Most numerical transient flow models that consider dynamic friction employ a finite differences approach or the method of characteristics. These models assume a single fluid (water only) with constant density and pres...Most numerical transient flow models that consider dynamic friction employ a finite differences approach or the method of characteristics. These models assume a single fluid (water only) with constant density and pressure wave velocity. But when transient flow modeling attempts to integrate the presence of air, which produces a variable density and pressure-wave velocity, the resolution scheme becomes increasingly complex. Techniques such as finite volumes are often used to improve the quality of results because of their conservative form. This paper focuses on a resolution technique for unsteady friction using the Godunov approach in a finite volume method employing single-equivalent twophase flow equations. The unsteady friction component is determined by taking into account local and convective instantaneous accelerations and the sign of both convective acceleration and velocity values. The approach is used to reproduce a set of transient flow experiments reported in the literature, and good agreement between simulated and experimental results is found.展开更多
This paper presents a cell-centered Godunov method based on staggered data distribu-tion in Eulerian framework.The motivation is to reduce the intrinsic entropy dissipation of classical Godunov methods in the calculat...This paper presents a cell-centered Godunov method based on staggered data distribu-tion in Eulerian framework.The motivation is to reduce the intrinsic entropy dissipation of classical Godunov methods in the calculation of an isentropic or rarefaction flow.At the same time,the property of accurate shock capturing is also retained.By analyzing the factors that cause nonphysical entropy in the conventional Godunov methods,we introduce two velocities rather than a single velocity in a cell to reduce kinetic energy dissipation.A series of redistribution strategies are adopted to update subcell quantities in order to improve accuracy.Numerical examples validate that the present method can dramatically reduce nonphysical entropy increase.Mathematics subject classification:35Q35,76N15,76M12.展开更多
This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the ...This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the scheme, numerical simulation for the weak entropy solution to the initial-boundary value problem of scalar conservation laws is conducted.展开更多
长距离输水管道水力瞬变过程中水体压强达到汽化压强时,将会发生水柱分离现象,水柱弥合将产生异常高压,导致管路振动、变形甚至爆管事故。已有的水柱分离弥合水锤数学模型主要采用特征线法(Method of characteristics,MOC)计算,并且很...长距离输水管道水力瞬变过程中水体压强达到汽化压强时,将会发生水柱分离现象,水柱弥合将产生异常高压,导致管路振动、变形甚至爆管事故。已有的水柱分离弥合水锤数学模型主要采用特征线法(Method of characteristics,MOC)计算,并且很少考虑动态摩阻引起的能量衰减。为提高水柱分离弥合水锤现象的计算精确度和稳定性,基于有限体积法二阶Godunov格式,建立了考虑动态摩阻的离散气体空穴模型(Discrete gas cavity model,DGCM)。为实现管道边界和内部单元的统一计算,提出虚拟边界的处理方法。将该模型模拟结果与实验数据以及已有的稳态摩阻模型的计算结果进行比较,并对网格数、压力修正系数等参数敏感性进行分析。结果表明,本模型能够准确模拟出纯水锤、水柱分离弥合水锤两种情况下瞬变压力,与实验数据基本一致;考虑动态摩阻的瞬态压力计算值与实验数据更吻合;与MOC相比,当库朗数小于1.0时,有限体积法二阶Godunov模型计算结果更准确、更稳定;尤其是,压力修正系数取值0.9及较密网格时数学模型能更为准确地再现实验结果。展开更多
We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to de...We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge-averaged quantities, which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [1]. However, [1] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [1]. The method is fourth order (both in space and time) for smooth flows, and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.展开更多
文摘Most numerical transient flow models that consider dynamic friction employ a finite differences approach or the method of characteristics. These models assume a single fluid (water only) with constant density and pressure wave velocity. But when transient flow modeling attempts to integrate the presence of air, which produces a variable density and pressure-wave velocity, the resolution scheme becomes increasingly complex. Techniques such as finite volumes are often used to improve the quality of results because of their conservative form. This paper focuses on a resolution technique for unsteady friction using the Godunov approach in a finite volume method employing single-equivalent twophase flow equations. The unsteady friction component is determined by taking into account local and convective instantaneous accelerations and the sign of both convective acceleration and velocity values. The approach is used to reproduce a set of transient flow experiments reported in the literature, and good agreement between simulated and experimental results is found.
基金supported by the National Natural Science Foundation of China(Grant Nos.11971071,12302377)by the Foundation of LCP(Grant No.6142A05220201)by the China Postdoctoral Science Foundation(Grant No.2022M722185).
文摘This paper presents a cell-centered Godunov method based on staggered data distribu-tion in Eulerian framework.The motivation is to reduce the intrinsic entropy dissipation of classical Godunov methods in the calculation of an isentropic or rarefaction flow.At the same time,the property of accurate shock capturing is also retained.By analyzing the factors that cause nonphysical entropy in the conventional Godunov methods,we introduce two velocities rather than a single velocity in a cell to reduce kinetic energy dissipation.A series of redistribution strategies are adopted to update subcell quantities in order to improve accuracy.Numerical examples validate that the present method can dramatically reduce nonphysical entropy increase.Mathematics subject classification:35Q35,76N15,76M12.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10671120）
文摘This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the scheme, numerical simulation for the weak entropy solution to the initial-boundary value problem of scalar conservation laws is conducted.
文摘长距离输水管道水力瞬变过程中水体压强达到汽化压强时,将会发生水柱分离现象,水柱弥合将产生异常高压,导致管路振动、变形甚至爆管事故。已有的水柱分离弥合水锤数学模型主要采用特征线法(Method of characteristics,MOC)计算,并且很少考虑动态摩阻引起的能量衰减。为提高水柱分离弥合水锤现象的计算精确度和稳定性,基于有限体积法二阶Godunov格式,建立了考虑动态摩阻的离散气体空穴模型(Discrete gas cavity model,DGCM)。为实现管道边界和内部单元的统一计算,提出虚拟边界的处理方法。将该模型模拟结果与实验数据以及已有的稳态摩阻模型的计算结果进行比较,并对网格数、压力修正系数等参数敏感性进行分析。结果表明,本模型能够准确模拟出纯水锤、水柱分离弥合水锤两种情况下瞬变压力,与实验数据基本一致;考虑动态摩阻的瞬态压力计算值与实验数据更吻合;与MOC相比,当库朗数小于1.0时,有限体积法二阶Godunov模型计算结果更准确、更稳定;尤其是,压力修正系数取值0.9及较密网格时数学模型能更为准确地再现实验结果。
文摘We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge-averaged quantities, which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [1]. However, [1] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [1]. The method is fourth order (both in space and time) for smooth flows, and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.
