Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-materia...Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-material interfaces is demonstrated. Discontinuous Galerkin finite element method is used to solve Euleri- an equations. And the fifth-order weighted essentially non-oscillatory （WENO） scheme is used to solve the level set equation for capturing multi-material interfaces. The ghost fluid method is used to deal with the interfacial boundary condition. Results are obtained for two bubble interacting with a moving shock. The contours of the constant density and the pressure at different time are given. In the computational domain, three different cases are considered, i.e. two helium bubbles, a helium bubble followed by an R22 bubble in the direction of the moving shock, and an R22 bubble followed by a helium bubble. Computational results indicate that multi-mate- rial interfaces can be properly captured by the level set method. Therefore, for problems involving the flow of three different materials with two different interfaces, each interface separating two different materials can be similarly handled.展开更多
In this paper, we are concerned with the local structural stability of one-dimensional shock waves in radiation hydrodynamics described by the isentropic Euler-Boltzmann equations. Even though in this radiation hydrod...In this paper, we are concerned with the local structural stability of one-dimensional shock waves in radiation hydrodynamics described by the isentropic Euler-Boltzmann equations. Even though in this radiation hydrodynamics model, the radiative effects can be understood as source terms to the isentropic Euler equations of hydrodynamics, in general the radiation field has singularities propagated in an angular domain issuing from the initial point across which the density is discontinuous. This is the major difficulty in the stability analysis of shocks. Under certain assumptions on the radiation parameters, we show there exists a local weak solution to the initial value problem of the one dimensional Euler-Boltzmann equations, in which the radiation intensity is continuous, while the density and velocity are piecewise Lipschitz continuous with a strong discontinuity representing the shock-front. The existence of such a solution indicates that shock waves are structurally stable, at least local in time, in radiation hydrodynamics.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(10476011)~~
文摘Numerical simulations are performed on the interface with large deformation induced by the interaction between a moving shock and two consecutive bubbles. The high performance of the level set method for multi-material interfaces is demonstrated. Discontinuous Galerkin finite element method is used to solve Euleri- an equations. And the fifth-order weighted essentially non-oscillatory （WENO） scheme is used to solve the level set equation for capturing multi-material interfaces. The ghost fluid method is used to deal with the interfacial boundary condition. Results are obtained for two bubble interacting with a moving shock. The contours of the constant density and the pressure at different time are given. In the computational domain, three different cases are considered, i.e. two helium bubbles, a helium bubble followed by an R22 bubble in the direction of the moving shock, and an R22 bubble followed by a helium bubble. Computational results indicate that multi-mate- rial interfaces can be properly captured by the level set method. Therefore, for problems involving the flow of three different materials with two different interfaces, each interface separating two different materials can be similarly handled.
基金supported by NNSF of China(10971134,11031001,91230102,11371250)
文摘In this paper, we are concerned with the local structural stability of one-dimensional shock waves in radiation hydrodynamics described by the isentropic Euler-Boltzmann equations. Even though in this radiation hydrodynamics model, the radiative effects can be understood as source terms to the isentropic Euler equations of hydrodynamics, in general the radiation field has singularities propagated in an angular domain issuing from the initial point across which the density is discontinuous. This is the major difficulty in the stability analysis of shocks. Under certain assumptions on the radiation parameters, we show there exists a local weak solution to the initial value problem of the one dimensional Euler-Boltzmann equations, in which the radiation intensity is continuous, while the density and velocity are piecewise Lipschitz continuous with a strong discontinuity representing the shock-front. The existence of such a solution indicates that shock waves are structurally stable, at least local in time, in radiation hydrodynamics.
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.
