In this paper, an efficient hybrid shock capturing scheme is proposed to obtain accurate results both in the smooth region and around discontinuities for compressible flows. The hybrid algorithm is based on a fifth-or...In this paper, an efficient hybrid shock capturing scheme is proposed to obtain accurate results both in the smooth region and around discontinuities for compressible flows. The hybrid algorithm is based on a fifth-order weighted essentially non-oscillatory （WENO） scheme in the finite volume form to solve the smooth part of the flow field, which is coupled with a characteristic-based monotone upstream-centered scheme for conservation laws （MUSCL） to capture discontinuities. The hybrid scheme is intended to combine high resolution of MUSCL scheme and low dissipation of WENO scheme. The two ingredients in this hybrid scheme are switched with an indicator. Three typical indicators are chosen and compared. MUSCL and WENO are both shock capturing schemes making the choice of the indicator parameter less crucial. Several test cases are carried out to investigate hybrid scheme with different indicators in terms of accuracy and efficiency. Numerical results demonstrate that the hybrid scheme in the present work performs well in a broad range of problems.展开更多
The Rayleigh-Taylor(R-T) instability of ferrofluid has been the subject of recent research,because of its implications on the stability of stellar.By neglecting the viscosity and rotation of magnetic fluid,and assumin...The Rayleigh-Taylor(R-T) instability of ferrofluid has been the subject of recent research,because of its implications on the stability of stellar.By neglecting the viscosity and rotation of magnetic fluid,and assuming that the magnetic particles are irrotational and temperature insensitive,we obtain a simplified R-T instability model of magnetic fluid.For the interface tracing,we use five-order weighted essentially non-oscillatory(WENO) scheme to spatial direction and three-order TVD R-K method to time direction on the uniform mesh,respectively.If the direction of the external magnetic field is the same as that of gravity,the velocities of the interface will be increased.But if the direction of the external magnetic field is in opposition to the direction of gravity,the velocities of the interface will be decreased.When the direction of the external magnetic field is perpendicular to the direction of gravity,the symmetry of the interface will be destroyed.Because of the action which is produced by perpendicular external magnetic field,there are other bubbles at the boudaries which parallel the direction of gravity.When we increase the magnetic susceptibility of the magnetic fluids,the effects of external magnetic fields will be more distinct for the interface tracing.展开更多
Recently, a kind of high order hybrid methods based on Runge-Kutta discontinu- ous Galerkin （RKDG） method and weighted essentially non-oscillatory finite difference （WENO-FD） scheme was proposed. Those methods are...Recently, a kind of high order hybrid methods based on Runge-Kutta discontinu- ous Galerkin （RKDG） method and weighted essentially non-oscillatory finite difference （WENO-FD） scheme was proposed. Those methods are computationally efficient, however stable problems might sometimes be encountered in practical applications. In this work, we first analyze the linear stabilities of those methods based on the Heuristic theory. We find that the conservative hybrid method is linearly unstable if the numerical flux at the coupling interface is chosen to be ＇downstream＇. Then we introduce two ways of healing this defect. One is to choose the numerical flux at the coupling interface to be ＇upstream＇. The other is to employ a slope limiter function to enforce the hybrid method satisfying the local total variation diminishing （TVD） condition. In the end, numerical experiments are provided to validate the effectiveness of the proposed methods.展开更多
A Weighted Essentially Non-Oscillatory scheme(WENO) is a solution to hyperbolic conservation laws,suitable for solving high-density fluid interface instability with strong intermittency. These problems have a large an...A Weighted Essentially Non-Oscillatory scheme(WENO) is a solution to hyperbolic conservation laws,suitable for solving high-density fluid interface instability with strong intermittency. These problems have a large and complex flow structure. To fully utilize the computing power of High Performance Computing(HPC) systems, it is necessary to develop specific methodologies to optimize the performance of applications based on the particular system’s architecture. The Sunway TaihuLight supercomputer is currently ranked as the fastest supercomputer in the world. This article presents a heterogeneous parallel algorithm design and performance optimization of a high-order WENO on Sunway TaihuLight. We analyzed characteristics of kernel functions, and proposed an appropriate heterogeneous parallel model. We also figured out the best division strategy for computing tasks,and implemented the parallel algorithm on Sunway TaihuLight. By using access optimization, data dependency elimination, and vectorization optimization, our parallel algorithm can achieve up to 172× speedup on one single node, and additional 58× speedup on 64 nodes, with nearly linear scalability.展开更多
文摘In this paper, an efficient hybrid shock capturing scheme is proposed to obtain accurate results both in the smooth region and around discontinuities for compressible flows. The hybrid algorithm is based on a fifth-order weighted essentially non-oscillatory （WENO） scheme in the finite volume form to solve the smooth part of the flow field, which is coupled with a characteristic-based monotone upstream-centered scheme for conservation laws （MUSCL） to capture discontinuities. The hybrid scheme is intended to combine high resolution of MUSCL scheme and low dissipation of WENO scheme. The two ingredients in this hybrid scheme are switched with an indicator. Three typical indicators are chosen and compared. MUSCL and WENO are both shock capturing schemes making the choice of the indicator parameter less crucial. Several test cases are carried out to investigate hybrid scheme with different indicators in terms of accuracy and efficiency. Numerical results demonstrate that the hybrid scheme in the present work performs well in a broad range of problems.
基金Projects(10771178,10676031) supported by National Natural Science Foundation of ChinaThe Project of National High-Tech (863) Program about ICFProject(20070530003) supported by the Research Fund for the Doctoral Program of Higher Education
文摘The Rayleigh-Taylor(R-T) instability of ferrofluid has been the subject of recent research,because of its implications on the stability of stellar.By neglecting the viscosity and rotation of magnetic fluid,and assuming that the magnetic particles are irrotational and temperature insensitive,we obtain a simplified R-T instability model of magnetic fluid.For the interface tracing,we use five-order weighted essentially non-oscillatory(WENO) scheme to spatial direction and three-order TVD R-K method to time direction on the uniform mesh,respectively.If the direction of the external magnetic field is the same as that of gravity,the velocities of the interface will be increased.But if the direction of the external magnetic field is in opposition to the direction of gravity,the velocities of the interface will be decreased.When the direction of the external magnetic field is perpendicular to the direction of gravity,the symmetry of the interface will be destroyed.Because of the action which is produced by perpendicular external magnetic field,there are other bubbles at the boudaries which parallel the direction of gravity.When we increase the magnetic susceptibility of the magnetic fluids,the effects of external magnetic fields will be more distinct for the interface tracing.
基金This work is partially supported under the National Natural Science Foundation of China No. 91530325, the Fundamental Research of Civil Aircraft MJ-F-2012-04, and National 973 project No.2012CB720205.
文摘Recently, a kind of high order hybrid methods based on Runge-Kutta discontinu- ous Galerkin （RKDG） method and weighted essentially non-oscillatory finite difference （WENO-FD） scheme was proposed. Those methods are computationally efficient, however stable problems might sometimes be encountered in practical applications. In this work, we first analyze the linear stabilities of those methods based on the Heuristic theory. We find that the conservative hybrid method is linearly unstable if the numerical flux at the coupling interface is chosen to be ＇downstream＇. Then we introduce two ways of healing this defect. One is to choose the numerical flux at the coupling interface to be ＇upstream＇. The other is to employ a slope limiter function to enforce the hybrid method satisfying the local total variation diminishing （TVD） condition. In the end, numerical experiments are provided to validate the effectiveness of the proposed methods.
基金supported by the National High-Tech Research and Development (863) Program of China (No. 2015AA015306)the Science and Technology Plan of Beijing Municipality (No. Z161100000216147)+2 种基金the National Natural Science Foundation of China (No. 61762074)Youth Foundation Program of Qinghai University (No. 2016-QGY-5)the National Natural Science Foundation of Qinghai Province (No. 2019-ZJ7034)
文摘A Weighted Essentially Non-Oscillatory scheme(WENO) is a solution to hyperbolic conservation laws,suitable for solving high-density fluid interface instability with strong intermittency. These problems have a large and complex flow structure. To fully utilize the computing power of High Performance Computing(HPC) systems, it is necessary to develop specific methodologies to optimize the performance of applications based on the particular system’s architecture. The Sunway TaihuLight supercomputer is currently ranked as the fastest supercomputer in the world. This article presents a heterogeneous parallel algorithm design and performance optimization of a high-order WENO on Sunway TaihuLight. We analyzed characteristics of kernel functions, and proposed an appropriate heterogeneous parallel model. We also figured out the best division strategy for computing tasks,and implemented the parallel algorithm on Sunway TaihuLight. By using access optimization, data dependency elimination, and vectorization optimization, our parallel algorithm can achieve up to 172× speedup on one single node, and additional 58× speedup on 64 nodes, with nearly linear scalability.
