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A High-Order Conservative Semi-Lagrangian Solver for 3D Free Surface Flows with Sediment Transport on Voronoi Meshes

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Communications on Applied Mathematics and Computation 2023年第2期5卷 596-637页

作者： Matteo Bergami Walter Boscheri Giacomo Dimarco Department of Mathematics and Computer Science University of FerraraVia Machiavelli 30I-44121 FerraraItaly

In this paper,we present a conservative semi-Lagrangian scheme designed for the numeri-cal solution of 3D hydrostatic free surface flows involving sediment transport on unstruc-tured Voronoi meshes.A high-order reconstruction procedure is employed for obtaining a piecewise polynomial representation of the velocity field and sediment concentration within each control *** is subsequently exploited for the numerical integration of the Lagrangian trajectories needed for the discretization of the nonlinear convective and viscous *** presented method is fully conservative by construction,since the transported quantity or the vector field is integrated for each cell over the deformed vol-ume obtained at the foot of the characteristics that arises from all the vertexes defining the computational *** semi-Lagrangian approach allows the numerical scheme to be unconditionally stable for what concerns the advection part of the governing ***,a semi-implicit discretization permits to relax the time step restriction due to the acoustic impedance,hence yielding a stability condition which depends only on the explicit discretization of the viscous terms.A decoupled approach is then employed for the hydrostatic fluid solver and the transport of suspended sediment,which is assumed to be *** accuracy and the robustness of the resulting conservative semi-Lagrangian scheme are assessed through a suite of test cases and compared against the analytical solu-tion whenever is *** new numerical scheme can reach up to fourth order of accu-racy on general orthogonal meshes composed by Voronoi polygons.

关键词： Conservative semi-Lagrangian Free surface flows Sediment transport High-order reconstruction hydrostatic model

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Methods for Calculation of Geogenetic Depth

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Journal of China University of Geosciences 2004年第2期15卷 145-151页

作者： LiuRuixun LuGuxian WangFangzheng WeiChangshan GuoChusun SchoolofEarthandSpaceSciences PekingUniversityBeijing100871China InstituteofGeomechanics ChineseAcademyofGeologicalSciencesBeijing100081China FacultyofEarthSciences ChinaUniversityofGeosciencesWuhan430074China InstituteofGeomechanics ChineseAcademyofGeologicalSciencesBeijing100081China

Some current methods for the calculation of the geogenetic depth are based on the hydrostatic model, it is induced that the depth in certain underground place is equal to the pressure divided by the specific weight of rock, on the assumption that the rock is hydrostatic and overlain by no other force but gravity. However, most of rock is in a deformation environment and non hydrostatic state, especially in an orogenic belt, so that the calculated depth may be exaggerated in comparison with the actual depth according to the hydrostatic formula. In the finite slight deformation and elastic model, the relative actual depth value from the 3 axis strain data was obtained with the measurement of strain including that of superimposed tectonic forces but excluding that of time factor for the strain. If some data on the strain speed are obtained, the depth would be more realistically calculated according to the rheological model because the geological body often experiences long term creep strains.

关键词： geogenetic depth ultrahigh pressure metamorphism hydrostatic model elastic dynamic model liquid-affecting fluid static model rheological dynamic model

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