This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity dis...This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.展开更多
How to solve the hypersonic aerothermodynamics around large-scale uncontrolled spacecraft during falling disintegrated process from outer space to earth,is the key to resolve the problems of the uncontrolled Tiangong-...How to solve the hypersonic aerothermodynamics around large-scale uncontrolled spacecraft during falling disintegrated process from outer space to earth,is the key to resolve the problems of the uncontrolled Tiangong-No.1 spacecraft reentry crash.To study aerodynamics of spacecraft reentry covering various flow regimes,a Gas-Kinetic Unified Algorithm(GKUA)has been presented by computable modeling of the collision integral of the Boltzmann equation over tens of years.On this basis,the rotational and vibrational energy modes are considered as the independent variables of the gas molecular velocity distribution function,a kind of Boltzmann model equation involving in internal energy excitation is presented by decomposing the collision term of the Boltzmann equation into elastic and inelastic collision terms.Then,the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions by developing the discrete velocity ordinate method and numerical quadrature technique.The unified algorithm of the Boltzmann model equation involving thermodynamics non-equilibrium effect is presented for the whole range of flow regimes.The gas-kinetic massive parallel computing strategy is developed to solve the hypersonic aerothermodynamics with the processor cores 500~45,000 at least 80%parallel efficiency.To validate the accuracy of the GKUA,the hypersonic flows are simulated including the reentry Tiangong-1 spacecraft shape with the wide range of Knudsen numbers of 220~0.00005 by the comparison of the related results from the DSMC and N-S coupled methods,and the low-density tunnel experiment etc.For uncontrolling spacecraft falling problem,the finite-element algorithm for dynamic thermalforce coupling response is presented,and the unified simulation of the thermal structural response and the hypersonic flow field is tested on the Tiangong-1 shape under reentry aerodynamic environment.Then,the forecasting analysis platform of end-of-life largescale spacecraft flying track is established on the basis of ballistic computation combined with reentry aerothermodynamics and deformation failure/disintegration.展开更多
In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excita...In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excitation,the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function.By constructing the corresponding conservative discrete velocity ordinate method for this model,the conservative properties during the collision procedure are preserved at the discrete level by the numerical method,decreasing the computational storage and time.Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly.Applying the new GKUA,some numerical examples are simulated,including the Sod Riemann problem,homogeneous flow rotational relaxation,normal shock structure,Fourier and Couette flows,supersonic flows past a circular cylinder,and hypersonic flow around a plate placed normally.The results obtained by the analytic,experimental,direct simulation Monte Carlo method,and other measurements in references are compared with the GKUA results,which are in good agreement,demonstrating the high accuracy of the present algorithm.Especially,some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.展开更多
Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of diffe...Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to construct an accurate and efficient numerical algorithm to faithfully represent multiscale flow physics across different regimes. In this paper, a unified gas-kinetic scheme(UGKS) is developed to study non-equilibrium multicomponent gaseous flows. Based on the Boltzmann kinetic equation, an analytical space-time evolving solution is used to construct the discretized equations of gas dynamics directly according to cell size and scales of time steps, i.e., the so-called direct modeling method. With the variation in the ratio of the numerical time step to the local particle collision time(or the cell size to the local particle mean free path), the UGKS automatically recovers all scale-dependent flows over the given domain and provides a continuous spectrum of the gas dynamics. The performance of the proposed unified scheme is fully validated through numerical experiments.The UGKS can be a valuable tool to study multiscale and multicomponent flow physics.展开更多
Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme （UGKS）. The numerical calculations are carfled out for a wide range of wave oscillating frequencies. ...Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme （UGKS）. The numerical calculations are carfled out for a wide range of wave oscillating frequencies. The corresponding rarefaction parameter is defined as the ratio of sound wave frequency to the intermolecular particle collision frequency. The simulation covers the flow regime from the continuum to free molecule one. The treatment of the os- cillating wall boundary condition and the methods for eval- uating the absorption coefficient and sound wave speed are presented in detail. The simulation results from the UGKS are compared to the Navier-Stokes solutions, the direct sim- ulation Monte Carlo （DSMC） simulation, and experimental measurements. Good agreement with the experimental data has been obtained in the whole flow regimes for the corresponding Knudsen number from 0.08 to 32. The cur- rent study clearly demonstrates the capability of the UGKS method in capturing the sound wave propagation and its usefulness for the rarefied flow study.展开更多
The unified gas-kinetic scheme （UGKS） is presented and used in this letter to study the slider air bearing problem. The UGKS solutions are first val- idated by comparison with direct simulation Monte Carlo results. ...The unified gas-kinetic scheme （UGKS） is presented and used in this letter to study the slider air bearing problem. The UGKS solutions are first val- idated by comparison with direct simulation Monte Carlo results. After valida- tion, the UGKS is used to study the air-bearing problem under different non- equilibrium conditions. On the surface of the slider, the dependency of the gas pressure and normal force on the Mach and Knudsen numbers are fully evaluated. The non-equilibrium effect on the force loading in the whole transition regime up to the free molecular limit is also studied.展开更多
Firefly algorithm is the new intelligent algorithm used for all complex engineering optimization problems. Power system has many complex optimization problems one of which is the optimal power flow (OPF). Basically, i...Firefly algorithm is the new intelligent algorithm used for all complex engineering optimization problems. Power system has many complex optimization problems one of which is the optimal power flow (OPF). Basically, it is minimizing optimization problem and subjected to many complex objective functions and constraints. Hence, firefly algorithm is used to solve OPF in this paper. The aim of the firefly is to optimize the control variables, namely generated real power, voltage magnitude and tap setting of transformers. Flexible AC Transmission system (FACTS) devices may used in the power system to improve the quality of the power supply and to reduce the cost of the generation. FACTS devices are classified into series, shunt, shunt-series and series-series connected devices. Unified power flow controller (UPFC) is shunt-series type device that posses all capabilities to control real, reactive powers, voltage and reactance of the connected line in the power system. Hence, UPFC is included in the considered IEEE 30 bus for the OPF solution.展开更多
Due to the large and frequent static data interaction between the Electric Information Acquisition System and the external business systems,researching on using limited server sources to do an efficient task schedulin...Due to the large and frequent static data interaction between the Electric Information Acquisition System and the external business systems,researching on using limited server sources to do an efficient task scheduling is becoming one of the key technologies of the unified interface platform.The information interaction structure of the unified interface platform is introduced.Task scheduling has been decomposed into two stages,task decomposition and task combination,based on the features(various types and dispersed)of large static data.The principle of the minimum variance of the subtasks data quantity is used to do the target task resolving in the decomposition stage.The thought of the Greedy Algorithm is used in the task combination.Breaking the target task with large static data into serval composed tasks with roughly same data quantity is effectively realized.Meanwhile,to avoid the situation of the GA falling into the local optimal solution,an improved combination method has been put forward.Moreover,the new method creates more average composed tasks and making the task scheduling more effective.Ultimately,the effectiveness of the proposed method is verified by the experimental data.展开更多
The purpose of this study is to establish an elastic-plastic damage constitutive model of shale and simulate the elastic-plastic damage characteristics of shale under stress.Based on the unified strength theory and th...The purpose of this study is to establish an elastic-plastic damage constitutive model of shale and simulate the elastic-plastic damage characteristics of shale under stress.Based on the unified strength theory and the mechanics of shale rock samples characterized in laboratory tests,a new elastic-plastic damage constitutive model for shale is established by introducing compression factors and damage variables.The main considerations include the compressibility of primary fractures and pores in the shale core,and the formation of secondary cracks in the rock matrix under stress.A fully implicit backward Euler regression mapping algorithm has been used to solve the model,and the numerical simulation results are in good agreement with the experimental results.The results show that the model established in this paper can accurately simulate the elastic-plastic damage characteristics of shale under stress,and that it provides a new numerical simulation method for describing the elastic-plastic damage in shale.展开更多
As an emerging trend in power grid development,the AC/DC hybrid power grid presents the characteristics of multi-type DC links and large-scale AC/DC interconnection.However,existing research on AC/DC power flow calcul...As an emerging trend in power grid development,the AC/DC hybrid power grid presents the characteristics of multi-type DC links and large-scale AC/DC interconnection.However,existing research on AC/DC power flow calculation is mainly based on single-object models,ignoring the complex interactions and interdependencies between the AC system and various types of DC links in the hybrid power grid,such as LCCHVDC,MMC-HVDC,and LCC-MMC hybrid HVDC.Therefore,this paper proposes a power flow calculation algorithm for large-scale AC/DC systems with multi-type DC links.Firstly,a CIM/XML document conversion strategy applicable to the AC/DC system is proposed.Then,a unified modeling method is used to derive the power flow model of the AC/DC system,and a unified iterative algorithm for the large-scale AC/DC system with multi-type DC links is proposed.Finally,the algorithm’s correctness and effectiveness are verified by comparing it with actual measurements from the Southern Power Grid of China,with a voltage deviation of less than 1%.The research shows that the proposed algorithm has good convergence and high computational efficiency,which is applicable to power flow calculations in large-scale DC-embedded hybrid AC/DC grids in the future.展开更多
针对相关滤波跟踪算法开展并行计算研究,首先介绍相关滤波跟踪算法的理论基础,分析其数学机理和并行计算的必要性;其次对最小输出平方误差和(Minimum Output Sum of Squared Error,MOSSE)相关滤波跟踪算法流程进行分解,设计中央处理器(C...针对相关滤波跟踪算法开展并行计算研究,首先介绍相关滤波跟踪算法的理论基础,分析其数学机理和并行计算的必要性;其次对最小输出平方误差和(Minimum Output Sum of Squared Error,MOSSE)相关滤波跟踪算法流程进行分解,设计中央处理器(Central Processing Unit,CPU)-图形处理器(Graphics Processing Unit,GPU)异构计算加速方案;最后进行不同大小目标跟踪时并行计算与串行计算的耗时对比,结果表明当目标模板大于一定值时,并行计算耗时小于串行计算,验证了并行加速的有效性。展开更多
In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh s...In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh size and time step scales,and the local cell’s Knudsen number determines the flow physics.The proposed scheme has the multiscale and asymptotic complexity diminishing properties.The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale,and preserve the asymptotic Euler,Navier-Stokes,and magnetohydrodynamics(MHD)when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path.The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number.In the continuum regime,the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver.In the UGKWP,the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables,and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale.For plasma transport,the current scheme provides a smooth transition from particle-in-cell(PIC)method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime.In the continuum limit,the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time.In the highly magnetized regime,the cell size and time step are not restricted by the Debye length and plasma cyclotron period.The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 91016027 and 91130018)
文摘This paper investigates the convergence proof of the Direct Simulation Monte Carlo(DSMC) method and the Gas-Kinetic Unified Algorithm in simulating the Boltzmann equation.It can be shown that the particle velocity distribution function obtained by the DSMC method converges to a modified form of the Boltzmann equation,which is the equation of the gas-kinetic unified algorithm to directly solve the molecular velocity distribution function.Their convergence is derived through mathematical treatment.The collision frequency is presented using various molecular models and the local equilibrium distribution function is obtained by Enskog expansion using the converged equation of the DSMC method.These two expressions agree with those used in the unified algorithm.Numerical validation of the converging consistency between these two approaches is illustrated by simulating the pressure driven Poiseuille flow in the slip transition flow regime and the two-dimensional and three-dimensional flows around a circular cylinder and spherical-cone reentry body covering the whole flow regimes from low speed micro-channel flow to high speed non-equilibrium aerothermodynamics.
基金The National Key Basic Research and Development Program(2014CB744100)and the National Natural Science Foundation of China(91530319 and 11325212)support the present researches in the design of the study and collection,analysis,and interpretation of data and in writing the manuscript.
文摘How to solve the hypersonic aerothermodynamics around large-scale uncontrolled spacecraft during falling disintegrated process from outer space to earth,is the key to resolve the problems of the uncontrolled Tiangong-No.1 spacecraft reentry crash.To study aerodynamics of spacecraft reentry covering various flow regimes,a Gas-Kinetic Unified Algorithm(GKUA)has been presented by computable modeling of the collision integral of the Boltzmann equation over tens of years.On this basis,the rotational and vibrational energy modes are considered as the independent variables of the gas molecular velocity distribution function,a kind of Boltzmann model equation involving in internal energy excitation is presented by decomposing the collision term of the Boltzmann equation into elastic and inelastic collision terms.Then,the gas-kinetic numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions by developing the discrete velocity ordinate method and numerical quadrature technique.The unified algorithm of the Boltzmann model equation involving thermodynamics non-equilibrium effect is presented for the whole range of flow regimes.The gas-kinetic massive parallel computing strategy is developed to solve the hypersonic aerothermodynamics with the processor cores 500~45,000 at least 80%parallel efficiency.To validate the accuracy of the GKUA,the hypersonic flows are simulated including the reentry Tiangong-1 spacecraft shape with the wide range of Knudsen numbers of 220~0.00005 by the comparison of the related results from the DSMC and N-S coupled methods,and the low-density tunnel experiment etc.For uncontrolling spacecraft falling problem,the finite-element algorithm for dynamic thermalforce coupling response is presented,and the unified simulation of the thermal structural response and the hypersonic flow field is tested on the Tiangong-1 shape under reentry aerodynamic environment.Then,the forecasting analysis platform of end-of-life largescale spacecraft flying track is established on the basis of ballistic computation combined with reentry aerothermodynamics and deformation failure/disintegration.
基金supported by the Project of manned space engineering technology(2018-14)“Large-scale parallel computation of aerodynamic problems of irregular spacecraft reentry covering various flow regimes”the National Natural Science Foundation of China(91530319).
文摘In this paper,a gas-kinetic unified algorithm(GKUA)is developed to investigate the non-equilibrium polyatomic gas flows covering various regimes.Based on the ellipsoidal statistical model with rotational energy excitation,the computable modelling equation is presented by unifying expressions on the molecular collision relaxing parameter and the local equilibrium distribution function.By constructing the corresponding conservative discrete velocity ordinate method for this model,the conservative properties during the collision procedure are preserved at the discrete level by the numerical method,decreasing the computational storage and time.Explicit and implicit lower-upper symmetric Gauss-Seidel schemes are constructed to solve the discrete hyperbolic conservation equations directly.Applying the new GKUA,some numerical examples are simulated,including the Sod Riemann problem,homogeneous flow rotational relaxation,normal shock structure,Fourier and Couette flows,supersonic flows past a circular cylinder,and hypersonic flow around a plate placed normally.The results obtained by the analytic,experimental,direct simulation Monte Carlo method,and other measurements in references are compared with the GKUA results,which are in good agreement,demonstrating the high accuracy of the present algorithm.Especially,some polyatomic gas non-equilibrium phenomena are observed and analysed by solving the Boltzmann-type velocity distribution function equation covering various flow regimes.
基金Project supported by the National Natural Science Foundation of China(Nos.11772281,91530319,and 11521091)the Hong Kong Research Grant Council(Nos.16207715 and 16206617)
文摘Compressible flows exhibit a diverse set of behaviors, where individual particle transports and their collective dynamics play different roles at different scales. At the same time, the atmosphere is composed of different components that require additional degrees of freedom for representation in computational fluid dynamics. It is challenging to construct an accurate and efficient numerical algorithm to faithfully represent multiscale flow physics across different regimes. In this paper, a unified gas-kinetic scheme(UGKS) is developed to study non-equilibrium multicomponent gaseous flows. Based on the Boltzmann kinetic equation, an analytical space-time evolving solution is used to construct the discretized equations of gas dynamics directly according to cell size and scales of time steps, i.e., the so-called direct modeling method. With the variation in the ratio of the numerical time step to the local particle collision time(or the cell size to the local particle mean free path), the UGKS automatically recovers all scale-dependent flows over the given domain and provides a continuous spectrum of the gas dynamics. The performance of the proposed unified scheme is fully validated through numerical experiments.The UGKS can be a valuable tool to study multiscale and multicomponent flow physics.
基金supported by Hong Kong Research Grant Council(621709,621011)HKUST grants SRFI11SC05 and RPC10SC11the Nanoscience and Nanotechnology Program at HKUST
文摘Sound wave propagation in rarefied monatomic gases is simulated using a newly developed unified gaskinetic scheme （UGKS）. The numerical calculations are carfled out for a wide range of wave oscillating frequencies. The corresponding rarefaction parameter is defined as the ratio of sound wave frequency to the intermolecular particle collision frequency. The simulation covers the flow regime from the continuum to free molecule one. The treatment of the os- cillating wall boundary condition and the methods for eval- uating the absorption coefficient and sound wave speed are presented in detail. The simulation results from the UGKS are compared to the Navier-Stokes solutions, the direct sim- ulation Monte Carlo （DSMC） simulation, and experimental measurements. Good agreement with the experimental data has been obtained in the whole flow regimes for the corresponding Knudsen number from 0.08 to 32. The cur- rent study clearly demonstrates the capability of the UGKS method in capturing the sound wave propagation and its usefulness for the rarefied flow study.
基金supported by Hong Kong Research Grant Council(621011 and 620813)HKUST(SRFI11SC05 and FSGRF13SC21)
文摘The unified gas-kinetic scheme （UGKS） is presented and used in this letter to study the slider air bearing problem. The UGKS solutions are first val- idated by comparison with direct simulation Monte Carlo results. After valida- tion, the UGKS is used to study the air-bearing problem under different non- equilibrium conditions. On the surface of the slider, the dependency of the gas pressure and normal force on the Mach and Knudsen numbers are fully evaluated. The non-equilibrium effect on the force loading in the whole transition regime up to the free molecular limit is also studied.
文摘Firefly algorithm is the new intelligent algorithm used for all complex engineering optimization problems. Power system has many complex optimization problems one of which is the optimal power flow (OPF). Basically, it is minimizing optimization problem and subjected to many complex objective functions and constraints. Hence, firefly algorithm is used to solve OPF in this paper. The aim of the firefly is to optimize the control variables, namely generated real power, voltage magnitude and tap setting of transformers. Flexible AC Transmission system (FACTS) devices may used in the power system to improve the quality of the power supply and to reduce the cost of the generation. FACTS devices are classified into series, shunt, shunt-series and series-series connected devices. Unified power flow controller (UPFC) is shunt-series type device that posses all capabilities to control real, reactive powers, voltage and reactance of the connected line in the power system. Hence, UPFC is included in the considered IEEE 30 bus for the OPF solution.
文摘Due to the large and frequent static data interaction between the Electric Information Acquisition System and the external business systems,researching on using limited server sources to do an efficient task scheduling is becoming one of the key technologies of the unified interface platform.The information interaction structure of the unified interface platform is introduced.Task scheduling has been decomposed into two stages,task decomposition and task combination,based on the features(various types and dispersed)of large static data.The principle of the minimum variance of the subtasks data quantity is used to do the target task resolving in the decomposition stage.The thought of the Greedy Algorithm is used in the task combination.Breaking the target task with large static data into serval composed tasks with roughly same data quantity is effectively realized.Meanwhile,to avoid the situation of the GA falling into the local optimal solution,an improved combination method has been put forward.Moreover,the new method creates more average composed tasks and making the task scheduling more effective.Ultimately,the effectiveness of the proposed method is verified by the experimental data.
基金supported by the National Natural Science Foundation of China(51704246)the National Science and Technology Major Project(2016ZX05052-002-04,2016ZX05024-005-008).
文摘The purpose of this study is to establish an elastic-plastic damage constitutive model of shale and simulate the elastic-plastic damage characteristics of shale under stress.Based on the unified strength theory and the mechanics of shale rock samples characterized in laboratory tests,a new elastic-plastic damage constitutive model for shale is established by introducing compression factors and damage variables.The main considerations include the compressibility of primary fractures and pores in the shale core,and the formation of secondary cracks in the rock matrix under stress.A fully implicit backward Euler regression mapping algorithm has been used to solve the model,and the numerical simulation results are in good agreement with the experimental results.The results show that the model established in this paper can accurately simulate the elastic-plastic damage characteristics of shale under stress,and that it provides a new numerical simulation method for describing the elastic-plastic damage in shale.
基金supported by the Science and Technology Project of China Southern Power Grid(ZDKJXM20200052).
文摘As an emerging trend in power grid development,the AC/DC hybrid power grid presents the characteristics of multi-type DC links and large-scale AC/DC interconnection.However,existing research on AC/DC power flow calculation is mainly based on single-object models,ignoring the complex interactions and interdependencies between the AC system and various types of DC links in the hybrid power grid,such as LCCHVDC,MMC-HVDC,and LCC-MMC hybrid HVDC.Therefore,this paper proposes a power flow calculation algorithm for large-scale AC/DC systems with multi-type DC links.Firstly,a CIM/XML document conversion strategy applicable to the AC/DC system is proposed.Then,a unified modeling method is used to derive the power flow model of the AC/DC system,and a unified iterative algorithm for the large-scale AC/DC system with multi-type DC links is proposed.Finally,the algorithm’s correctness and effectiveness are verified by comparing it with actual measurements from the Southern Power Grid of China,with a voltage deviation of less than 1%.The research shows that the proposed algorithm has good convergence and high computational efficiency,which is applicable to power flow calculations in large-scale DC-embedded hybrid AC/DC grids in the future.
文摘针对相关滤波跟踪算法开展并行计算研究,首先介绍相关滤波跟踪算法的理论基础,分析其数学机理和并行计算的必要性;其次对最小输出平方误差和(Minimum Output Sum of Squared Error,MOSSE)相关滤波跟踪算法流程进行分解,设计中央处理器(Central Processing Unit,CPU)-图形处理器(Graphics Processing Unit,GPU)异构计算加速方案;最后进行不同大小目标跟踪时并行计算与串行计算的耗时对比,结果表明当目标模板大于一定值时,并行计算耗时小于串行计算,验证了并行加速的有效性。
基金supported by National Numerical Windtunnel project and National Science Foundation of China 11772281,91852114.
文摘In this paper,we extend the unified gas-kinetic wave-particle(UGKWP)methods to the multi-species gas mixture and multiscale plasma transport.The construction of the scheme is based on the direct modeling on the mesh size and time step scales,and the local cell’s Knudsen number determines the flow physics.The proposed scheme has the multiscale and asymptotic complexity diminishing properties.The multiscale property means that according to the cell’s Knudsen number the scheme can capture the non-equilibrium flow physics when the cell size is on the kinetic mean free path scale,and preserve the asymptotic Euler,Navier-Stokes,and magnetohydrodynamics(MHD)when the cell size is on the hydrodynamic scale and is much larger than the particle mean free path.The asymptotic complexity diminishing property means that the total degrees of freedom of the scheme reduce automatically with the decreasing of the cell’s Knudsen number.In the continuum regime,the scheme automatically degenerates from a kinetic solver to a hydrodynamic solver.In the UGKWP,the evolution of microscopic velocity distribution is coupled with the evolution of macroscopic variables,and the particle evolution as well as the macroscopic fluxes is modeled from a time accumulating solution of kinetic scale particle transport and collision up to a time step scale.For plasma transport,the current scheme provides a smooth transition from particle-in-cell(PIC)method in the rarefied regime to the magnetohydrodynamic solver in the continuum regime.In the continuum limit,the cell size and time step of the UGKWP method are not restricted by the particle mean free path and mean collision time.In the highly magnetized regime,the cell size and time step are not restricted by the Debye length and plasma cyclotron period.The multiscale and asymptotic complexity diminishing properties of the scheme are verified by numerical tests in multiple flow regimes.
