In this paper,we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible twomedium flow on unstructured meshes.A Riemann problem is constructed i...In this paper,we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible twomedium flow on unstructured meshes.A Riemann problem is constructed in the normal direction in the material interfacial region,with the goal of obtaining a compact,robust and efficient procedure to track the explicit sharp interface precisely.Extensive numerical tests including the gas-gas and gas-liquid flows are provided to show the proposed methodologies possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow and the interfacial vicinities of the two-medium flow in many occasions.展开更多
波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风...波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。展开更多
基金The research was supported by the National Basic Research Program of China(”973”Program)under grant No.2014CB046200NSFC grants 11432007,11372005,11271188Additional support is provided by a project funded by the Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions。
文摘In this paper,we extend using the Runge-Kutta discontinuous Galerkin method together with the front tracking method to simulate the compressible twomedium flow on unstructured meshes.A Riemann problem is constructed in the normal direction in the material interfacial region,with the goal of obtaining a compact,robust and efficient procedure to track the explicit sharp interface precisely.Extensive numerical tests including the gas-gas and gas-liquid flows are provided to show the proposed methodologies possess the capability of enhancing the resolutions nearby the discontinuities inside of the single medium flow and the interfacial vicinities of the two-medium flow in many occasions.
文摘波动方程系数矩阵对称化是整合不同类别波动方程、降低波传播模拟难度的有效方法,目前已成功应用于声波方程、各向同性与各向异性介质弹性波动方程。该研究将推导出双项介质波动方程的系数矩阵对称式;随后,引入多轴完全匹配层,采用迎风格式分部求和-一致逼近项(summation by parts-simultaneous approximation terms,SBP-SAT)有限差分方法离散波动方程,并通过能量法进行稳定性评估。通过数值仿真,表明所提出的离散框架具有整合度高,稳定性好和拓展性强等特点。此外,该方法可以稳定模拟曲线域中的波传播并降低其实现成本,表明了波动方程系数矩阵对称化方法及其离散框架在波传播模拟领域具有广泛的应用前景。
