Performance of the LSFD method is compared with conventional FD schemes. Generally, 9-point stencils for 2D cases and 27-point stencils for 3D cases are used for the approximation of the first and second order derivat...Performance of the LSFD method is compared with conventional FD schemes. Generally, 9-point stencils for 2D cases and 27-point stencils for 3D cases are used for the approximation of the first and second order derivatives obtained with conventional central difference schemes. When the same stencils are used, explicit LSFD formulations for approximation of the first and second order derivatives are presented. The LSFD formulations are actually a combination of conventional central difference schemes along relevant mesh lines. It has been found that LSFD formulations need much less iteration steps than the conventional FD schemes to converge, and the ratio of mesh spacing in the x and y directions is an important parameter in the LSFD application, with a great impact on stability of LSFD computation.展开更多
A new mesh free method proposed by the authors was presented, in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian fra...A new mesh free method proposed by the authors was presented, in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian frame in an autonomous manner, so that without any element it could be considered as a completely mesh free method. The method was tested with a numerical example, and reliable solution was obtained with high accuracy and efficiency.展开更多
An efficient compressible Euler equation solver for vortex-dominated flows is presented based on the adaptive hybrid Cartesian mesh and vortex identifying method.For most traditional grid-based Euler solvers,the exces...An efficient compressible Euler equation solver for vortex-dominated flows is presented based on the adaptive hybrid Cartesian mesh and vortex identifying method.For most traditional grid-based Euler solvers,the excessive numerical dissipation is the great obstruction for vortex capturing or tracking problems.A vortex identifying method based on the curl of velocity is used to identify the vortex in flow field.Moreover,a dynamic adaptive mesh refinement(DAMR)process for hybrid Cartesian gird system is employed to track and preserve vortex.To validate the proposed method,a single compressible vortex convection flow is involved to test the accuracy and efficiency of DAMR process.Additionally,the vortex-dominated flow is investigated by the method.The obtained results are shown as a good agreement with the previous published data.展开更多
In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary unde...In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.展开更多
对传统直角坐标网格进行改进,根据计算机图形学对与物面相交的正方形网格进行切割,使单元与物面贴体,并能根据流场的变化对网格区域进行局部加密。结合直角坐标网格与非结构网格的特点,编写了自适应直角坐标网格的生成程序,并发展了基...对传统直角坐标网格进行改进,根据计算机图形学对与物面相交的正方形网格进行切割,使单元与物面贴体,并能根据流场的变化对网格区域进行局部加密。结合直角坐标网格与非结构网格的特点,编写了自适应直角坐标网格的生成程序,并发展了基于切割单元直角坐标网格的直接模拟蒙特卡洛(Direct simulation Monte Carlo,DSMC)方法。同时通过当地模拟分子数、动态时间步长技术优化DSMC方法,提升计算效率。数值结果表明,本方法在计算过程中使搜索效率得到大大提升,同时也保证了物面网格单元的贴体性,提高了物面附近流场的计算精度,还易于实现网格自适应。展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10872005, 10532010)
文摘Performance of the LSFD method is compared with conventional FD schemes. Generally, 9-point stencils for 2D cases and 27-point stencils for 3D cases are used for the approximation of the first and second order derivatives obtained with conventional central difference schemes. When the same stencils are used, explicit LSFD formulations for approximation of the first and second order derivatives are presented. The LSFD formulations are actually a combination of conventional central difference schemes along relevant mesh lines. It has been found that LSFD formulations need much less iteration steps than the conventional FD schemes to converge, and the ratio of mesh spacing in the x and y directions is an important parameter in the LSFD application, with a great impact on stability of LSFD computation.
基金Project supported by the Nation-al Natural Science Foundation of China(No.10372055)the Shanghai Leading Academic Discipline Project(No.Y0103)
文摘A new mesh free method proposed by the authors was presented, in which the derivatives at each node were constructed using whole derivative formulas through the nodes selected around the node using local Cartesian frame in an autonomous manner, so that without any element it could be considered as a completely mesh free method. The method was tested with a numerical example, and reliable solution was obtained with high accuracy and efficiency.
基金Supported by the National Natural Science Foundation of China(11102179)
文摘An efficient compressible Euler equation solver for vortex-dominated flows is presented based on the adaptive hybrid Cartesian mesh and vortex identifying method.For most traditional grid-based Euler solvers,the excessive numerical dissipation is the great obstruction for vortex capturing or tracking problems.A vortex identifying method based on the curl of velocity is used to identify the vortex in flow field.Moreover,a dynamic adaptive mesh refinement(DAMR)process for hybrid Cartesian gird system is employed to track and preserve vortex.To validate the proposed method,a single compressible vortex convection flow is involved to test the accuracy and efficiency of DAMR process.Additionally,the vortex-dominated flow is investigated by the method.The obtained results are shown as a good agreement with the previous published data.
基金Project supported by the National Natural Science Foundation of China (Nos. 11901555, 11901213,11871448, and 11732016)the National Numerical Windtunnel Project (No. NNW2019ZT4-B10)。
文摘In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.
文摘对传统直角坐标网格进行改进,根据计算机图形学对与物面相交的正方形网格进行切割,使单元与物面贴体,并能根据流场的变化对网格区域进行局部加密。结合直角坐标网格与非结构网格的特点,编写了自适应直角坐标网格的生成程序,并发展了基于切割单元直角坐标网格的直接模拟蒙特卡洛(Direct simulation Monte Carlo,DSMC)方法。同时通过当地模拟分子数、动态时间步长技术优化DSMC方法,提升计算效率。数值结果表明,本方法在计算过程中使搜索效率得到大大提升,同时也保证了物面网格单元的贴体性,提高了物面附近流场的计算精度,还易于实现网格自适应。
