The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the water depth is always positiv...The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the water depth is always positive. In this paper, we choose four test problems with exact solutions for the 1D SWEs. Each test problem is a RP with one of the four possible wave patterns as its solution. These problems are numerically solved using schemes from the family of Weighted Essentially Non-Oscillatory (WENO) methods. For comparison purposes, we also include results obtained from the Random Choice Method (RCM). This study has three main objectives. Firstly, we outline the procedures for the implementation of the methods employed in this paper. Secondly, we assess the performance of the schemes in conjunction with a second-order Total Variation Diminishing (TVD) flux on a variety of RPs for the 1D SWEs (for both short- and long-time simulations). Thirdly, we investigate if a single method yields optimal outcomes for all test problems. Optimal outcomes refer to numerical solutions devoid of spurious oscillations, exhibiting high resolution of discontinuities, and attaining high-order accuracy in the smooth parts of the solution.展开更多
A study of a nanosecond laser irradiation on the titanium-layer-buried gold planar target is presented. The timeresolved x-ray emission spectra of titanium tracer are measured by a streaked crystal spectrometer. By co...A study of a nanosecond laser irradiation on the titanium-layer-buried gold planar target is presented. The timeresolved x-ray emission spectra of titanium tracer are measured by a streaked crystal spectrometer. By comparing the simulated spectra obtained by using the FLYCHK code with the measured titanium spectra, the temporal plasma states, i.e.,the electron temperatures and densities, are deduced. To evaluate the feasibility of using the method for the characterization of Au plasma states, the deduced plasma states from the measured titanium spectra are compared with the Multi-1D hydrodynamic simulations of laser-produced Au plasmas. By comparing the measured and simulated results, an overall agreement for the electron temperatures is found, whereas there are deviations in the electron densities. The experiment–theory discrepancy may suggest that the plasma state could not be well reproduced by the Multi-1D hydrodynamic simulation, in which the radial gradient is not taken into account. Further investigations on the spectral characterization and hydrodynamic simulations of the plasma states are needed. All the measured and FLYCHK simulated spectra are given in this paper as datasets. The datasets are openly available at http://www.doi.org/10.57760/sciencedb.j00113.00032.展开更多
文摘The solution of the Riemann Problem (RP) for the one-dimensional (1D) non-linear Shallow Water Equations (SWEs) is known to produce four potential wave patterns for the scenario where the water depth is always positive. In this paper, we choose four test problems with exact solutions for the 1D SWEs. Each test problem is a RP with one of the four possible wave patterns as its solution. These problems are numerically solved using schemes from the family of Weighted Essentially Non-Oscillatory (WENO) methods. For comparison purposes, we also include results obtained from the Random Choice Method (RCM). This study has three main objectives. Firstly, we outline the procedures for the implementation of the methods employed in this paper. Secondly, we assess the performance of the schemes in conjunction with a second-order Total Variation Diminishing (TVD) flux on a variety of RPs for the 1D SWEs (for both short- and long-time simulations). Thirdly, we investigate if a single method yields optimal outcomes for all test problems. Optimal outcomes refer to numerical solutions devoid of spurious oscillations, exhibiting high resolution of discontinuities, and attaining high-order accuracy in the smooth parts of the solution.
基金Project supported by the National Key Research and Development Program of China (Grant No.2017YFA0403300)the National Natural Science Foundation of China (Grant Nos.12074352 and 11675158)Fundamental Research Funds for the Central Universities in China (Grant No.YJ202144)。
文摘A study of a nanosecond laser irradiation on the titanium-layer-buried gold planar target is presented. The timeresolved x-ray emission spectra of titanium tracer are measured by a streaked crystal spectrometer. By comparing the simulated spectra obtained by using the FLYCHK code with the measured titanium spectra, the temporal plasma states, i.e.,the electron temperatures and densities, are deduced. To evaluate the feasibility of using the method for the characterization of Au plasma states, the deduced plasma states from the measured titanium spectra are compared with the Multi-1D hydrodynamic simulations of laser-produced Au plasmas. By comparing the measured and simulated results, an overall agreement for the electron temperatures is found, whereas there are deviations in the electron densities. The experiment–theory discrepancy may suggest that the plasma state could not be well reproduced by the Multi-1D hydrodynamic simulation, in which the radial gradient is not taken into account. Further investigations on the spectral characterization and hydrodynamic simulations of the plasma states are needed. All the measured and FLYCHK simulated spectra are given in this paper as datasets. The datasets are openly available at http://www.doi.org/10.57760/sciencedb.j00113.00032.
