Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics ...Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated aad analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.展开更多
This paper introduces techniques in Gaussian process regression model for spatiotemporal data collected from complex systems.This study focuses on extracting local structures and then constructing surrogate models bas...This paper introduces techniques in Gaussian process regression model for spatiotemporal data collected from complex systems.This study focuses on extracting local structures and then constructing surrogate models based on Gaussian process assumptions.The proposed Dynamic Gaussian Process Regression(DGPR)consists of a sequence of local surrogate models related to each other.In DGPR,the time-based spatial clustering is carried out to divide the systems into sub-spatio-temporal parts whose interior has similar variation patterns,where the temporal information is used as the prior information for training the spatial-surrogate model.The DGPR is robust and especially suitable for the loosely coupled model structure,also allowing for parallel computation.The numerical results of the test function show the effectiveness of DGPR.Furthermore,the shock tube problem is successfully approximated under different phenomenon complexity.展开更多
基金supported by the National Natural Science Foundation of China (No.10621062)the Research Fund for Next Generation of General Armament Department (No.9140A13050207KG29)
文摘Several kinds of explicit and implicit finite-difference schemes directly solving the discretized velocity distribution functions are designed with precision of different orders by analyzing the inner characteristics of the gas-kinetic numerical algorithm for Boltzmann model equation. The peculiar flow phenomena and mechanism from various flow regimes are revealed in the numerical simulations of the unsteady Sod shock-tube problems and the two-dimensional channel flows with different Knudsen numbers. The numerical remainder-effects of the difference schemes are investigated aad analyzed based on the computed results. The ways of improving the computational efficiency of the gaskinetic numerical method and the computing principles of difference discretization are discussed.
基金co-supported by the National Natural Science Foundation of China(No.12101608)the NSAF(No.U2230208)the Hunan Provincial Innovation Foundation for Postgraduate,China(No.CX20220034).
文摘This paper introduces techniques in Gaussian process regression model for spatiotemporal data collected from complex systems.This study focuses on extracting local structures and then constructing surrogate models based on Gaussian process assumptions.The proposed Dynamic Gaussian Process Regression(DGPR)consists of a sequence of local surrogate models related to each other.In DGPR,the time-based spatial clustering is carried out to divide the systems into sub-spatio-temporal parts whose interior has similar variation patterns,where the temporal information is used as the prior information for training the spatial-surrogate model.The DGPR is robust and especially suitable for the loosely coupled model structure,also allowing for parallel computation.The numerical results of the test function show the effectiveness of DGPR.Furthermore,the shock tube problem is successfully approximated under different phenomenon complexity.
