A Well-Balanced Runge-Kutta Discontinuous Galerkin Method for Multilayer ShallowWater Equations with Non-Flat Bottom Topography  

作　　者：Nouh Izem Mohammed Seaid 

机构地区：[1]Laboratory of Engineering Sciences LabSI,Faculty of Science,Ibn Zohr University Agadir,Morocco [2]Department of Engineering,University of Durham,South Road,Durham DH13LE,UK [3]InternationalWater Research Institute,University Mohammed VI Polytechnic,Benguerir,Morocco

出　　处：《Advances in Applied Mathematics and Mechanics》2022年第3期725-758,共34页应用数学与力学进展（英文）

摘　　要：A well-balanced Runge-Kutta discontinuous Galerkin method is presented for the numerical solution of multilayer shallow water equations with mass exchange and non-flat bottom topography.The governing equations are reformulated as a non-linear system of conservation laws with differential source forces and reaction terms.Coupling between theflow layers is accounted for in the system using a set of ex-change relations.The considered well-balanced Runge-Kutta discontinuous Galerkin method is a locally conservativefinite element method whose approximate solutions are discontinuous across the inter-element boundaries.The well-balanced property is achieved using a special discretization of source terms that depends on the nature of hydrostatic solutions along with the Gauss-Lobatto-Legendre nodes for the quadra-ture used in the approximation of source terms.The method can also be viewed as a high-order version of upwindfinite volume solvers and it offers attractive features for the numerical solution of conservation laws for which standardfinite element methods fail.To deal with the source terms we also implement a high-order splitting operator for the time integration.The accuracy of the proposed Runge-Kutta discontinuous Galerkin method is examined for several examples of multilayer free-surfaceflows over bothflat and non-flat beds.The performance of the method is also demonstrated by comparing the results obtained using the proposed method to those obtained using the incompressible hydrostatic Navier-Stokes equations and a well-established kinetic method.The proposed method is also applied to solve a recirculationflow problem in the Strait of Gibraltar.

关 键 词：Discontinuous Galerkin method well-balanced discretization Runge-Kutta scheme multilayer shallow water equations free-surfaceflows mass exchange wind-drivenflows strait of Gibraltar 

分 类 号：O17[理学—数学]