We present an extension of the flux globalization based well-balanced pathconservative central-upwind scheme to the one-and two-dimensional thermal rotating shallow water equations.The scheme is well-balanced in the s...We present an extension of the flux globalization based well-balanced pathconservative central-upwind scheme to the one-and two-dimensional thermal rotating shallow water equations.The scheme is well-balanced in the sense that it can exactly preserve a variety of physically relevant steady states.In the one-dimensional case,it can preserve different“lake-at-rest”equilibria,thermo-geostrophic equilibria,as well as general moving-water steady states.In the two-dimensional case,preserving general moving-water steady states is difficult,and to the best of our knowledge,none of existing schemes can achieve this ultimate goal.The proposed scheme can exactly preserve the x-and y-directional jets in the rotational frame as well as certain genuinely two-dimensional equilibria.Furthermore,our approach employs a path-conservative technique for discretizing nonconservative product terms,which are incorporated into the global fluxes.This allows the developed scheme to exactly preserve some of the discontinuous steady states as well.We provide a number of numerical examples to demonstrate the advantages of the proposed scheme over some alternative finitevolume methods.展开更多
We present a model for hyperpycnal plumes or turbidity currents that takes into account the interaction between the turbidity current and the bottom,considering deposition and erosion effects as well as solid transpor...We present a model for hyperpycnal plumes or turbidity currents that takes into account the interaction between the turbidity current and the bottom,considering deposition and erosion effects as well as solid transport of particles at the bed load due to the current.Water entrainment from the ambient water in which the turbidity current plunges is also considered.Motion of ambient water is neglected and the rigid lid assumption is considered.The model is obtained as a depth-average system of equations under the shallow water hypothesis describing the balance of fluid mass,sediment mass and mean flow.The character of the system is analyzed and numerical simulations are carried out using finite volume schemes and path-conservative Roe schemes.展开更多
基金supported in part by China Postdoctoral Science Foundation(No.2022M721481)The work of A.Kurganov was supported in part by NSFC grant 12171226 and by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design(No.2019B030301001)The work of Y.Liu was supported in part by SNFS grants 200020204917 and FZEB-0-166980.
文摘We present an extension of the flux globalization based well-balanced pathconservative central-upwind scheme to the one-and two-dimensional thermal rotating shallow water equations.The scheme is well-balanced in the sense that it can exactly preserve a variety of physically relevant steady states.In the one-dimensional case,it can preserve different“lake-at-rest”equilibria,thermo-geostrophic equilibria,as well as general moving-water steady states.In the two-dimensional case,preserving general moving-water steady states is difficult,and to the best of our knowledge,none of existing schemes can achieve this ultimate goal.The proposed scheme can exactly preserve the x-and y-directional jets in the rotational frame as well as certain genuinely two-dimensional equilibria.Furthermore,our approach employs a path-conservative technique for discretizing nonconservative product terms,which are incorporated into the global fluxes.This allows the developed scheme to exactly preserve some of the discontinuous steady states as well.We provide a number of numerical examples to demonstrate the advantages of the proposed scheme over some alternative finitevolume methods.
基金This research has been partially supported by the Spanish Government Research projects MTM2006-08075 and P06-RNM-01594.The numerical computations have been performed at the Laboratory of Numerical Methods of the University of Malaga.
文摘We present a model for hyperpycnal plumes or turbidity currents that takes into account the interaction between the turbidity current and the bottom,considering deposition and erosion effects as well as solid transport of particles at the bed load due to the current.Water entrainment from the ambient water in which the turbidity current plunges is also considered.Motion of ambient water is neglected and the rigid lid assumption is considered.The model is obtained as a depth-average system of equations under the shallow water hypothesis describing the balance of fluid mass,sediment mass and mean flow.The character of the system is analyzed and numerical simulations are carried out using finite volume schemes and path-conservative Roe schemes.
