In this paper, a new Riemann-solver-free class of difference schemes are const ructed to 2-D scalar nonlinear hyperbolic conservation laws. We proved thatthese schemes had second order accurate in space and time, and ...In this paper, a new Riemann-solver-free class of difference schemes are const ructed to 2-D scalar nonlinear hyperbolic conservation laws. We proved thatthese schemes had second order accurate in space and time, and satisfied MmB properties under the appropriate CFL limitation. Moreover, these schemes hadbeen extended to systems of 2-D conservation laws. Finally, several numericalexperients show that the performance of these schemes are quite satisfactory.展开更多
This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves itu uniqueness. A new method of solution constructing is applied, which ...This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves itu uniqueness. A new method of solution constructing is applied, which is different from the usual self-similar transformation. The author also discusses some generalized concepts in multi-dimensional situation (such as 'convex condition', 'left value' and 'right value', etc). An example is finally given to demonstrate that rarefaction wave solution of (1.1)(1.2) is not self-similar.展开更多
This paper generalizes the finite element method and discusses the issues of weighting functions, residual and realization of the integral conservation laws.
In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat ro...In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals.展开更多
In this paper, the super spectral viscosity （SSV） method is developed by introducing a spectrally small amount of high order regularization which is only activated on high frequencies. The resulting SSV approximatio...In this paper, the super spectral viscosity （SSV） method is developed by introducing a spectrally small amount of high order regularization which is only activated on high frequencies. The resulting SSV approximation is stable and convergent to the exact entropy solution. A Gegenbauer-Chebyshev post-processing for the SSV solution is proposed to remove the spurious oscillations at the disconti-nuities and recover accuracy from the spectral approximation. The ssv method is applied to the scahr periodic Burgers equation and the one-dimensional system of Euler equations of gas dynamics. The numerical results exhibit high accuracy and resolution to the exact entropy solution,展开更多
文摘In this paper, a new Riemann-solver-free class of difference schemes are const ructed to 2-D scalar nonlinear hyperbolic conservation laws. We proved thatthese schemes had second order accurate in space and time, and satisfied MmB properties under the appropriate CFL limitation. Moreover, these schemes hadbeen extended to systems of 2-D conservation laws. Finally, several numericalexperients show that the performance of these schemes are quite satisfactory.
基金National Tian-Yuan Mathematics Foundation of China!Grant No: 1937015
文摘This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves itu uniqueness. A new method of solution constructing is applied, which is different from the usual self-similar transformation. The author also discusses some generalized concepts in multi-dimensional situation (such as 'convex condition', 'left value' and 'right value', etc). An example is finally given to demonstrate that rarefaction wave solution of (1.1)(1.2) is not self-similar.
文摘This paper generalizes the finite element method and discusses the issues of weighting functions, residual and realization of the integral conservation laws.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11262019 and 10972143)
文摘In this paper, we investigate the Noether symmetry and Noether conservation law of elastic rod dynamics with two independent variables： time t and arc coordinate s. Starting from the Lagrange equations of Cosserat rod dynamics, the criterion of Noether symmetry with Lagrange style for rod dynamics is given and the Noether conserved quantity is obtained. Not only are the conservations of generalized moment and generalized energy obtained, but also some other integrals.
文摘In this paper, the super spectral viscosity （SSV） method is developed by introducing a spectrally small amount of high order regularization which is only activated on high frequencies. The resulting SSV approximation is stable and convergent to the exact entropy solution. A Gegenbauer-Chebyshev post-processing for the SSV solution is proposed to remove the spurious oscillations at the disconti-nuities and recover accuracy from the spectral approximation. The ssv method is applied to the scahr periodic Burgers equation and the one-dimensional system of Euler equations of gas dynamics. The numerical results exhibit high accuracy and resolution to the exact entropy solution,
