In[SIAM J.Sci.Comput.,35(2)(2013),A1049–A1072],a class of multi-domain hybrid DG and WENO methods for conservation laws was introduced.Recent applications of this method showed that numerical instability may encounter if the DG flux with Lagrangian interpolation is applied as the interface flux during the moment of conservative coupling.In this continuation paper,we present a more robust approach in the construction of DG flux at the coupling interface by using WENO procedures of reconstruction.Based on this approach,such numerical instability is overcome very well.In addition,the procedure of coupling a DG method with a WENO-FD scheme on hybrid meshes is disclosed in detail.Typical testing cases are employed to demonstrate the accuracy of this approach and the stability underthe flexibility of using either WENO-FD flux or DG flux at the moment of requiring conservative coupling.
We extend the traditional kinetic scheme for ideal gases to the Euler equations with the equation of state for a multi-component stiffened gas. Based on a careful analysis of the oscillation mechanism of the traditional kinetic scheme across contact discontinuities, we propose a new non-oscillatory kinetic （NOK） scheme for multi-component stiffened gases. The basic idea in the construction is to use a flux splitting technique to construct numerical fluxes which do not depend on the concrete form of the equilibrium state. The new scheme can not only can avoid spurious oscillations of the pressure and velocity near a material interface which are observed in the traditional kinetic schemes such as the kinetic flux vector splitting （KFVS） and BGK schemes, but also can deal with the stiffened gas equation of state. Moreover, we also carry out a careful analysis on the consistency condition, truncation error and positivity of the NOK scheme. A number of 1D and 2D numerical tests are presented which demonstrate the accuracy and robustness of the new scheme in the simulation of problems with smooth, weak and strong shock wave regions.
The modified ghost fluid method(MGFM)provides a robust and efficient interface treatment for various multi-medium flow simulations and some particular fluid-structure interaction(FSI)simulations.However,this methodology for one specific class of FSI problems,where the structure is plate,remains to be developed.This work is devoted to extending the MGFM to treat compressible fluid coupled with a thin elastic plate.In order to take into account the influence of simultaneous interaction at the interface,a fluid-plate coupling system is constructed at each time step and solved approximately to predict the interfacial states.Then,ghost fluid states and plate load can be defined by utilizing the obtained interfacial states.A type of acceleration strategy in the coupling process is presented to pursue higher efficiency.Several one-dimensional examples are used to highlight the utility of this method over looselycoupled method and validate the acceleration techniques.Especially,this method is applied to compute the underwater explosions(UNDEX)near thin elastic plates.Evolution of strong shock impacting on the thin elastic plate and dynamic response of the plate are investigated.Numerical results disclose that this methodology for treatment of the fluid-plate coupling indeed works conveniently and accurately for different structural flexibilities and is capable of efficiently simulating the processes of UNDEX with the employment of the acceleration strategy.
在控制系统中,时间延迟的不确定性往往会影响控制策略的准确性.为了进一步分析时间延迟对系统性能的影响,该文在传统RMPC(Robust Model based Predictive Control)的基础上引入了不确定时间延迟,分析了不确定时间延迟下系统的保代价区域.首先,介绍了线性矩阵不等式约束下的RMPC,并分析了相应的保代价区域.接下来,在RMPC中引入不确定时间延迟,通过对系统状态空间进行放大,使其包含了更多的历史状态信息.最后,依据最大时间延迟分析了不确定性对控制系统性能的影响,并分析了相应的保代价区域.仿真实验表明,控制系统的保代价区域随着时间延迟的增加而逐渐减小,并且时间延迟的不确定性范围越大系统的保代价区域越小.
In this work,the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system.In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling,the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates.Furthermore,to take into account the influence of material deformation and nonlinear wave interaction at the interface,an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states.Numerical tests are presented to verify the resultant method.
In this paper, a general high-order multi-domain hybrid DG/WENO-FD method, which couples a p^th-order （p ≥ 3） DG method and a q^th-order （q ≥ 3） WENO-FD scheme, is developed. There are two possible coupling approaches at the domain interface, one is non-conservative, the other is conservative. The non-conservative coupling approach can preserve optimal order of accuracy and the local conservative error is proved to be upmost third order. As for the conservative coupling approach, accuracy analysis shows the forced conservation strategy at the coupling interface deteriorates the accuracy locally to first- order accuracy at the ＇coupling cell＇. A numerical experiments of numerical stability is also presented for the non-conservative and conservative coupling approaches. Several numerical results are presented to verify the theoretical analysis results and demonstrate the performance of the hybrid DG/WENO-FD solver.
