, a lid-driven cavity flow, shock structures, and flow past a semi-cylinder. The first case is subjected to continuum conditions, while the latter two span a broad range of Knudsen numbers. The results demonstrate that the proposed method achieves high solution accuracy and computational efficiency across both continuum and rarefied flow regimes.

physics.flu-dyn↗

arXiv2026

A Discrete Adjoint Gas-Kinetic Scheme for Aerodynamic Shape Optimization in Turbulent Continuum Flows

This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation (AD), the adjoint solver is rigorously verified against a duality-preserving linearized GKS solver generated via forward-mode AD. The robustness and practical effectiveness of the solver are evaluated through three benchmark cases: the inverse design of turbine blades, lift-to-drag ratio enhancement, and shock-strength reduction for a NACA 0012 airfoil. To capture realistic flow physics, fully turbulent optimizations are conducted using the one-equation Spalart--Allmaras (SA) model. Numerical results demonstrate excellent agreement between the discrete adjoint and linearized solvers, exhibiting matching sensitivity convergence behaviors, identical asymptotic residual decay rates, and negligible discrepancies in final sensitivity predictions. Furthermore, the optimization studies confirm that targeted design objectives are consistently achieved within a limited number of design cycles, highlighting the solver's computational efficiency, accuracy, and suitability for complex aerodynamic geometries.

physics.flu-dyn↗

arXiv2025

Modeling Atmospheric Ion Escape from Kepler-1649 b and c over Time

Rocky planets orbiting M-dwarf stars are prime targets for atmospheric characterization, yet their long-term evolution under intense stellar winds and high-energy radiation remains poorly constrained. The Kepler-1649 system, hosting two terrestrial exoplanets orbiting an M5V star, provides a valuable laboratory for studying atmospheric evolution in the extreme environments typical of M-dwarf systems. In this Letter we show that both planets could have retained atmospheres over gigayear timescales. Using a multi-species magnetohydrodynamic model, we simulate atmospheric ion escape driven by stellar winds and extreme ultraviolet radiation from 0.8 to 4.0 Gyr. The results reveal a clear decline in total ion escape rates with stellar age, as captured by a nonparametric LOWESS regression, with O$^{+}$ comprising 98.3%-99.9% of the total loss. Escape rates at 4.0 Gyr are two to three orders of magnitude lower than during early epochs. At 0.8 Gyr, planet b exhibits 3.79$\times$ higher O$^{+}$ escape rates than planet c, whereas by 4.0 Gyr its O$^{+}$ escape rate becomes 39.5$\times$ lower. This reversal arises from a transition to sub-magnetosonic star-planet interactions, where the fast magnetosonic Mach number, $M_f$, falls below unity. Despite substantial early atmospheric erosion, both planets may have retained significant atmospheres, suggesting potential long-term habitability. These findings offer predictive insight into atmospheric retention in the Kepler-1649 system and inform future JWST observations of similar M-dwarf terrestrial exoplanets aimed at refining habitability assessments.

astro-ph.EP↗

arXiv2025

A unified gas-kinetic framework from Boltzmann to Navier-Stokes scales

Neither molecular kinetics nor continuum fluid dynamics alone is adequate to describe multiscale gas flows across different regimes. Bridging these regimes within a single self-consistent framework has long been a central challenge in fluid mechanics. We propose a unified gas kinetic framework that classifies molecules by their collision histories over an observation timescale. This formulation recovers the Boltzmann and Navier-Stokes equations as limiting cases, providing a transparent connection between kinetic and hydrodynamic descriptions. Beyond practical advantages for multiscale modeling, this framework offers a new perspective on Hilbert's sixth problem by linking microscopic dynamics to continuum mechanics through a tunable observational scale.

physics.flu-dyn↗

arXiv2024

Kinetic representation of the unified gas-kinetic wave-particle method and beyond

The unified gas-kinetic wave-particle (UGKWP) method is a hybrid method for multiscale flow simulations, in which the contributions to the whole gas evolution from deterministic hydrodynamic wave and stochastic particle transport are combined simultaneously. Originally, the UGKWP method was developed as a direct modeling approach at discrete level. In this work, we revisit the time evolution of each part of the involved simulation particles and wave molecules in UGKWP, and present the corresponding kinetic equations. The resultant kinetic system can be viewed as a collision decomposition of the original kinetic equation, which can serve as a basis for developing other kinetic methods for flows in all flow regimes.

physics.comp-ph↗

arXiv2023

Unified gas-kinetic wave-particle method for frequency-dependent radiation transport equation

The multi-frequency radiation transport equation (RTE) system models the photon transport and the energy exchange process between the background material and different frequency photons. In this paper, the unified gas-kinetic wave-particle (UGKWP) method for multi-frequency RTE is developed to capture the multiscale non-equilibrium transport in different optical regimes. In the UGKWP, a multiscale evolution process is properly designed to obtain both non-equilibrium transport in the optically thin regime and thermal diffusion process in the optically thick regime automatically. At the same time, the coupled macroscopic energy equations for the photon and material are solved implicitly by the matrix-free source iteration method. With the wave-particle decomposition strategy, the UGKWP method has a dynamic adaptivity for different regime physics. In the optically thick regime, no particles will be sampled in the computational domain and the thermal diffusion solution for the photon transport will be recovered. While in the optically thin regime, stochastic particles will play a dominant role in the evolution and the non-equilibrium free transport of photon is automatically followed. In the frequency-dependent transport, the frequency carried by the simulating particle will be determined by a linear-frequency sampling strategy. In addition, to better resolve the sharp of opacity in the photon transport across a cell interface, the free streaming time of simulating particle in the UGKWP method will be reset when it passes through the interface. Moreover, the numerical relaxation time is properly defined to increase the particle proportion in the sharp opacity transition region in order to avoid numerical oscillation. Several typical test cases for the RTE system have been calculated to demonstrate the accuracy and reliability of the current frequency-dependent UGKWP method.

physics.comp-ph↗

arXiv2022

Unified gas-kinetic wave-particle methods VII: diatomic gas with rotational and vibrational nonequilibrium

Hypersonic flow around a vehicle in near space flight is associated with multiscale non-equilibrium physics at a large variation of local Knudsen number from the leading edge highly compressible flow to the trailing edge particle free transport. To accurately capture the solution in all flow regimes from the continuum Navier-Stokes solution to the rarefied gas dynamics in a single computation requires genuinely multiscale method. The unified gas-kinetic wave-particle (UGKWP) method targets on the simulation of such a multicale transport. Due to the wave-particle decomposition, the dynamics in the Navier-Stokes wave and kinetic particle transport has been unified systematically and efficiently under the unified gas-kinetic scheme (UGKS) framework. In this study, the UGKWP method with the non-equilibrium among translation, rotation and vibration modes, is developed based on a multiple temperature relaxation model. The real gas effect for high speed flow in different flow regimes has been properly captured. Numerical tests, including Sod tube, normal shock structure, hypersonic flow around two-dimensional cylinder and three-dimensional flow around a sphere and space vehicle, have been conducted to validate the UGKWP method. In comparison with the discrete velocity method (DVM)-based Boltzmann solver and particle-based direct simulation Monte Carlo (DSMC) method, the UGKWP method shows remarkable advantages in terms of computational efficiency, memory reduction, and automatic recovering of multiscale solution.

physics.flu-dyn↗

arXiv2022

High-order Unified Gas-kinetic Scheme

In this paper, we present a high-order unified gas-kinetic scheme (UGKS) using the weighted essentially non-oscillatory with adaptive-order (WENO-AO) method for spatial reconstruction and the two-stage fourth-order scheme for time evolution. Since the UGKS updates both the macroscopic flow variables and microscopic distribution function, and provides an adaptive flux function by combining the equilibrium and non-equilibrium parts, it is possible to take separate treatment of the equilibrium and non-equilibrium calculation in the UGKS for the development of high-order scheme. Considering the fact that high-order techniques are commonly required for continuum flow with complex structures, and the rarefied flow structure are relatively simple and smooth in the physical space, we apply the high-order techniques in the equilibrium part of the UGKS for the capturing of macroscopic flow evolution, and retain the calculation of distribution function as a second-order method, so that a balance of computational cost and numerical accuracy could be well achieved. The high-order UGKS has been validated by several numerical test cases, including sine-wave accuracy test, sod-shock tube, Couette, oscillating Couette, lid-driven cavity and oscillating cavity flow. It is shown that the current method preserves the multiscale property of the original UGKS and obtains more accurate solutions in several cases.

physics.comp-ph↗

arXiv2022

Measurement of the vertical atmospheric density profile from the X-ray Earth occultation of the Crab Nebula with Insight-HXMT

In this paper, the X-ray Earth occultation (XEO) of the Crab Nebula is investigated by using the Hard X-ray Modulation Telescope (Insight-HXMT). The pointing observation data on the 30th September, 2018 recorded by the Low Energy X-ray telescope (LE) of Insight-HXMT are selected and analyzed. The extinction lightcurves and spectra during the X-ray Earth occultation process are extracted. A forward model for the XEO lightcurve is established and the theoretical observational signal for lightcurve is predicted. The atmospheric density model is built with a scale factor to the commonly used MSIS density profile within a certain altitude range. A Bayesian data analysis method is developed for the XEO lightcurve modeling and the atmospheric density retrieval. The posterior probability distribution of the model parameters is derived through the Markov Chain Monte Carlo (MCMC) algorithm with the NRLMSISE-00 model and the NRLMSIS 2.0 model as basis functions and the best-fit density profiles are retrieved respectively. It is found that in the altitude range of 105--200 km, the retrieved density profile is 88.8% of the density of NRLMSISE-00 and 109.7% of the density of NRLMSIS 2.0 by fitting the lightcurve in the energy range of 1.0--2.5 keV based on XEOS method. In the altitude range of 95--125 km, the retrieved density profile is 81.0% of the density of NRLMSISE-00 and 92.3% of the density of NRLMSIS 2.0 by fitting the lightcurve in the energy range of 2.5--6.0 keV based on XEOS method. In the altitude range of 85--110 km, the retrieved density profile is 87.7% of the density of NRLMSISE-00 and 101.4% of the density of NRLMSIS 2.0 by fitting the lightcurve in the energy range of 6.0--10.0 keV based on XEOS method. This study demonstrates that the XEOS from the X-ray astronomical satellite Insight-HXMT can provide an approach for the study of the upper atmosphere.

astro-ph.EP↗

arXiv2021

General Implicit Iterative Method for Unified Gas-kinetic Scheme

In order to further enhance the computational efficiency of the implicit unified gas-kinetic scheme (IUGKS, JCP 315 (2016) 16-38) for multi-scale flow simulation, a two-step IUGKS is proposed in this paper. The multiscale solution of the UGKS is determined by the integral solution of the kinetic model equation, which is composed of the Lagrangian integration of the equilibrium and the free particle transport of the nonequilibrium state. With the implicit evaluation of the macroscopic variables in the first iterative step, the integration of the equilibrium can be directly used in the flux calculation of macroscopic flow variables in the second iterative step. This is equivalent to include the viscous flux in the implicit scheme to accelerate the convergence of the solution instead of using the Euler flux in the iterative process of the original IUGKS. In the present IUGKS, the update of macroscopic flow variables are closely coupled with the implicit evolution of the gas distribution function. At the same time, in order to get the more accurate solution, the full Boltzmann collision term is incorporated into the current scheme through the penalty method. Different iterative techniques, such as LU-SGS and multi-grid, are used for solving the linear algebraic system of coupled macroscopic and microscopic equations. The efficiency of the IUGKS has reached a favorable level among all implicit schemes for the kinetic equations in the literature. Several numerical examples are used to validate the performance of the IUGKS. Accurate solutions have been obtained efficiently in all flow regimes from low speed to hypersonic ones.

physics.comp-ph↗

arXiv2021

The first decade of unified gas kinetic scheme

In 2010, the unified gas kinetic scheme (UGKS) was proposed by Xu et al . (A unified gas-kinetic scheme for continuum and rarefied flows, Journal of Computational Physics, 2010). In the past decade, many numerical techniques have been developed to improve the capability of the UGKS in the aspects of efficiency increment, memory reduction, and physical modeling. The methodology of the direct modeling of the UGKS on discretization scale provides a general framework for construction of multiscale method for multiscale transport processes. This paper reviews the development and extension of the UGKS in its first decade.

physics.comp-ph↗

arXiv2020

A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes

In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Following the direct modeling methodology of the unified gas-kinetic scheme (UGKS), the UGKWP method models the flow dynamics uniformly in different regime and gets the local cell's Knudsen number dependent numerical solution directly without the requirement of kinetic scale cell resolution. The UGKWP method is composed of evolution of deterministic wave and stochastic particles. With the dynamic wave-particle decomposition, the UGKWP method is able to capture the continuum wave interaction and rarefied particle transport under a unified framework and achieves the high efficiency in different flow regime. The UGKWP flow solver is validated by many three-dimensional test cases of different Mach and Knudsen numbers, which include 3D shock tube problem, lid-driven cavity flow, high-speed flow passing through a cubic object, and hypersonic flow around a space vehicle. The parallel performance has been tested on the Tianhe-2 supercomputer, and reasonable parallel performance has been observed up to one thousand core processing. Due to wave-particle formulation, the UGKWP method has great potential in solving three-dimensional multiscale transport with the co-existence of continuum and rarefied flow regimes, especially for the high-speed rarefied and continuum flow around space vehicle in near space flight.

physics.comp-ph↗

arXiv2019

Ray Effect in Rarefied Flow Simulation

Ray effect usually appears in the radiative transfer when using discrete ordinates method (DOM) in the simulations. The cause and remedy for the ray effect have been intensively investigated in the radiation community. For rarefied gas flow, the ray effect is also associated with the discrete velocity method (DVM). However, few studies have been carried out in the rarefied community. In this paper, we take a detailed investigation of the ray effect in the rarefied flow simulations. Starting from a few commonly used benchmark tests, the root of the ray effect has been analyzed theoretically and validated numerically. At the same time, the influence of the ray effect on the quality of the numerical results of rarefied flow is estimated quantitatively. After understanding the nature of the ray effect, the strategy to minimize the ray effect through the discretization of the particle velocity space is presented and applied in the numerical simulations. An optimal velocity discretization for DVM is problem dependent and can be hardly obtained in the complex flow simulations. Due to the intrinsic self-adaptation of particle velocity, the stochastic particle methods are free from the ray effect. In rarefied regimes, the particle method seems more appropriate in the capturing of highly non-equilibrium flow behavior.

physics.comp-ph↗

arXiv2019

Unified Gas-kinetic Wave-Particle Methods III: Multiscale Photon Transport

In this paper, we extend the unified gas-kinetic wave-particle (UGKWP) method to the multiscale photon transport. In this method, the photon free streaming and scattering processes are treated in an un-splitting way. The duality descriptions, namely the simulation particle and distribution function, are utilized to describe the photon. By accurately recovering the governing equations of the unified gas-kinetic scheme (UGKS), the UGKWP preserves the multiscale dynamics of photon transport from optically thin to optically thick regime. In the optically thin regime, the UGKWP becomes a Monte Carlo type particle tracking method, while in the optically thick regime, the UGKWP becomes a diffusion equation solver. The local photon dynamics of the UGKWP, as well as the proportion of wave-described and particle-described photons are automatically adapted according to the numerical resolution and transport regime. Compared to the $S_n$ -type UGKS, the UGKWP requires less memory cost and does not suffer ray effect. Compared to the implicit Monte Carlo (IMC) method, the statistical noise of UGKWP is greatly reduced and computational efficiency is significantly improved in the optically thick regime. Several numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the UGKWP method. In comparison to the $S_n$ -type UGKS and IMC method, the UGKWP method may have several-order-of-magnitude reduction in computational cost and memory requirement in solving some multsicale transport problems.

physics.comp-ph↗

arXiv2019

Unified Gas-kinetic Wave-Particle Methods II: Multiscale Simulation on Unstructured Mesh

In this paper, we present a unified gas-kinetic wave-particle (UGKWP) method on unstructured mesh for multiscale simulation of continuum and rarefied flow. Inheriting from the multicale transport in the unified gas-kinetic scheme (UGKS), the integral solution of kinetic model equation is employed in the construction of UGKWP method to model the flow physics in the cell size and time step scales. A novel wave-particle adaptive formulation is introduced in the UGKWP method to describe the flow dynamics in each control volume. The local gas evolution is constructed through the dynamical interaction of the deterministic hydrodynamic wave and the stochastic kinetic particle. Within the resolution of cell size and time step, the decomposition, interaction, and evolution of the hydrodynamic wave and the kinetic particle depend on the ratio of the time step to the local particle collision time. In the rarefied flow regime, the flow physics is mainly recovered by the discrete particles and the UGKWP method performs as a stochastic particle method. In the continuum flow regime, the flow behavior is solely followed by macroscopic variable evolution and the UGKWP method becomes a gas-kinetic hydrodynamic flow solver for the viscous and heat-conducting Navier--Stokes solutions. In different flow regimes, many numerical test cases are computed to validate the UGKWP method on unstructured mesh. The UGKWP method can get the same UGKS solutions in all Knudsen regimes without the requirement of the time step and mesh size being less than than the particle collision time and mean free path. With an automatic wave-particle decomposition, the UGKWP method becomes very efficient. For example, at Mach number 30 and Knudsen number 0.1, in comparison with UGKS several-order-of-magnitude reductions in computational cost and memory requirement have been achieved by UGKWP.

physics.comp-ph↗

arXiv2018

Unified Gas-kinetic Wave-Particle methods I: Continuum and Rarefied Gas Flow

The unified gas-kinetic scheme (UGKS) provides a framework for simulating multiscale transport with the updates of both gas distribution function and macroscopic flow variables on the cell size and time step scales. The multiscale dynamics in UGKS is achieved through the coupled particle transport and collision in the particle evolution process within a time step. In this paper, under the UGKS framework, we propose an efficient multiscale unified gas-kinetic wave-particle (UGKWP) method. The gas dynamics in UGKWP method is described by the individual particle movement coupled with the evolution of the probability density function (PDF). During a time step, the trajectories of simulation particles are tracked until collision happens, and the post-collision particles are evolved collectively through the evolution of the corresponding distribution function. The evolution of simulation particles and distribution function is guided by evolution of macroscopic variables. The two descriptions on a gas particle, i.e. wave and particle, switch dynamically with time. A new concept of multiscale multi-efficiency preserving (MMP) method is introduced, and the UGKWP method is shown to be an MMP scheme. The UGKWP method is specially efficient for hypersonic flow simulation in all regimes in comparison with the wave-type discrete ordinate methods, and presents a much lower stochastic noise in the continuum flow regime in comparison with the particle-based Monte Carlo methods. Numerical tests for flows over a wide range of Mach and Knudsen numbers are presented. The examples include mainly the hypersonic flow passing a circular cylinder at Mach numbers $20$ and $30$ and Knudsen numbers $1$ and $10^{-4}$, low speed lid-driven cavity flow, and laminar boundary layer. These results validate the accuracy, efficiency, and multiscale property of UGKWP method.

math.NA↗

arXiv2018

A Unified Gas-kinetic Particle Method for Multiscale Photon Transport

In this work, we present a unified gas-kinetic particle (UGKP) method for the simulation of multiscale photon transport. The multiscale nature of the particle method mainly comes from the recovery of the time evolution flux function in the unified gas-kinetic scheme (UGKS) through a coupled dynamic process of particle transport and collision. This practice improves the original operator splitting approach in the Monte Carlo method, such as the separated treatment of particle transport and collision. As a result, with the variation of the ratio between numerical time step and local photon's collision time, different transport physics can be fully captured in a single computation. In the diffusive limit, the UGKP method could recover the solution of the diffusion equation with the cell size and time step being much larger than the photon's mean free path and the mean collision time. In the free transport limit, it presents an exact particle tracking process as the original Monte Carlo method. In the transition regime, the weights of particle free transport and collision are determined by the ratio of local numerical time step to the photon's collision time. Several one-dimensional numerical examples covering all transport regimes from the optically thin to optically thick are computed to validate the accuracy and efficiency of the current scheme. In comparison with the $S_N$ discrete ordinate method, the UGKP method is based on particles and avoids the discretization of particle velocity space, which does not suffer from the ray effect.

physics.comp-ph↗