arXiv subjects

Junzhe Cao

Publications and source records attributed to Junzhe Cao.

30 records · Page 2Linked to original sources

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↗

arXiv2025

A Multi-Scale Boltzmann Equation for Complex Systems of Neutral Gases across All Flow Regimes

A Multi-scale Boltzmann Equation (MBE) is found from the gas-kinetic theory and the direct modeling philosophy as a master equation for complex physical systems of neutral gases across all flow regimes, which locates between the continuum limit and the free-molecular limit, covering a vast range of applications such as hypersonic flows over aerospace crafts and delicate flows around MEMS. The most explicit characteristic of MBE is evolving the variable observation time in the expression, which distinguishes the MBE from the single-scale master or governing equation where a fixed scale is implied in the assumptions. The fundamental properties of MBE, such as the asymptotic property, are proved theoretically, while a concise numerical scheme is developed for MBE to demonstrate its validity by benchmark multi-scale problems.

physics.comp-ph↗

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

Unified gas-kinetic scheme for reactive flow with multi-scale transport and chemical non-equilibrium

Reactive flows for rarefied gas mixtures involve a multi-scale transport characterized by particle collisions and free streaming, and non-equilibrium physics containing multi-species interactions, and chemical non-equilibrium. These flows are pivotal in aerospace engineering and semiconductor manufacturing, impacting spacecraft control and thermal protection in near-space flight, and plasma etching for chip processing. Therefore, the simulation of these multi-scale and non-equilibrium flow is of scientific and industrial significance. Following the methodology of direct modeling, the unified gas-kinetic scheme (UGKS) is constructed to describe the multi-scale transport of gas molecules across all flow regimes. This study extends the UGKS to the reactive flows with chemical non-equilibrium for the capture of more complex flow physics. Test cases, including shock structures, hypersonic flows around a two-dimensional cylinder and the three-dimensional re-entry and space vehicle, and nozzle plume flow into a vacuum, are used to validate the UGKS through the comparison with the direct simulation Monte Carlo method. The study shows that the methodology of direct modeling and the extended UGKS have great potential for simulating multi-scale flows with complex non-equilibrium physics.

physics.flu-dyn↗

arXiv2024

Simplified unified wave-particle method for diatomic gases based on Rykov model

During the past decades, the numerical methods based on Navier-Stokes (N-S) equations and direct simulation Monte Carlo (DSMC) methods have been proved effective in simulating flows in the continuum and rarefied regimes, respectively. However, as single-scale methods, they face challenges in addressing common multi-scale problems, which are essential to simulate hypersonic flows around near-space vehicles and the flows in the micro-electro-mechanical systems. Hence, there is an urgent need for a method to predict multi-scale flows. In this work, a quantified model-competition (QMC) mechanism for diatomic multi-scale flows is derived from the integral solution of the Rykov model equations. This mechanism encapsulates both continuum and rarefied behaviors in a cell, weighted according to its local physical scale. By building upon the QMC mechanism, the N-S solver and DSMC solver are directly integrated within a cell to devise a simplified unified wave-particle (SUWP) method for diatomic gases. Specifically, the two-temperature equations considering the rotational energy are introduced into the kinetic inviscid flux (KIF) scheme and the N-S solver. As to the particle part, the collisionless DSMC solver is utilized to describe the non-equilibrium phenomenon. The proposed SUWP method for diatomic gases undergoes validation across a series of cases, including zero-dimensional homogeneous gas relaxation, one-dimensional normal shock structure, two-dimensional flow around the flat and the cylinder, and three-dimensional flows past the sphere and the blunt cone. Additionally, the implementation details of multi-scale wave-particle methods analysis and discussion are also undertaken in this work.

physics.flu-dyn↗

arXiv2024

Simulating the Integration of Urban Air Mobility into Existing Transportation Systems: A Survey

Urban air mobility (UAM) has the potential to revolutionize transportation in metropolitan areas, providing a new mode of transportation that could alleviate congestion and improve accessibility. However, the integration of UAM into existing transportation systems is a complex task that requires a thorough understanding of its impact on traffic flow and capacity. In this paper, we conduct a survey to investigate the current state of research on UAM in metropolitan-scale traffic using simulation techniques. We identify key challenges and opportunities for the integration of UAM into urban transportation systems, including impacts on existing traffic patterns and congestion; safety analysis and risk assessment; potential economic and environmental benefits; and the development of shared infrastructure and routes for UAM and ground-based transportation. We also discuss the potential benefits of UAM, such as reduced travel times and improved accessibility for underserved areas. Our survey provides a comprehensive overview of the current state of research on UAM in metropolitan-scale traffic using simulation and highlights key areas for future research and development.

cs.RO↗

arXiv2023

A direct unified wave-particle method for simulating non-equilibrium flows

In this work, the Navier-Stokes (NS) solver is combined with the Direct simulation Monte Carlo (DSMC) solver in a direct way, under the wave-particle formulation [J. Comput. Phys. 401, 108977 (2020)]. Different from the classical domain decomposition method with buffer zone for overlap, in the proposed direct unified wave-particle (DUWP) method, the NS solver is coupled with DSMC solver on the level of algorithm. Automatically, in the rarefied flow regime, the DSMC solver leads the simulation, while the NS solver leads the continuum flow simulation. Thus advantages of accuracy and efficiency are both taken. At internal flow regimes, like the transition flow regime, the method is accurate as well because a kind of mesoscopic modeling is proposed in this work, which gives the DUWP method the multi-scale property. Specifically, as to the collision process, at $t < τ$, it is supposed that only single collision happens, and the collision term of DSMC is just used. At $t > τ$, it is derived that $1-τ/Δt$ of particles should experience multiple collisions, which will be absorbed into the wave part and calculated by the NS solver. Then the DSMC and NS solver can be coupled in a direct and simple way, bringing about multi-scale property. The governing equation is derived and named as multi-scale Boltzmann equation. Different from the original wave-particle method, in the proposed DUWP method, the wave-particle formulation is no more restricted by the Boltzmann-BGK type model and the enormous research findings of DSMC and NS solvers can be utilized into much more complicated flows, like the thermochemical non-equilibrium flow. In this work, one-dimensional cases in monatomic argon gas are preliminarily tested, such as shock structures and Sod shock tubes.

physics.comp-ph↗

arXiv2023

Adaptive wave-particle decomposition in UGKWP method for high-speed flow simulations

With wave-particle decomposition, a unified gas-kinetic wave-particle (UGKWP) method has been developed for the multiscale flow simulations. The UGKWP method captures the transport process in all flow regimes without kinetic solver's constraint on the numerical mesh size and time step being less than the particle mean free path and collision time. In the current UGKWP method, the cell's Knudsen number, defined as the ratio of collision time to numerical time step, is used to distribute the components in the wave-particle decomposition. However, the adaptation of particle in UGKWP is mainly for the capturing of the non-equilibrium transport, and the cell's Knudsen number alone is not enough to identify the non-equilibrium state. For example, in the equilibrium flow regime with a Maxwellian distribution function, even at a large cell's Knudsen number, the flow evolution can be still modelled by the Navier-Stokes solver. Therefore, to further improve the efficiency, an adaptive UGKWP (AUGKWP) method will be developed with the introduction of an additional local flow variable gradient-dependent Knudsen number. As a result, the wave-particle decomposition in UGKWP will be determined by both cell's and gradient's Knudsen numbers, and the particle in UGKWP is solely used to capture the non-equilibrium flow transport. The AUGKWP becomes much more efficient than the previous one with the cell's Knudsen number only in the determination of wave-particle composition. Many numerical tests, including Sod tube, shock structure, flow around a cylinder, flow around a reentry capsule, and an unsteady nozzle plume flow, have been conducted to validate the accuracy and efficiency of AUGKWP. Compared with the original UGKWP, the AUGKWP achieves the same accuracy but has advantages in memory reduction and computational efficiency in the simulation for the flow with the co-existing of multiple regimes.

physics.flu-dyn↗

arXiv2022

Multiple solutions of nonlinear coupled constitutive relation model and its rectification in non-equilibrium flow computation

In this study, the multiple solutions of Nonlinear Coupled Constitutive Relation (NCCR) model are firstly observed and a way for identifying the physical solution is proposed. The NCCR model proposed by Myong is constructed from the generalized hydrodynamic equations of Eu, and aims to describe rarefied flows. The NCCR model is a complicated nonlinear system. Many assumptions have been used in the schemes for solving the NCCR equations. The corresponding numerical methods may be associated with unphysical solution and instability. At the same time, it is hard to analyze the physical accuracy and stability of NCCR model due to the uncertainties in the numerical discretization. In this study, a new numerical method for solving NCCR equations is proposed and used to analyze the properties of NCCR equations. More specifically, the nonlinear equations are converted into the solutions of an objective function of a single variable. Under this formulation, the multiple solutions of the NCCR system are identified and the criteria for picking up the physical solution are proposed. Therefore, a numerical scheme for solving NCCR equations is constructed. A series of flow problems in the near continuum and low transition regimes with a large variation of Mach numbers are conducted to validate the numerical performance of proposed method and the physical accuracy of NCCR model.

physics.comp-ph↗

arXiv2021

A direct relaxation process for particle methods in gas kinetic theory

The multi-scale flow mechanism is crucial for force and heat loaded on near-space and reentry vehicles, the control of spacecraft by thrusters, the propelling and cooling of MEMS, etc. Since the continuum flow and rarefied flow often exist simultaneously, the modeling and prediction for such a multi-scale flow field is very complicated. One important and efficient way of predicting the multi-scale flow is constructing numerical methods by adapting the multi-scale properties of the temporal integral solutions (or equivalent characteristic line solutions) for the model equations in the gas-kinetic theory. The model equations can be classified into FP-type and BGK-type, and the numerical methods can have deterministic form or stochastic particle form. Since these numerical methods are strictly based on model equations, they are also restricted by the model equations. The difficulty and complexity in constructing model equation that has complete asymptotic preserving property for gas mixture with non-equilibrium internal energy will prevent the further extension of these methods. Therefore, this paper addresses the question whether a multi-scale numerical method can be established not on the model equations, but directly adapts the relaxation rates of macroscopic variables such as stress and heat flux. Since the algorithm of multi-scale particle method based on BGK-type equation is clear and simple, its collision step is modified in this work, where the macroscopic variables firstly evolve according to their relaxation rates, and then the molecules that participate in inter-molecular collisions get their after-collision velocities from the after-evolution macroscopic variables. Therefore, this direct relaxation process does not depend on the model equations anymore. Finally, the validity and accuracy of the particle method with direct relaxation process are examined with five test cases.

physics.comp-ph↗

arXiv2020

An implicit kinetic inviscid flux for predicting continuum flows in all speed regimes

In this study, the kinetic inviscid flux (KIF) is improved and an implicit strategy is coupled. The recently proposed KIF is a kind of inviscid flux, whose microscopic mechanism makes it good at solving shock waves, with advantages against the shock instability phenomenon. When developing the implicit KIF, a phenomenon is noticed that the kinetic flux vector splitting (KFVS) part in boundary layers not only reduces the accuracy, but seriously reduces the Courant-Friedrichs-Lewy (CFL) number as well. As a result, in this paper, a new weight is proposed about how to combine the KFVS method well with the totally thermalized transport (TTT) method. Besides admitting the using of larger CFL numbers, this new weight brings about more accurate numerical results like pressure, friction coefficient and heat flux when solving shock waves, boundary layers and complex supersonic/hypersonic flows. In order to examine the validity, accuracy and efficiency of the present method, six numerical test cases, covering the whole speed regime, are conducted, including the hypersonic viscous flow past a cylinder, the hypersonic double-cone flow, the hypersonic double-ellipsoid flow, the laminar shock boundary layer interaction, the supersonic flow around a ramp segment and the lid-driven cavity flow. The advantages of this scheme and corresponding mechanisms are to be discussed in detail.

physics.flu-dyn↗

arXiv2020

A multi-scale kinetic inviscid flux extracted from the gas-kinetic scheme for simulating incompressible and compressible flows

A Kinetic Inviscid Flux (KIF) is proposed for simulating incompressible and compressible flows. It is constructed based on the direct modeling of multi-scale flow behaviors, which is used in the Gas-Kinetic Scheme (GKS), the Unified Gas-Kinetic Scheme (UGKS), the Discrete Unified Gas-Kinetic Scheme (DUGKS), etc.. In KIF, the discontinuities (such as the shock wave) that can not be well resolved by mesh cells are mainly solved by the Kinetic Flux Vector Splitting (KFVS) method representing the free transport mechanism (or micro-scale mechanism), while in other flow regions that are smooth, the flow behavior is solved mainly by the central-scheme-like Totally Thermalized Transport (TTT). The weights of KFVS and TTT in KIF is automatically determined by those in the theory of direct modeling. Two ways of choosing the weights in KIF are proposed, which are actually the weights adopted in the UGKS and the DUGKS, respectively. By using the test cases of Sod shock tube, rarefaction wave, the boundary layer of flat plate, the cavity flow and hypersonic flow over circular cylinder, the validity and accuracy of the present method are examined. The KIF does not suffer from the carbuncle phenomenon, and does not introduce extra numerical viscosity in smooth regions. Especially, in the case of hypersonic cylinder, it gives a quite sharp and clear density and temperature contours. The KIF can be viewed as an inviscid-viscous splitting version of the GKS. By the doing this splitting, it is easy to be used in the traditional CFD frameworks. It can also be classified as a new type in the numerical schemes based on the kinetic theory that are represented by the works in Ref. \cite{SunA} and Ref. \cite{ohwada2018a}, except the weights are determined by the weights of direct modeling.

physics.comp-ph↗