本文提出了求解具有不连续孔隙度和底部地形的一维多孔浅水方程的高阶平衡保正有限差分AWENO格式,所提出的格式保持了静水稳态的良好平衡特性。在这个数值框架中,采用静水重构方法具有两个主要优点:1) 使用任意单调通量和重新表述源项...本文提出了求解具有不连续孔隙度和底部地形的一维多孔浅水方程的高阶平衡保正有限差分AWENO格式,所提出的格式保持了静水稳态的良好平衡特性。在这个数值框架中,采用静水重构方法具有两个主要优点:1) 使用任意单调通量和重新表述源项的方法获得了良好平衡特性。2) 采用Lax-Friedrichs (LF)通量的一阶方案在适当的时间步长内保持了水高保正性。通过大量的数值算例验证了该格式具有高阶精度和良好平衡特性,所有算例的数值结果与解析解一致。In this paper, we propose a higher-order well-balanced and positivity-preserving finite-difference AWENO scheme for solving the one-dimensional porous shallow water equation with discontinuous porosity and bottom topography. The proposed format maintains the well-balanced property of the hydrostatic steady state. In this numerical framework, the hydrostatic reconstruction (HR) method is employed with two main advantages: 1) The method using arbitrary monotone fluxes and reformulated source terms obtains the well-balanced property. 2) The first-order scheme using Lax-Friedrichs (LF) fluxes and the HR method maintains the water height preserving properties with an appropriate time step. We verify that the scheme has high-order accuracy and well-balanced properties through a large number of numerical examples, and the numerical results of all cases agree with the analytical solutions.展开更多
The Ripa model consists of the shallow water equations and terms which take the horizontal temperature fluctuations into account.The pollutant transport model describes the transport and diffusion of pollutants in sha...The Ripa model consists of the shallow water equations and terms which take the horizontal temperature fluctuations into account.The pollutant transport model describes the transport and diffusion of pollutants in shallow water flows.Both models admit hydrostatic solutions in which the gradient of the flux term is exactly balanced by the source term on the right-hand side.In this paper,we write both models in a unified form and propose a well-balanced fifth-order finite difference alternative weighted essentially non-oscillatory(AWENO)scheme,which allows using arbitrary monotone,Lipschitz continuous and consistent numerical flux.For illustration purposes,the Lax-Friedrichs flux is employed.In order to design a well-balanced AWENO scheme,reformulation of the source term and linearization of the WENO interpolation operator are made.The well-balancedness of the proposed method will be analysed theoretically in this paper.Numerical examples verify the well-balanced property,high-order accuracy and effectiveness of our approach.展开更多
文摘本文提出了求解具有不连续孔隙度和底部地形的一维多孔浅水方程的高阶平衡保正有限差分AWENO格式,所提出的格式保持了静水稳态的良好平衡特性。在这个数值框架中,采用静水重构方法具有两个主要优点:1) 使用任意单调通量和重新表述源项的方法获得了良好平衡特性。2) 采用Lax-Friedrichs (LF)通量的一阶方案在适当的时间步长内保持了水高保正性。通过大量的数值算例验证了该格式具有高阶精度和良好平衡特性,所有算例的数值结果与解析解一致。In this paper, we propose a higher-order well-balanced and positivity-preserving finite-difference AWENO scheme for solving the one-dimensional porous shallow water equation with discontinuous porosity and bottom topography. The proposed format maintains the well-balanced property of the hydrostatic steady state. In this numerical framework, the hydrostatic reconstruction (HR) method is employed with two main advantages: 1) The method using arbitrary monotone fluxes and reformulated source terms obtains the well-balanced property. 2) The first-order scheme using Lax-Friedrichs (LF) fluxes and the HR method maintains the water height preserving properties with an appropriate time step. We verify that the scheme has high-order accuracy and well-balanced properties through a large number of numerical examples, and the numerical results of all cases agree with the analytical solutions.
基金supported by the National Key Research and Development Program of China(No.2021YFF0704002)supported by the Natural Science Foundation of Hebei Province,China(No.A2020210047)+2 种基金National Natural Science Foundation of China(No.11801383)supported by the National Natural Science Foundation of China(No.12301505)the China Postdoctoral Science Foundation(No.2021M703040).
文摘The Ripa model consists of the shallow water equations and terms which take the horizontal temperature fluctuations into account.The pollutant transport model describes the transport and diffusion of pollutants in shallow water flows.Both models admit hydrostatic solutions in which the gradient of the flux term is exactly balanced by the source term on the right-hand side.In this paper,we write both models in a unified form and propose a well-balanced fifth-order finite difference alternative weighted essentially non-oscillatory(AWENO)scheme,which allows using arbitrary monotone,Lipschitz continuous and consistent numerical flux.For illustration purposes,the Lax-Friedrichs flux is employed.In order to design a well-balanced AWENO scheme,reformulation of the source term and linearization of the WENO interpolation operator are made.The well-balancedness of the proposed method will be analysed theoretically in this paper.Numerical examples verify the well-balanced property,high-order accuracy and effectiveness of our approach.
